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Numerical Analysis of Seepage Induced Earthern Slope Failures 5
Numerical Analysis of Seepage Induced Earthern Slope Failures
침투가 고려된 토사사면파괴의 수치해석
Seo, Young-Kyo1서 영 교
요 지
침투에 의한 토사사면의 붕괴는 기상학적인 현상과 더불어 많은 양의 지하수의 유입에 의하여 발생한다 토사사면.
속에존재하는지하수의흐름은심각한재산및인명손실의잠재적인요인으로작용한다 이러한침투에의한토사사면.
의 안정성 문제는 지반공학에서 중요한 문제로 인식되어져 오고 있다 본 연구는 기존의 유체 및 고체의 상호 작용에.
대한 수치모델링 기법을이용하여 침투에 의한 토사사면붕괴의 이해및 이를 예측하기 위하여 수행되었다 본 연구는.
지반공학에서 중요히 다루는 사면안정화기법 연구에 효과적인 기술적 기여에 중점이 있다.
Abstract
Seepage induced earthern slope failures occurs in concert with meteorological events when large quantities of
groundwater are channeled into slopes through infiltration. The presence of flowing groundwater in earthern slopes can
induce ground failures that result in significant property damage and potential loss of life. Seepage induced earthen
slope failures represent a serious problem in geotechnical engineering. This research applies existing fluid-solid numerical
modeling capabilities to the study and prediction of seepage induced earthen slope failures. Study of the targeted application
holds potential for much needed advances in geotechnical engineering analysis technology which could be used to design
more effective engineering slope stabilization interventions.
Keywords : Finite element method, Numerical method, Seepage, Slope stability
1 Assistant Prof., Div. of Ocean Development Engrg., Korea Maritime Univ., [email protected]
Jour. of the KGS, Vol. 24, No. 9. September 2008, pp. 5 11~
1. Introduction and Motivation
Pore water in soils can strongly influence the physical
interactions between soil grains. Changes of pore press-
ures can directly impact the effective stresses which in
turn impact both the shear strength and consolidation
behaviors of soils. Moreover, the water in the void spaces
of soils is not static, particularly in slopes. Therefore, the
analysis of pore fluid seepage plays an important role in
the solution of many geotechnical problems, especially
those concerning the stability analysis of slopes and
retaining structures. Stability analysis of slopes in which
seepage is occurring involves solving boundary value pro-
blems for coupled field equations on spatial domains part
of whose boundaries (the so called free surface or phreatic
line) are unknown and remain to be determined as a part
of the solution. The major difficulty in solving free-
boundary problems numerically is associated with the
nonlinearity introduced by the unknown free surfaces.
Solving stability analysis problems for slopes in which
unconfined seepage occurs involves mainly two
difficulties. The first involves the fact that the soil can
undergo inelastic deformation under gravity and seepage
forces, while the second involves locating the equilibrium
6 Jour. of the KGS, Vol. 24, No. 9, September 2008
free boundary of fluid in the soil. In the slope stability
analyses considered in this paper only steady state seepage
effects are considered, but transient effects could also be
considered if one knew the changing hydrologic conditions.
The objective of this paper is first to develop a general
methodology for solving the coupled slope stability
analysis problem, which involves simultaneously solving
the fluid pressure and velocity fields as well as the
phreatic surface, and also the stress and deformation fields
in the slope including the limit state failure mechanism.
As an approximation to the fully coupled problem, a
simplified two-step decoupling is then introduced, im-
plemented and solved. The first step involves solving the
unconfined seepage problem in the soil while assuming
that the soil skeleton is rigid and does not deform. The
fluid pore pressure field is then imposed on the slope and
fixed while the slope stability problem is solved using the
‘Strength Reduction Method’ introduced in Swan and Seo
(1999). The de-coupled procedure is then applied to assess
the stability of slope systems in which steady state,
unconfined seepage is occurring.
2. Literature Survey
Fluid flow through porous media occurs and plays an
important role in many geotechnical problems. Due to the
intrinsically irregular geometries associated with most of
real problems, analytical solutions can be obtained only
for relatively simple situations (Harr, 1962). The analysis
of more complex cases can be carried out through numerical
procedures based on various discretization techniques
which are becoming increasingly popular and are replacing
traditional procedures like hand-drawn graphical flow nets
(Cedergren, 1967). Among numerical techniques, the
finite element method and the boundary integral equation
method are those most widely used. Confining attention
here to the finite element approaches, Zienkiewicz et al.
(1966) first presented the solution of confined seepage
flow problems. Thereafter, adaptive mesh methods (Desai,
1972; Chen et al., 1973) and fixed domain methods
(Desai, 1976; Lancy et al., 1987; Cividini et al., 1989)
have been widely used to find free surfaces.
The adaptive mesh methods solve the seepage problem
with a trial free surface, iteratively modifying the geometry
of the saturated soil mesh so that the free surface coincides
with element boundaries until a sufficient approximation
of the correct shape of the flow domain is reached. In
the first step, the mesh is usually defined between given
physical boundaries and an assumed location of free
surface, then the Laplace equation is solved for the
domain below the trial free surface, then the flow domain
is modified based on computed velocities at the free
surface. With the modified flow domain and free-surface,
the problem is then re-meshed and solved again. The
iterative procedure continues until the flow domain con-
verges. While this method is general and can define the
free surface very accurately (Isaacs, 1980), it requires
significant amounts of computational effort and potential
human intervention in the re-meshing at each iteration.
Moreover, this method, as pointed out by Oden and
Kikuchi (1980), often presents stability problems during
the iterative solution process, which in some cases leads
to apparently non-uniqueness of solutions. Difficulties have
also been encountered in problems involving inhomo-
geneous permeabilities. In order for these methods to work
reliably, one must typically start with a mesh that very
closely approximates the actual flow domain.
In order to overcome these difficulties, progress has
been made in formulating and solving the problems on
the entire domain. These so-called fixed domain methods
do not change the geometry of the finite element mesh
during the iterative solution process. Instead, the conditions
on the free boundary are observed in the field quantities,
which are then enforced within the spatial problem domain.
Once a trial pressure field is computed, the free surface
is then computed a posteriori as some suitable level set
within this fixed domain. For the spatial region above the
trial phreatic surface the permeability is then decreased
(penalized) to model the lack of flow in this region.
3. Problem Statement for Unconfined Seepage
in a Coupled Porous Medium
The description of the problem is shown in Figure 1.
Numerical Analysis of Seepage Induced Earthern Slope Failures 7
Let ⊂ represent the porous medium domain in
3-dimensional space. Let ⊂ represent the saturatedpart of which is the flow region, and let the com-
plementary part, represent a dry region. Withcapillarity, partial saturation and evaporation effects
neglected, the soil domain is decomposed strictly into
fully saturated () and fully dry () regions. Theexternal boundary of the porous medium domain consists
of three parts: is the impermeable part, is the part
in contact with the air, and is the part in contact with
water reservoirs. The boundary of the saturated region
is assumed to have four parts; ⊂ is the impermeable
part; ⊂ is the internal free surface boundary; is the boundary with the water reservoir; and ⊂ is
the seepage face [Refer from (Borja, 1991)].
3.1 Strong Form
With steady state seepage of an incompressible fluid
assumed, the coupled boundary value problem is stated
as follows: Find the skeletal displacement field ×
and the pressure field ×→ such that thefollowing equations are satisfied:
Balance of linear momentum of the fluid and solid
media moving together;
∇∙′ in , and (3.1)
Conservation of mass for the fluid phase;
∇∙
∙∇
∇∙
(3.2)
where ′ is the effective stress tensor, is the pore
pressure, is the permeability tensor, is the body force
vector, is the total density of the soil mass, is the
second order unit tensor and is a fluid source term.
The displacement and force boundary conditions for
theis problem are stated as following:
on (3.3)
∙′ on ∪ (3.4)
where and are prescribed displacements and surface
tractions, respectively, and is the outward unit normal
to .
The pressure and fluid flow boundary conditions in and
on are as follows;
in ; elsewhere (3.5)
∙ on (3.6)
and ∙ on (3.7)
on (3.8)
and ∙ ≤ on (3.9)
where, as an example associated with Figure 1,
on the right side of the damon the left side of the dam
(3.10)
The fluid velocity field is determined from Darcy’slaw as
∙
(3.11)
where is the permeability tensor, is unit weight of
water and is elevation head.
3.2 Penalized Problem and Matrix Equations
To define the weak form, a collection of trial solid dis-
placement and fluid pressure solutions satisfying the two
respective differential equations and boundary conditions
are required, in addition to trial weighting functions which
vanish on the regions where essential boundary conditions
are imposed. Trial solutions for the skeletal displacement
field, and the fluid pressure field, satisfy the fol-
lowing requirements
∈ (3.12)
⊂ ⊂
Fig. 1. The problem geometry
8 Jour. of the KGS, Vol. 24, No. 9, September 2008
∈ (3.13)
The virtual skeletal displacement functions and the
virtual pressure function satisfy the following requirements
∈ (3.14)
∈ (3.15)
Using these quantities, the variational equation of linearmomentum balance (Eq. 3.1) can be written as follows
′
′
∪
(3.16)
where
∪
In addition, the variational equation for mass balanceof the fluid (Eq. 3.2) takes the form
≤ (3.17)
where the inequality implies that the pore fluid may beseeping outward across the unknown seepage face . The
domain of integration for the third term in Eq. (3.17) canbe extended to the entire region using Heavysidefunction, .
≤ (3.18)
where
lim→
≤
≥
(3.19)
the above inequality can be converted into equality using
penalty function, .
(3.20)
where and is defined by
∗ (3.21)
In the above equation, represents a small penalty
parameter which smooths the step function. It is generally
chosen as a function of mesh discretization size.
These coupled equations can be re-written in matrix
form as follows
(3.22)
where
(3.23)
′
(3.24)
While the coupled field equations of equations (3.22)-(3.24) can be in principle be solved, such transient coupledproblems are characterized by singular and non-symmetricstiffness matrices. To overcome such difficulties, directsimultaneous time integration of the coupled semi-discreteequation has been used (Prevost, 1983; Zienkiewicz, 1985)and the resulting algorithms have been shown to beunconditionally stable. However, such implementationshave several limitations (Charbal et al., 1991). First, theyrequire the development of special software modules tosolve the coupled field equations. Second, result in verylarge matrix problems, especially for three-dimensionalcases. For these reasons, staggered solution algorithms(Park et al., 1980; Zienkiewicz, 1988) have been suggestedin which the skeletal displacement and pore pressure fieldequations are solved separately assuming that the fieldvariables of the other subsystems are known (via a predictor)and temporarily frozen. There are many advantages to such
Numerical Analysis of Seepage Induced Earthern Slope Failures 9
staggered procedures: (1) modularity features which allowthe coupled equations to be processed by separate programmodules taking full advantage of specialized features anddisciplinary expertise built into independently developedsingle-field analyzers; (2) resulting algorithmic structurewhich allows the set of analyzers to be synchronized tooperate in sequential or parallel fashion. However, simple,straight forward implementations of staggered proceduresare known to be at best only conditionally stable. Implicitintegrations are used for the individual modules. To dealwith this, various stabilization procedures have beenproposed (Park et al., 1983; Park, 1983).
4. Problem Statement for De-coupled Seepage
Analysis
In the previous section, the fully coupled seepage pro-blem with free boundaries and the skeletal equilibriumproblem with pore fluid pressure effects were developed,culminating in Eq. (3.22). While such a fully coupledsystem of equation can indeed be solved in principle, itwould require the development of special purpose solutionalgorithms such as those noted. To avoid such com-plexities, a simplification is proposed here. First, the porefluid pressure field equations are solved, including locationof the free-surface, while assuming that the soil skeleton
is rigid and does not deform ( ). Once the porepressure field is found in this manner, it is applied tothe slope domain and used in finding the equilibriumdeformation state of the slope. During the limit statestructural analysis of the slope, it is assumed that defor-mations of the slope do no result in changes of the porepressure field.
With the assumption that , the strong form ofthe uncoupled equation governing conservation of the pore
fluid is;
∇
∙∇
(4.1)
which results in the following matrix systems ofequations.
(4.2)
Brezis et al (1978) showed the existence and uniqueness
of the pressure field to the penalized problem, in the
limit as tends to zero. In the first iteration of the solution
procedure, the penalty function is assumed to be
unity throughout the entire domain. In regions of negative
pressure the step function is applied, and the problem
re-solved. In subsequent iterations, the stiffness matrix and
forces vectors are pressure dependent. The iterative
solution procedure terminates when the pressure field
satisfies Eq. (4.2).
4.1 Slope Stability Analysis with De-coupled Seepage
In the following, de-coupled slope stability problems
are solved with pore pressure fields resulting from seepage
analysis by the strength reduction methods discussed in
Swan and Seo (1999). The basic equilibrium field
equations solved are
∇∙′ in (4.3)
where the pressure field is solved from de-coupled
seepage analysis and imposed on the slope domain; ′denotes the effective stress in the soil; and denotes the
mass density of the soil (dry density above the phreatic
surface and saturated density below the phreatic surface).
In the examples that follow the intention is to compare
the stability characteristics of slopes both with and without
seepage. The example problems include earthen slopes
having both purely cohesive soils and purely frictional
soils. The soil strength parameters used are the same as
those listed in Table 1.
Table 1. Clay and sand material parameters used in slope analysis
Material
ParameterClay Values Sandy Values
× ×
10 Jour. of the KGS, Vol. 24, No. 9, September 2008
Non-Frictional, Purely Cohesive Soils
In this analysis of a purely cohesive soil slope, the free
surface of the headwater is taken to be below the
ground surface and tailwater level corresponds to the toe
level of the slope. The calculated free surface and pore
pressure field are shown in Figure 2a. Slope stability
analysis is then preformed and the deformed shape of the
slope at the limit state is shown in Figure 2b. An analysis
of the same slope was considered in Swan and Seo (1999)
without seepage effects. While the mechanisms of failure
are virtually the same, stability analysis without seepage
yielded while in this analysis .
This represents a reduction of thirty three percent in the
factor of safety.
Analysis with Purely Frictional Soils
In these examples for various heights of frictional sandy
slopes, the free surface is also calculated from a certain level
of the slope as shown in Figure 3. The free surface head
water was also taken as the same with non-frictional, purely
cohesive soil. The deformed shapes and compared factor of
safeties are shown in Figure 4. In general, the results indicate
that the presence of flowing water in the slopes modeled
can reduce the stability factors by between 18% and 22%,
with the larger reductions corresponding to higher slopes.
5. Summary and Closure
The strength reduction method was applied to the
earthern slopes, in which active, unconfined steady state
seepage is occurring. As an approximation, the problem
is de-coupled from the fully coupled problem of slope
stability analysis. In the first step of analysis, the
unconfined seepage was performed for the pressure field
in the slope. Then the fluid pore pressure field is imposed
on the slope stability problem. In the example of the
boundary problem some of published problems were
computed and compared. The seepage induced slop
analysis was then performed to compare the results of
dry slope which was done in Swan and Seo (1999). The
results show that the presence of water can reduce the
factors of safety.
(a)
(b)
Fig. 2. Undeformed configuration with free surface and deformed
failure mechanisms for 30 meter clay slope with a response
angle of 49°
Fig. 3. Undeformed configuration of a 20° slope with free surface
and piezometric head distribution
Dry slope Seepage effects included
Fig. 4. Limit state mechanisms and stability factors computed for
a 20° purely sand slope of varying heights and saturated
conditions with seepage.
Numerical Analysis of Seepage Induced Earthern Slope Failures 11
References
1. Borja R. I. and Kishnani, S. S. “On the solution of ellipticfree-boundary problems via Newton’s method”, Comp. Meth. Mech.Eng. 88, pp.341-361, 1991.
2. Brezis, H. D. Kinderlehrer and G. Stamppacchia, “Sur une nouvelleformulation du problem de 1’ecoulement a travers une digue”, C.R. Acas. Sci. Paris 287 (ser. A) pp.711-714, 1978.
3. Cedergren, H, R. (1967), “Seepage, drainage and flow nets”, NewYork: Willey.
4. Chen, R. T. S. and Li, C. Y. (1973), “On the solution of transientfree-surface flow problems in porous media by the finite elementmethod”, J. Hydrol. 20, pp.49-63.
5. Cividini, A. and Gioda, G. (1989), “On the variable mesh finiteelement analysis of unconfined seepage problems”, Geotechnique,London, England, (2) pp.251-267.
6. Desai, C. S. (1972), “Seepage analysis fo earth banks underdrawdown”, J. Soil Mech. Found. Div., A.S.C.E., 98(SM11), pp.1143-1162.
7. Harr, M. E. (1962), “Groundwater and seepage”, New York:McGraw-Hill.
8. Isaacs, L, T. (1980), “Location df free surface in finite elementanalyses”, Civil Engineering Transaction (Australia), CE-22(1) pp.9-16.
9. Lacy, S. J. and Prevost, J. H. (1987), “Flow through porous media:a procedure for locating the free surface”, Int. J. Numer. Anal.Methods Geomech. 11, No.6, pp.585-601
10. Oden, J. T. and Kikuchi, N. (1980), “Recent advances: theory ofvariational inequalitied with applications to problems of flowthrough porous media”, Int. J. Eng. Sci., 18, pp.1173-1284.
11. Park, K. C. (1983), “Stablization of partitioned solution procedurefor pore fluid-soil interaction analysis”, Int. J. Num. Mech. Eng.19, pp.1669-1673.
12. Park, K. C. and Felippa, C. A. (1983), “Partioned analysisprocedures for coupled systemed”, in Computational methods fortransient analysis, Eds T. Belytschko and T. J. R. Hughes,North-Holland, Amsterdam. pp.158-219.
13. Park, K. C. and Felippa, C. A. (1980), “Partitioned transient analysisprocedures for coupled field problems: accuracy analysis”, J. Appl>Mech., 47, pp.919-926.
14. Prevost, J. H. (1983), “Implicit-Explicit schemes for nonlinearconsolidation”, Comp. Mech. Appl. Mech. Eng., 39, pp.225-239.
15. Swan, C. C. and Seo. Young-kyo (1999), “Limit Analysis ofEarthern Slopes using dual continuum/FEM approaches”, Int. J.Numer. Anal. Methods Geomech. 3, No. 12, pp.1359-1371.
16. Zienkiewicz, P., Mayer, P. and Cheung, Y. K. (1966), “Solutionof anisotropic seepage by finite element method”, J. Eng. Mech.Div., A.S.C.E., 92(EMI), pp.111-120.
17. Zienkiewicz, O. C., Paul, D. K., and Chan, A. H. C. (1988),“Unconditionally stable staggered solution procedure for soil-fluidinteraction problems”, Int. J. Num. Mech. Eng., 26, pp.1039-1055.
18. Zienkiewicz, O. C. and Taylor R. L. (1985), “Coupled problems-asimple time stepping procedure”, Comm. Appl. Num. Mech., 1, pp.233-239.
(received on Jun. 18, 2008, accepted on Jul. 23, 2008)
The Interference of Organic Matter in the Characterization of Aquifers Contaminated with LNAPLs by Partitioning Tracer Method 13
The Interference of Organic Matter in the Characterization ofAquifers Contaminated with LNAPLs by Partitioning Tracer Method
오염 지반에 분배성 추적자 시험법 적용 시LNAPLs
유기물질의 영향에 관한 연구
Khan, Sherin Momand1칸 쉐 린
Rhee, Sung-Su2이 성 수
Park, Jun-Boum3박 준 범
요 지
분배성 추적자 시험법은 로 오염된 지반을 조사하는데 아주 유용한LNAPLs(light nonaqueous phase liquids)방법이다 하지만 토양 내 유기물질로 흡착되는 분배성 추적자는 잠재적으로 분배성 추적자 시험법의 정확성에.영향을 끼칠 수 있다 연구 결과 추적자의 액상 간 분배 계수는 선형 관계를 보였다 토양의 흠착능력을. , -LNAPL .평가하기 위해 흡착 등은 실험을 수행한 결과 흡착 등은 양상과 거의 일치하였고 추적자의 흡착, Freundlich ,정도는 토양 내 유기물질 함량이 증가함에 따라 증가하였다 또한 토양 유기물의 흡착능에 따른 잠재적 영향을. ,판단하고 추적자 시험법에 의한 예측의 오차를 수정하기 위해 서로 다른 유기물 함량을 가진 개의, LNAPLs 4컬럼 실험을 수행하였다 컬럼 실험 결과 오염물질이 없더라도 주문진 표준사와 유기물질이 섞인 컬럼에서는. ,추적자의분리현상이발생하였다 오염물질로케로진을주입한이후에다시추적자시험법을수행하여파괴곡선.을구한결과 토양유기물질에대한추적자의흡착으로인해추적자의지연계수 가커졌고 의오염도가, (R) LNAPLs과대평가되었다 또한컬럼실험결과를바탕으로유기물함량과 의예측도사이의관계식을제안하였다. LNAPLs .
Abstract
Partitioning tracer method is a useful tool to characterize large domains of the aquifers contaminated with lightnonaqueous phase liquids (LNAPLs). Sorption of the partitioning tracers to the organic matter content of soil canpotentially influence the efficacy of partitioning tracer method. LNAPL-water partitioning coefficients of tracers(Knw), measured by static method, showed linear relationship. Sorption isotherm tests were conducted to evaluatethe sorption capacity of the soils packed in the columns and the results were appropriately represented by Freundlichsorption isotherm. The sorption of tracers proportionally increased with the increase of the organic matter contentof the soil. Laboratory experiments were conducted in four columns each packed with soils of different organicmatter contents to determine the potential interference effects of sorption to soil organic matter content and correctionfactors for the errors in estimation of LNAPLs by partitioning tracer method. Though there were no contaminantsadded, breakthrough curves from columns packed with mixture of Jumunjin standard sand and organic matter showedseparation of tracers. Columns were then contaminated to residual saturation with kerosene and breakthrough curveswere obtained. The results show that sorption of tracers to soil organic matter leads to an increase in the retardationfactor (R) and hence, to an overestimation of the saturation of LNAPLs. A relation between the percentage oforganic matter content and the corresponding percentage error in the estimation of NAPLs has been developed.
Keywords : Column Test, LNAPLs Monitoring, Partitioning Tracer Test, Soil Organic Matter, Sorption Test, Tracer Test
1 Graduate Student, Dept. of Civil and Environmental Eng., Seoul National Univ.2 Member, Graduate Student, Dept. of Civil and Environmental Eng., Seoul National Univ.3 Member, Prof., Dept. of Civil and Environmental Eng., Seoul National Univ., [email protected], Corresponding Author
Jour. of the KGS, Vol. 24, No. 9. September 2008, pp. 13 21~
14 Jour. of the KGS, Vol. 24, No. 9, September 2008
1. Introduction
Sub-Surface contamination by light nonaqueous phase
liquids (LNAPLs) has proven to be a formidable challenge
for environmental engineers and its presence is often the
single most important factor limiting remediation of sites
contaminated by organic compounds (National Research
Council, 1994). Potential for further contamination is also
a concern when considering the presence of LNAPLs
sources in the subsurface (e.g. underground storage tanks
and oil/gas pipelines). Proper characterization, which
involves the location, composition and quantification of
LNAPLs, is required for accurate risk assessments and
effective remediation (Jacksons and Pickens, 1994). As
many LNAPLs are both sparingly soluble and highly
mobile, assessing their time-varying concentrations and
sub-surface distribution can be extremely difficult, particularly
in complex, near-surface industrial environment. Furthermore,
considering the various constraints to mass transfer and
the generally low maximum contaminant levels, LNAPLs
are now widely accepted to be a long-term source of both
vapor phase and ground water contamination (National
Research Council, 1994).
Light NAPLs remain floating on the top of the capillary
fringe but the fluctuation of the water table creates a smear
zone of LNAPLs at the residual saturation within the
upper portion of the saturated subsurface. It is due to these
unusual behaviors that make the detection and quantifi-
cation of LNAPLs extremely difficult in the subsurface
with the point sampling techniques of site characterization
like core sampling, cone penetrometer, and geophysical
logging (Cain et al., 2000). The sample of these methods
has relatively small volume of the subsurface and thus,
accurate characterization of the given domain is very
difficult without a cost prohibitive amount of sampling.
Thus, partitioning tracer method has been proposed as a
means to characterize the sites contaminated with
LNAPLs. This method, with a particular advantage over
the point sampling techniques covers large volume of the
subsurface, produces more reliable estimates of the
quantity and distribution of LNAPLs (Jin et al., 1995).
Partitioning tracer method is based on performing a tracer
test in the subsurface of the site, potentially contaminated
with LNAPLs. Chemical tracers with known NAPL-water
partition coefficients are injected into the subsurface to
detect the presence of LNAPLs and to estimate LNAPLs’
saturation within the zone swept by the tracers. The
LNAPLs reversibly retain the partitioning tracers with
respect to nonpartitioning tracers causing the former to
lag behind the later. The extent of separation depends on
the residence time of tracers, which are a function of its
partition coefficient and the saturation of LNAPLs. Thus, the
magnitude of measured separation of the partitioning tracers
can be translated into quantifying NAPLs present within
the zone swept through by the tracers (Jin et al., 1995).
The partition tracer method can be used as an
innovative and effective technique for the detection and
quantification of LNAPLs’ contamination in the subsurface
as well as to evaluate the remediation performance.
However, the results can be affected by many factors such
as rate limited transfer, subsurface heterogeneities, multiphase
retention, biochemical degradation, and sorption on to the
soil organic matter of chemical tracers, which leads to
inappropriate characterization of the site under conside-
ration (Brusseau et al., 2003). Hence, partition tracer
method needs to be evaluated to determine the effect of
influencing factors. The purpose of this paper is to present
the effect of sorption of the chemical tracers to the soil
organic matter on partition tracer method from column
scale experiments in laboratory. A comparison of the
saturation of LNAPLs determined from partition tracer
test conducted in a column packed with Jumunjin standard
sand and columns packed with different weight ratios of
Jumunjin standard sand and organic matter provided a
measure of the effect of sorption.
2. Theory and Analysis Techniques
2.1 Method of Moments
It has been shown that the method of moment’s theory
can be used to determine LNAPLs’ saturations in a
subsurface, given the difference in mean residence times
between two different tracers by using partitioning tracer
method (Jin et al., 1995). Partitioning tracer method is
The Interference of Organic Matter in the Characterization of Aquifers Contaminated with LNAPLs by Partitioning Tracer Method 15
based on the chromatographic separation of two or more
selected tracers as they flow with ground water through the
LNAPLs’ contaminated aquifer. The partition coefficient
(Knw, unitless) of a partitioning tracer quantifies the
fraction of tracer in LNAPLs’ phases and water phase
at equilibrium (Jin et al., 1995). It is defined as the ratio
of the concentration of tracer in the LNAPLs phase (Cn,
unit: mg/L) to the concentration of tracer in the water
phase (Cw, unit: mg/L), or
Knw=Cn/Cw (1)
Nonpartitioning tracers have a partition coefficient of
zero with respect to LNAPLs, whereas the partitioning
tracers have partition coefficients with non zero positive
value. A set of partitioning and nonpartitioning tracers is
selected to get the greatest degree of separation between
tracer pairs in a reasonably short period of time. The
magnitude of retardation is a function of LNAPLs saturation
and partition coefficient (Brusseau et al., 2003). The R
value (unitless) determined from the tracer test is equated
to the mass-balance definition of R, given for aqueous-
phase transport as:
( )
11 nw
p b nd
n w n
t SR K K
t Sρθ
⎡ ⎤⎛ ⎞= = + + ⎢ ⎥⎜ ⎟ −⎢ ⎥⎝ ⎠ ⎣ ⎦
(2)
Where, tp is the travel time of the partitioning tracer, tnis the travel time for the nonpartitioning tracer, ρb is bulk
density of porous media (unit: g/cm3), θw is the water-
filled porosity (unitless), Kd is the water-aquifer solids
partition coefficient (unit: cm3/g), and Sn is the effective
LNAPLs’ saturation (unitless) degree.
The previous researchers have neglected the second
term on the right side of the equation (2) assuming that
liquid-liquid partitioning is much greater than the
liquid-solid partitioning. It was further supported that the
large volume of the LNAPLs in the subsurface would
cause the liquid - liquid partitioning to dominate tracers’
retardation (Cain et al., 2000). No previous research has
been carried out to support this assumption. We have
considered the second term i.e. sorption, in our calculations
to evaluate the authenticity of this assumption. The
sorption can occur with organic matter or clay material.
But, this study focuses on the effect of organic matter.
The detailed procedure for the quantification of LNAPLs
using partitioning tracer theory can be found in Jin et al.
(1994, 1995).
The total volume of LNAPLs in subsurface may often
be underestimated using partitioning tracer method because
of factors such as rate-limited transfer, bypass flow and
mass loss, but the contrary can be true in case of sorption
of the tracers to soil organic matter (Hatfield and Stauffer,
1993). We have demonstrated how the saturation of
LNAPLs is an overestimate of the true value because of
sorption to the soil organic matter using columns packed
with selected soils of known sorption capacities.
3. Material and Methods
3.1 Composition of Soil
Jumunjin standard sand was packed in column 1 and
mixture of Jumunjin standard sand and organic fertilizer
in columns 2~4 in ratios 19:1, 9:1, and 4:1 respectively.
Organic fertilizer, passing No. 10 sieve (0.200 mm
opening size) and retained by No. 40 sieve (0.420 mm
opening size), was used to represent the soil organic
matter. The organic matter content in the organic fertilizer
and Jumunjin standard sand was determined by the
loss-on-ignition method (Veres, 2002) and was found to
be 5.35% and 0.50% respectively. X-Ray Fluorescence
(XRF) analysis and X-ray Diffraction (XRD) analysis of
Jumunjin standard sand and organic fertilizers were
conducted and are given in Table 1. Jumunjin standard
sand and its mixture with organic fertilizer in different
ratios were used to ascertain the effect of concentration
of the organic matter content on tracers’ breakthrough
curves. Jumunjin standard sand was used in column
marked as number “1” and the columns marked as “2,
3 and 4 were packed with the mixture of organic fertilizer
and Jumunjin standard sand with organic matter content
of 2.64, 5.29 and 10.58, respectively.
3.2 Tracers
Methanol and chloride ions were used as non-
16 Jour. of the KGS, Vol. 24, No. 9, September 2008
partitioning tracers while 2-ethyl-1-butanol, 4-methyl-2-
pentanol, 1-pentanol, 1-hexanol, and 2,3-dimethyle-2-
pentanol were used as partitioning tracers in the column
experiments and were chosen to yield breakthrough curves
in a reasonably short time, and yet they ensured good
separation of the partitioning and nonpartitioning tracers
(Varandarajan and Garry Pope, 1998). Kerosene dyed
with Sudan IV was used as a representative LNAPLs in
columns packed with selected soils.
3.3 Batch-Partitioning Experiments
Batch-partitioning experiments were conducted todetermine kerosene-water partition coefficients (Knw) forthe group of selected tracers. Batch partitioning tests, in20 mL septa-capped vials with equal volumes of keroseneand water (10 mL each), were conducted with methanol,2-ethyl-1-butanol, 4-methyl-2-pentanol, 1-pentanol, 1-hexanol,and 2,3-dimethyle-2-pentanol ranging in concentrationfrom 50 to 800 mg/L. Vigorous mixing on an orbital mixerfor thirty one hours equilibrated the vials. Followingequilibration, a 2 mL aqueous sample was collected viasyringe after centrifuging the sample in the centrifuge for30 minutes at 3500 rmp, and placed into a 2 mL septavial for alcohol analysis with a Hewlett-Packard (HP)6890 gas chromatograph (GC). The GC was equippedwith a 30.0 m long by 0.25 mm PAG capillary column(Supelco 2-4223) and a flame ionization detector (FID).The FID signal was acquired and integrated with personal
computer (PC) using HP Chemstation software.
3.4 Sorption Isotherm Experiments
Sorption isotherm experiments were conducted to
determine soil-water partition coefficients of tracers and
the sorption capacity of the selected soils. The tests were
conducted in 20 mL, septa-capped vials with 4 grams of
the selected soil and measured amount of the tracer
solution to make the head space almost zero. Vigorous
mixing on an orbital mixer for 48 hours equilibrated the
vials. Following equilibration, a 2 mL aqueous sample
was collected via syringe after centrifuging the sample
in the centrifuge for 40 minutes at 3800 rmp, and placed
into a 2 mL septa vial for alcohol analysis with GC.
3.5 Column-Scale Experiments
Figure 1 shows the schematic diagram of the equipment
setup for column experiment. Jumunjin standard sand and
its mixture with organic fertilizer were packed under
dynamic compaction in the glass columns, each 40 cm
long and with an inner diameter of 3.5 cm.
Packed columns were saturated with DI (deionized)
water at a constant flow rate of 0.1 ml/min after purging
by CO2 gas to remove the air bubbles and get full
saturation of the packed soils. The flow rate was slow
enough to give sufficient time for reversible reaction to
occur between tracers and the other media. Sodium azide
Table 1. Composition of Jumunjin standard sand and organic fertilizer from XRF and XRD analysis
Jumunjin standard sand Organic fertilizer
XRF analysis XRD analysis XRF analysis XRD analysis
Weight (%) Weight (%) Weight (%) Weight (%)
SiO2 88.50 Quartz 74.70 SiO2 60.04 Quartz 43.80
Al2O3 6.59 Plagioclase 7.20 Al2O3 11.85 Plagioclase 7.70
TiO2 0.08 K-feldspar 18.10 TiO2 0.57 K-feldspar 14.10
Fe2O3 0.04 Muscovite 0.00 Fe2O3 6.55 Muscovite 16.40
MgO 0.02 Calcite 0.00 MgO 1.98 Calcite 2.70
CaO 0.21 Goethite 0.00 CaO 7.34 Goethite 15.10
Na2O 0.12 Na2O 0.54
K2O 3.81 K2O 3.78
MnO 0.03 MnO 0.37
P2O5 0.02 P2O5 1.33
Loss on ignition 0.50 Loss on ignition 5.35
The Interference of Organic Matter in the Characterization of Aquifers Contaminated with LNAPLs by Partitioning Tracer Method 17
solution was injected to kill the bacteria in the packed
columns as they may biodegrade the chemical tracers.
Tracer test in the columns was conducted before and after
contamination with kerosene. A known volume of dyed
kerosene was injected as a representative of the LNAPLs
contamination. Residual contamination was insured by
continuously injecting DI water until there was no
movement of the dyed kerosene. The method of volume
measurement was adopted to determine the volume of
residual kerosene saturation in the columns which
involves the measurement of the volume of the injected
kerosene and the volume produced during the DI water
flood (Jin et al., 1995). The tracers’ pulse was 0.15 pore
volume for all the columns. Effluents were collected every
hour and were analyzed with GC.
4. Results and Discussions
4.1 Batch Tests and Tracer Screening
The results of batch-partitioning experiments conducted
to determine kerosene-water partition coefficients for the
selected group suite of alcohol tracers are shown in Table
2. The Results in Figure 2 indicate that kerosene-water
partitioning is linear with respect to alcohol tracers’
concentrations employed in this study. Measured partition
coefficients, reflected as the slope of the linear trend, are
constant with increasing aqueous tracer concentration. The
retention times from our GC analysis for methanol,
2-ethyl-1-butanol, 4-methyl-2-pentanol, 1-pentanol, 1-hexanol,
and 2,3-dimethyl-2-pentanol were 1.64, 7.13, 4.76, 4.78,
7.14, and 8.27 respectively. The results from batch tests
and a column test were screened to determine the most
suitable group of tracers for producing breakthrough
responses in a reasonably short time and yet ensuring good
separation of tracers. 1-Pentanol and 2,3-dimethyl-2-
pentanol were discarded because of its similar retention
time with 4-methyl-2-pentanol and 2-ethyl-1-butanol
respectively and hence, their peaks cannot be differentiated
in the GC. Another reason for discarding 2,3-dimethyl-2-
pentanol was that it was restrained for unreasonably long
Fig. 1. Schematic diagram of column setup and sampling
Table 2. Kerosene-water partitioning coefficients of tracers
Tracer Formula Molar mass (g/mol) Knw R2
Methanol CH3OH 32.04 0.003 0.9204
1-Pentanol CH3(CH2)4OH 88.15 2.276 0.9233
1-Hexanol CH3(CH2)5OH 102.17 4.293 0.9958
2-Ethyl-1-butanol (C2H5)2CHCH2OH 102.18 3.656 0.9987
4-Methyl-2-pentanol (CH3)2CHCH2CH(OH)CH3 102.18 2.677 0.9713
2,4-Dimethyl-3-pentanol (CH3)2CHCH(OH)CH(CH3)2 116.20 11.257 0.9996
0
100
200
300
400
500
600
0 100 200 300 400 500 600 700The concentration of tracer in water, mg/L
The
con
cent
ratio
n of
trac
er in
kero
sene
, mg/
L
MethanolPentanol2-Ethyl-1-butanol4-Methyl-2-pentanol2,4-Dimethyl-3-pentanolHexanol
Fig. 2. Partitioning of tracers between kerosene and water
18 Jour. of the KGS, Vol. 24, No. 9, September 2008
time in the columns packed with mixture of selected soils.
Measured partition coefficients were used in conjunction
with measured partitioning tracer retardations to predict
kerosene volume within zone swept by the tracers.
4.2 Sorption Isotherm Experiments
The results of sorption isotherm experiments conducted
to determine soil-water partition coefficients for the
selected group of alcohols are shown in Table 3.
Freundlich sorption isotherm is used which is mathematically
expressed as below:
S=KCN (3)
Where, S is the mass of the tracers sorbed per unit dry
mass of solid in mg/kg, C is the concentration of the
tracers in solution at equilibrium in mg/L, and K is the
distribution coefficient in L/kg.
The equation (3) is linearized by plotting log of C
verses log S. The slope of the straight line is N and the
intercept is equal to log K. It is the most commonly used
isotherm in contaminant migration analysis and is
generally valid at low contaminant concentration ranges.
Results indicate the solute concentration sorbed onto the
soil and the concentration of the tracer in solution phase
in equilibrium. The capacity of the soil to remove the
traces i.e. solutes is a function of the concentration of
the solute within the same test soil. The sorptive process
is rapid initially but an equilibrium condition of solute
is reached with the amount sorbed onto the soil within
certain duration. The results clearly demonstrate that the
sorption capacity of Jumunjin standard sand is negligible
and that its mixture with organic fertilizer shows
considerable sorption capacity. The sorption of tracers
increased proportionally to the percentage of soil organic
matter content.
4.3 Column Experiments
The breakthrough curves obtained from column 1
(packed with Jumunjin standard sand) show no separation
of tracers as given in Figure 3, which indicate that there
is no partitioning of tracers to the media swept through
Table 3. Results from sorption isotherm experiments using Freundlich isotherm
Column
number
Organic matter
content (%)Tracers Kf N R
2
1 0.00
4-Methyl-2-pentanol 1.7814 0.3011 0.7646
Hexanol 2.3799 0.1809 0.9765
2-Ethyl-1-butanol -0.9913 1.3293 0.9990
2 2.64
4-Methyl-2-pentanol 1.7814 0.3011 0.9773
Hexanol 2.3799 0.1809 0.6671
2-Ethyl-1-butanol -0.9913 1.3293 0.9187
3 5.29
4-Methyl-2-pentanol 1.7814 0.3011 0.9514
Hexanol 2.3799 0.1809 0.9351
2-Ethyl-1-butanol -0.9913 1.3293 0.9772
4 7.93
4-Methyl-2-pentanol 1.7814 0.3011 0.8518
Hexanol 2.3799 0.1809 0.9907
2-Ethyl-1-butanol -0.9913 1.3293 0.9845
0.0
0.2
0.4
0.6
0.8
1.0
0 100 200 300 400 500 600 700 800Cumulative volume, mL
Rela
tive c
oncentr
ati
on
Methanol
4-Methyl-2-pentanol
2-Ethyl-1-butanol
Hexanol
Chloride ion
Fig. 3. Breakthrough curves from pre-contaminated column 1
which has 0% organic matter content
The Interference of Organic Matter in the Characterization of Aquifers Contaminated with LNAPLs by Partitioning Tracer Method 19
by the tracers and hence no contamination was detected.
The breakthrough curves from the pre-contaminated
columns 3~5 which contain known percentage of organic
matter content, show significant separation of tracers and
a marked increase in the separation of tracers was
observed with the increase in the percentage of organic
matter content as shown in the Figures 4~6. It is evident
from this phenomenon that partitioning of tracers occurred
only between water and organic matter content of soil
as the columns were precontaminated and that Jumunjin
standard sand caused no separation of tracers. A situation
like this can be quite misleading as it can be taken for
contamination in the subsurface or, at least, exaggerate
the quantity of the contaminants.
The breakthrough curves from the post-contaminated
columns are given in Figures 7~10 and measured versus
predicted volumes of kerosene are shown for homo-
geneously distributed residual saturation of kerosene in
different columns in Table 4. The retardation factor is
0.0
0.2
0.4
0.6
0.8
1.0
0 100 200 300 400 500 600 700 800Cumulative volume, mL
Rela
tive c
oncen
trati
on
Methanol
4-Methyl-2-pentanol
2-Ethyl-1-butanol
Hexanol
Chloride ion
Fig. 4. Breakthrough curves from pre-contaminated column 2
which has 2.64% organic matter content
0.0
0.2
0.4
0.6
0.8
1.0
0 100 200 300 400 500 600 700 800Cumulative volume, mL
Rela
tive c
oncen
trati
on
Methanol
4-Methyl-2-pentanol
2-Ethyl-1-butanol
Hexanol
Chloride ion
Fig. 5. Breakthrough curves from pre-contaminated column 3
which has 5.29% organic matter content
0.0
0.2
0.4
0.6
0.8
1.0
0 100 200 300 400 500 600 700 800Cumulative volume, mL
Rela
tive c
oncen
trati
on
Methanol
4-Methyl-2-pentanol
2-Ethyl-1-butanol
Hexanol
Chloride ion
Fig. 6. Breakthrough curves from pre-contaminated column 4
which has 10.58% organic matter content
0.0
0.2
0.4
0.6
0.8
1.0
0 100 200 300 400 500 600 700 800Cumulative volume, mL
Rela
tive
co
nce
ntr
ati
on
Methanol
4-Methyl-2-pentanol
2-Ethyl-1-butanol
Hexanol
Chloride ion
Fig. 7. Breakthrough curves from post-contaminated column 1
which has 0% organic matter content
0.0
0.2
0.4
0.6
0.8
1.0
0 100 200 300 400 500 600 700 800Cumulative volume, mL
Rela
tive c
oncen
trati
on
Methanol
4-Methyl-2-pentanol
2-Ethyl-1-butanol
Hexanol
Chloride ion
Fig. 8. Breakthrough curves from post-contaminated column 2
which has 2.64% organic matter content
20 Jour. of the KGS, Vol. 24, No. 9, September 2008
between 1.2 and 4 for all the partitioning tracers which
are desirable for partitioning tracer method to have
appropriate estimation of kerosene in the subsurface. The
magnitude of retardation is a function of the kerosene
saturation and the partition coefficients for column 1 as
the partioning of racer to the Jumunjin standard stand is
negligible but in the cases of columns 2~4, sorption of
the tracers to the soil organic contents also contributes
to the magnitude of retardation. To get appropriate
estimation of the kerosene saturation, it is imperative
to determine the appropriate correction factor. The
hexanol breakthrough curve was retarded more with
4-methyl-2-pentanol and 2-ethyl-1-butanol. The methanol
and chloride ions were used as nonpartitioning tracers and
were not retarded at all. The predicted values by
partioning tracer method vary linearly from under
estimation to overestimation with the increase in organic
matter contents of the soil as shown in Figure 10. This
significant difference is due to the sorption of tracers to
the organic matter in the columns. Based on these results,
the error in the estimated values of kerosene can be
corrected for the known percentage of the organic matter
content. From this data we have been able to express the
error estimation as a function of organic content of the
soil.
Estimation Error (%) = 13.7 × [Organic Matter
Contents] – 37.5 (4)
Thus, knowing only the organic content in the soil will
enable us to determine the error estimation from now on.
0.0
0.2
0.4
0.6
0.8
1.0
0 100 200 300 400 500 600 700 800Cumulative volume, mL
Rela
tive c
oncen
trati
on
Methanol
4-Methyl-2-pentanol
2-Ethyl-1-butanol
Hexanol
Chloride ion
Fig. 9. Breakthrough curves from post-contaminated column 3
which has 5.29% organic matter content
0.0
0.2
0.4
0.6
0.8
1.0
0 100 200 300 400 500 600 700 800Cumulative volume, mL
Rela
tive c
oncen
trati
on
Methanol
4-Methyl-2-pentanol
2-Ethyl-1-butanol
Hexanol
Chloride ion
Fig. 10. Breakthrough curves from post-contaminated column 4
which has 10.58% organic matter content
y = 13.671x - 37.142R2 = 0.9995
-100
-50
0
50
100
150
0 2 4 6 8 10 12 14Organic Matter Content (%)
Esti
mati
on
Err
or
(%)
Fig. 11. The error in estimation of kerosene by partition tracer
method caused by the organic matter content in the soil
Table 4. The percentage error in predicted values of kerosene by partitioning tracer method
Column
Number
Organic matter
content (%)
Measured
contamination (ml)
Average estimated
contamination (ml)
Percentage
error
1 0.00 28.01 17.97 -35.83
2 2.64 29.35 28.87 -1.65
3 5.29 34.72 46.33 33.44
4 10.58 27.48 57.30 108.51
The Interference of Organic Matter in the Characterization of Aquifers Contaminated with LNAPLs by Partitioning Tracer Method 21
5. Conclusions
Most of the current subsurface characterization methods
provide measurements for very small spatial domains,
even for point values. While such methods can provide
accurate data for small scales, their use for characterizing
larger domains is generally constrained by sample-size
limitations. Thus, partition tracer method that provides
measurements at larger scales has been developed to
complement the point-sampling methods. The experimental
and theoretical basis for these tracer techniques is well
established. However, there is a major concern about its
application in the subsurface organic soil to provide
reliable in-situ measures of the relative quantities of
LNAPLs due the sorption of tracers to the organic matter.
In our study, we only test with the mixture of organic
fertilizer and Jumunjin standard soil to evaluate the
interference of organic soil in partitioning tracer method.
The tracers tests conducted in the pre-contaminated columns,
with known amount of organic matter, demonstrate that
tracers can be retarded with marked separation. Thus, the
accurate quantity estimation of LNAPL using partitioning
tracer test should be considered by conducting partitioning
tracer test without soils containing organic matter. The
presence of organic matter caused a linear increase in the
overestimation of the predicted values and thus can be
corrected for the known percentage of the organic matter
in the subsurface soil under given conditions.
Acknowledgement
The authors wish to acknowledge the financial support
by SNU SIR BK21 Research Program funded by Ministry
of Education, Science and Technology.
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(received on Jul. 21, 2008, accepted on Sep. 23, 2008)
Global Stability of Geosynthetic Reinforced Segmental Retaining Walls in Tiered Configuration 23
Global Stability of Geosynthetic Reinforced Segmental RetainingWalls in Tiered Configuration
계단식 블록식 보강토 옹벽의 전체 안정성
Yoo, Chungsik1유 충 식
Kim, Sun-Bin2김 선 빈
요 지
본논문에서는계단식형태로시공되는블록식보강토옹벽의전체안정성이고려된설계에관한내용을다루었
다 다양한제원과이격거리로설계된네가지설계사례에대해현재통용되고있는 및 설계기준에. FHWA NCMA근거하여내 외적안정해석을수행하고그결과를토대로두설계기준의차이점을검토하였다 아울러대상옹벽.・에대해한계평형해석에근거한사면안정해석과연속체역학기반의강도감소기법해석을수행하여계단식옹벽의
설계를지배하는파괴메카니즘을고찰하였다 그결과내 외적안정성공히 에서채택하고있는설계기준. FHWA・이 보다 보수적인 결과낮은 안전율를 주는 것으로 나타났다 또한 계단식 옹벽의 보강재의 소요 포설NCMA ( ) .길이는 전반적으로 전체 안정성에 좌우되는 것으로 검토되었으며 상부 옹벽의 보강재의 길이는 현 설계기준
보다 현저히 증가시켜야 하는 것으로 검토되었다.
Abstract
This paper presents the global stability of geosynthetic reinforced segmental retaining walls in tiered configuration.Four design cases of walls with different geometries and offset distances were analyzed based on the FHWA andNCMA design guidelines and the discrepancies between the different guidelines were identified. A series of globalslope stability analyses were conducted using the limit-equilibrium analysis and the continuum mechanics basedshear strength reduction method with the aim of identifying failure patterns and the associated factors of safety.The results indicated among other things that the FHWA design approach yields conservative results both in theexternal and internal stability calculations, i.e., lower factors of safety, than the NCMA design approach. It wasalso found that required reinforcement lengths are usually governed by the global slope stability requirement ratherthan the external stability calculations. Also shown is that the required reinforcement lengths for the upper tiersare much longer than those based on the current design guidelines.
Keywords : Geosynthetic-reinforced segmental retaining Wall, Geosynthetics, Global stability, Limit equilibrium,
Finite element analysis, Shear strength reduction
1 Professor, Dept. of Civil & Envir. Engrg, Sungkyunkwan Univ.2 Graduate Student. Dept. of Civil & Environ. Engrg., Sungkyunkwan Univ., [email protected], Corresponding Author
1. Introduction
Geosynthetic reinforced segmental retaining walls (GR-
SRWs) have been well accepted in practice as alternatives
to conventional retaining wall systems due to several
benefits such as sound performance, aesthetics, cost and
Jour. of the KGS, Vol. 24, No. 9. September 2008, pp. 23 32~
24 Jour. of the KGS, Vol. 24, No. 9, September 2008
expediency of construction. This is especially true in Korea
since its first appearance in the early 1990’s. Recently
the application of the GR-SRWs has been extended to
public sectors such as roadway and railway constructions,
especially in Japan as well as north America. For example,
GR-SRWs are frequently adopted in bridge construction
in public sectors, as the form of geosynthetic-reinforced
soil (GRS) abutments in bridge applications (Lee and Wu,
2004).
There are many situations where GR-SRWs are constructed
in tiered configuration for a variety of reasons such as
aesthetics, stability, and construction constraints, etc. Yoo
and Kim (2002), however, reported that the interaction
between the upper and lower tiers is not insignificant for
walls with an intermediate offset distance as per the
FHWA design guideline (Elias and Christopher 1997),
thus yielding larger wall deformation and reinforcements
forces than what might be anticipated. In addition, the
currently available design guidelines such as the NCMA
(Collins, 1997) and FHWA design guidelines are somewhat
empirical and geometrically derived.
Surprisingly, studies concerning GR-SRWs in tiered
configuration are scarce. For example, Yoo (2003), Yoo
and Jung (2004) reported the instrumentation results of
a full-scale, 5 m high two tier segmental retaining wall
that was constructed to investigate the short and long term
performance of the segmental retaining wall. Leshchinsky
and Han (2004) performed a series of finite difference
analyses on multi-tiered segmental retaining walls in order
to examine the failure mechanisms and to assess the
required tensile strength as a function of reinforcement
length, stiffness, offset distance, among others. Later, Yoo
and Kim (2006) conducted a numerical investigation on
two-tier segmental retaining walls with different offset
distances. More recently, Yoo et al. (2005) investigated
the deformation behavior of two-tier segmental retaining
walls on competent foundation having different wall
geometries as well as reinforcement layouts. Yoo and
Song (2006) later extended the work by Yoo et al. (2005)
for cases constructed on yielding foundation. Although
these studies provided valuable information as the subject
relevant to this study, in-depth studies are warranted in
order to accumulate required data for improving the
currently available design guidelines.
In this study four design case histories of geosynthetic
reinforced segmental retaining walls in tiered configuration
were considered, intending; 1) to highlight inherent
differences between the currently available design guidelines,
2) to demonstrate the governing failure mechanism that
yields the smallest factor of safety is the global failure,
3) to highlight the importance of carrying out the global
stability analysis as part of design. This study presents
the results of a series of analyses conducted in parallel
using two independent type of analyses: one based on
limiting equilibrium (LE) and the other based on
continuum mechanics. This paper is intended to be an
extension of the previous work done by Yoo and Kim
(2006).
2. Review of Design Guidelines
2.1 NCMA (National Concrete Masonry Association)
The NCMA design approach basically replaces the
DH 2
q
αα
qeq = f (D)
H1
L1
L1
H1
Fig. 1. Equivalent surcharge model (NCMA)
Global Stability of Geosynthetic Reinforced Segmental Retaining Walls in Tiered Configuration 25
upper tier with an equivalent surcharge of which the
magnitude is determined according to the offset distance
D (Figure 1). External and internal stability calculations
of the lower tier are performed assuming the lower tier
being a single wall under the equivalent surcharge (qeq).
The upper wall is designed as if it were a single wall
without taking into consideration of the possible interaction
between the upper and the lower tiers. As for a single
wall, the local stability calculations for the connection
failure, local overturning, and internal sliding should be
performed for both tiers. Details of the design procedure
are available in Collin (1997).
2.2 FHWA (Federal Highway Association)
In the FHWA design guideline, the required reinforcement
lengths for the upper and lower tiers are determined based
on the maximum tension line criteria given in Figure 2.
For example, no interaction is assumed and each tier is
designed independently when D> H1 tan(90 – ). When
D≤ 1 / 20(H1 + H2), on the other hand, the wall is
designed as if it were a single wall with a height of H =
H1 + H2. For walls with an intermediate offset distance
of 1 / 20(H1 + H2)< D≤ H1 tan(90 – ), the lower and
upper tier reinforcement lengths are taken as L1≥ 0.6H1
and L2≥ 0.6H2, respectively. Where, H1 = lower tier
height, H2 = upper wall height, L1 and L2 = reinforcement
length of lower and upper tier, respectively, and =
internal friction angle of backfill.
For internal stability calculations, additional vertical
stresses at depths due to the upper tier are computed based
on the criteria shown in Figure 3. Note, however, that
these criteria are geometrically derived and empirical in
nature. As for the NCMA approach, no provision is made
to take into account the possible interaction between the
upper and the lower tiers when designing the upper tier.
The connection failure should also be checked for both tiers
as part of internal stability check based on the procedure
for a single wall (Elias and Christopher, 1997).
As discussed, the external and internal stability calculation
models adopted in the two design guidelines are somewhat
different, thus yielding different stability calculation results
in terms of the factors of safety for most of the cases.
In addition, although the two aforementioned design
guidelines require to perform a global stability analysis
to ensure overall stability, it is general practice that no
global stability analysis is usually carried out in routine
designs. Further study is warranted to fill the gap between
the two design guidelines.
Note that in the FHWA and NCMA design guidelines
Fig. 2. Maximum tension line (FHWA)
26 Jour. of the KGS, Vol. 24, No. 9, September 2008
outlined above, same minimum factors of safety for
internal and external failure modes for a single wall are
applicable for a multi-tiered wall. In addition, for the
minimum factor of safety for global slope stability, a
typical value used in a geotechnical project can be used.
3. Field Walls Considered
Figure 4 shows four field walls considered in this study.
As summarized in Table 1, the total exposed wall heights
range from 4 to 12 m with the offset distance ranging
0.23~0.45 times the total wall height (H). The reinforce-
ment lengths vary as (0.38~0.56)H. Note that the walls
are designed based on either NCMA or FHWA design
approaches with the design parameters given in Table 2.
4. Stability Analysis
4.1 Internal and External Stability Analysis
The above field walls were re-analyzed by NCMA and
FHWA design approaches with the aiming of demonstrating
the inherent differences in the stability calculations. Table
2 summarizes the design parameters for the backfill and
the reinforcement used in the stability analyses. Note that
these parameters reflect the practice adopted in Korea.
The results of the external and the internal calculations
are summarized in Table 3. Importance findings can
H1
H2
D
σf
φγH2ζj
γi
ζ1
ζ2
σi
γH2
φς tan1 D= ⎟⎠⎞
⎜⎝⎛ +=
245tan2
φς oD
212
1 Hjf γ
ςςςς
σ−
−=
⎟⎠⎞
⎜⎝⎛ −≤
245tan1
φoHD
( )φ−> o90tan1HD 0=iσ
2Hi γσ =
( )φφ−≤<⎟
⎠⎞
⎜⎝⎛ − oo 90tan
245tan 11 HDH
σj
where: ,
245 φ
+o
Fig. 3. Calculation model for vertical stress increase due to upper tier (FHWA)
Table 1. Summary of wall geometry and reinforcement length
Wall
Height (m)Offset distance
D (m)
Reinforcement length (m)
Lower
Tier, H1
Upper
Tier, H2
Total
H1
Lower tier
L1
Upper tier
L2
A 3.8 5.4 8.8 2.5(0.34H) 4.9(0.56H) 3.5(0.7H2)
B 5.6 5.6 10.5 2.5(0.23H) 5.3(0.50H) 3.8(0.8H2)
C 8.8 4.4 12.4 5.0(0.40H) 7.0(0.56H) 5.0(1.3H2)
D 2.6 2.2 4.6 2.0(0.45H) 1.6(0.38H) 1.6(0.8H2)
Note) 1exposed height
Table 2. Design parameters for backfill and reinforcement used in stability analysis
Wall BackfillReinforcement
Reduction factor1
Tall (kN/m)2
A
c=0,
RFD RFID RFCR FS 6T=16, 8T=21.5, 10T=27
B
1.05 1.1 2.15 1.5
6T=16, 10T=27
C TYPE1=15, TYPE2=22 TYPE3=30
D N/A
Note)1Reduction factors represent general practice;
2Tall=allowable strength
Global Stability of Geosynthetic Reinforced Segmental Retaining Walls in Tiered Configuration 27
10T L=4.9M10T L=4.9M
10T L=4.9M
8T L=4.9M
8T L=5.9M8T L=3.5M8T L=3.5M
8T L=3.5M
8T L=3.5M
6T L=3.5M6T L=3.5M
6T L=3.5M
6T L=4.0M
2500
1:0.12
800
3400
5000
q=10 kPa
PG 6T H=0.2 L=5.28M
PG 10T H=0.8 L=5.28M
PG 10T H=1.4 L=5.28M
PG 10T H=2.0 L=5.28M
PG 6T H=2.6 L=5.28M
PG 6T H=3.2 L=5.28M
PG 6T H=4.0 L=5.28M
PG 6T H=4.8 L=5.28MPG 6T H=0.2 L=3.78M
PG 6T H=1.0 L=3.78M
PG 6T H=1.6 L=3.78M
PG 6T H=2.4 L=3.78M
PG 6T H=3.2 L=3.78M
PG 6T H=4.0 L=3.78M
PG 6T H=4.8 L=3.78M
5000
500
5100
400
2500
q=13.0 kPa
q=100.0kPa
150
150
116
116
(a) Wall A (b) Wall B
*All numbers are in mm unless otherwise indicated
300
L1 TYPE3 H=0.6M L=7.0ML1 TYPE3 H=1.2M L=7.0ML1 TYPE3 H=1.8M L=7.0ML1 TYPE2 H=2.4M L=7.0ML1 TYPE2 H=3.0M L=7.0ML1 TYPE2 H=3.6M L=7.0ML2 TYPE2 H=4.2M L=7.5ML2 TYPE2 H=4.8M L=7.5ML2 TYPE2 H=5.6M L=7.5ML2 TYPE1 H=6.4M L=7.5ML2 TYPE1 H=7.2M L=7.5M
L1 TYPE1 H=0.6M L=5.0ML1 TYPE1 H=1.2M L=5.0ML1 TYPE1 H=1.8M L=5.0M
L1 TYPE1 H=3.8M L=5.0ML1 TYPE1 H=3.0M L=5.0ML1 TYPE1 H=2.4M L=5.0M
18
18
400
4000
8000
2000
30050
028
0012
400
6000 500 6850
300
650
2000
2000
4650
G.L
2000
L1 TYPE H=1.6M L=1.6M
L1 TYPE H=0.6M L=1.6M
L1 TYPE H=1.6M L=1.6M
L1 TYPE H=1.6M L=1.6M
(c) Wall C (d) Wall D
Fig. 4. Field walls considered
Table 3. Results of external and internal stability calculations for field walls
Wall
External Internal
FSbsl FSot Ti,max (kN/m) Le (m)
NCMA FHWA NCMA FHWA NCMA FHWA NCMA FHWA
A 3.13 1.27 8.87 2.13 19.7 30.5 3.4 4.1
B 2.19 1.23 4.53 1.76 19.8 36.9 1.5 2.5
C 2.79 2.02 6.09 5.01 16.0 37.5 2.4 3.9
D 1.28 1.67 3.54 1.65 9.9 19.7 0.3 0.3
Note) 1) FSbsl = factor of safety against base sliding 2) FSot = factor of safety against overturning 3) Ti,max = maximum reinforcement
force within lower tier 4) Le = embedded length beyond active zone for top-most reinforcement in lower tier 5) For Wall D, FHWA design
guideline assumes no interaction.
28 Jour. of the KGS, Vol. 24, No. 9, September 2008
be summarized as follow. As seen in Table 3, the FHWA
design guideline tends to give smaller factors of safety in
the external analysis except for the wall D. For example,
according to the NCMA design approaches walls A, B,
and C satisfy the requirement for base sliding while the
opposite is true according to the FHWA design approach.
Additional global stability analyses in fact support the
instability against base sliding as the factors of safety
against global/compound stability for all the walls are less
than the minimum of 1.2 (to be shown later), which
suggests that the global/compound stability analysis should
be conducted as required in the two design approaches.
In terms of the internal stability calculations, the FHWA
design approach gives significantly larger maximum rein-
forcement loads and the embedment lengths beyond active
failure line than the NCMA design approach giving larger
pullout capacities. Apart from the different design earth
pressures adopted in these design approaches, the differences
in the calculation models (i.e., the way in which the upper
tier is treated) adopted in the two design approaches may
also be responsible for the discrepancies. Note that the
NCMA and the FHWA design guidelines adopt the
Coulomb and Rankine active earth pressures, respectively.
Such differences may give designers confusion to some
extent in selecting proper reinforcements in terms of
strength. Further study is warranted to fill the gap between
the two design approaches.
4.2 Global Slope Stability Analysis
A series of global slope stability analyses were additionally
performed on the field walls, aiming at examining if the
reinforcement layouts of the walls also satisfy the global
stability requirement. The limit-equilibrium (LE) as well
as the continuum mechanics based slope stability analyses
were performed using, MSEW ver. 1.0 (Leshchinsky 1999)
and Phase2 (Rocscience, 2005), respectively. Note that the
finite element analysis in conjunction with the shear
strength reduction method (Griffths and Lane 1999) was
employed as the continuum mechanics based approach.
Two different approaches were adopted in this study to
see if the two independent types of analyses would yield
similar results so that an acceptable level of confidence
in the results can be afforded. One of the advantages of the
finite element analysis with the shear strength reduction
(FEM-SSR) over traditional limit equilibrium approach is
that no assumption needs to be made a priori regarding
the shape or location of the failure surface.
In the finite element analysis with the shear strength
reduction method (FE-SSR), the factor of safety (FS) of
a slope can be defined as the number by which the original
shear strength parameters must be divided in order to
bring the slope to the point of failure (Griffths and Lane,
1999) so that the factored shear strength parameters (c'f,
'f) can be defined as:
FScc f'' = (1)
(a) LEM, FS=1.05 (b) FE-SSR, FS=0.92
Fig. 4. Global stability analysis : Wall A
Global Stability of Geosynthetic Reinforced Segmental Retaining Walls in Tiered Configuration 29
FSf'' φφ = (2)
Note here that this definition of FS is the same as that
adopted in the traditional LE methods. When adopting the
shear strength reduction approach, there are several possible
definitions of failure, e.g., non-convergence of the solution
(Zienkiewicz and Talyor, 1989) or acceleration of slope
displacement, etc. Details of the FE-SSR can be found
in Griffths and Lane (1999).
The results of the global stability analyses, in terms
of the minimum factors of safety and the corresponding
failure surfaces, are given in Figures 4~7. The factors of
safety values for each wall are summarized in Table 4.
Note that the LE slope stability analyses were conducted
based on the modified Bishop method. Salient features
that can be observed in these figures are two-fold. First,
for a given wall, the minimum factors of safety computed
by the LE and the FE-SSR analyses are in good agree-
ment, although the factors of safety from the FE-SSR are
somewhat smaller (less than 10%) than those from the
LE approach. Second, the potential failure surfaces from
the two approaches are also similar in shape. These results
demonstrate that the FE-SSR approach can also be effec-
tively used in the global stability analysis of reinforced
earth structures with an acceptable level of confidence.
Another important observation is that for all the walls
investigated, the minimum global factor of safety is smaller
than those of the external stability calculations for the base
sliding and over turning failure modes. Such a trend
implies that the governing failure mechanism in terms of
external stability is the global slope failure for walls in
tiered configuration with an intermediate offset distance.
A global stability check must be performed in addition
(a) LEM, FS=0.96 (b) FE-SSR, FS=0.93
Fig. 5. Global stability analysis : Wall B
(a) LEM, FS=1.01 (b) FE-SSR, FS=0.98
Fig. 6. Global stability analysis : Wall C
30 Jour. of the KGS, Vol. 24, No. 9, September 2008
to the external stability check when determining the
reinforcement lengths.
4.5 Reinforcement Distribution to Meet Global Stability
Requirement
Another series of global stability analyses were performed
to determine the reinforcement distributions that meet the
global stability requirement, taking the required minimum
factor of safety as FSmin = 1.20. The results are given
in Table 5 and Figure 8.
The results indicate that both the upper and lower tier
reinforcement lengths need to be increased as great as
by 50% to meet the global stability requirement. The
results also show that the lower and upper parts of the
upper and lower tiers, respectively, require much longer
reinforcement lengths than those satisfying the external
stability. Such a trend stresses that the global stability
analysis is not an option but a requirement when
designing GR-SRWs in tiered configuration with an
intermediate offset distance. Another important observation
is that the revised reinforcement lengths for the upper tiers
in all walls are significantly longer than those required
by the design guideline in which the upper tier is designed
as an independent wall. The fact that both tiers’ reinforce-
ment lengths need to be increased to ensure the global
stability requirement suggests that the interaction between
the upper and lower tiers can be explicitly accounted for
by performing the global stability analysis.
5. Summary and Conclusions
This paper presents the results of stability analyses on
geosynthetic reinforced segmental retaining walls in tiered
(a) LEM, FS=0.90 (b) FE-SSR, FS=0.82
Fig. 7. Global stability analysis : Wall D
Table 4. Summary of global stability analysis
Factor of Safety
Wall A Wall B Wall C Wall D
LE 1.05 0.96 1.01 0.90
FEM-SSR 0.92 0.93 0.98 0.82
Table 5. Summary of revised reinforcement lengths to meet global stability
WallOffset distance
D (m)
FSReinforcement length (m)
Lower tier (L1) Upper tier (L2)
as-designed1
revised as-designed revised2
as designed revised2
A 2.5(0.34H) 0.92 1.20 4.9(0.55H) 7(0.80H) 3.5(0.65H2) 6(1.11H2)
B 2.5(0.23H) 0.93 1.20 5.3(0.50H) 8(0.76H) 3.8(0.68H2) 6(1.07H2)
C 5.0(0.40H) 0.98 1.20 7.0(0.56H) 12(0.97H) 5.0(1.13H2) 7(1.49H2)
D 2.0(0.45H) 0.82 1.26 1.6(0.35H) 3(0.65H) 1.6(0.73H2) 2(0.91H2)
Note)1based on FE-SSR;
2maximum length
Global Stability of Geosynthetic Reinforced Segmental Retaining Walls in Tiered Configuration 31
configuration. Four design cases of walls with different
geometries and offset distances were considered. Based
on the results of stability analyses using the FHWA and
NCMA design guidelines, the discrepancies between the
two different guidelines were identified. A series of global
slope stability analyses were conducted using the limit-
equilibrium analysis and the continuum mechanics based
shear strength reduction method aiming at investigating
governing mode of failure for walls with an intermediate
offset distance.
The results indicated among other things that the FHWA
design approach yields conservative results both in the
external and internal stability calculations, i.e, lower factors
of safety, than the NCMA design approach. In addition
to the different design earth pressures, the differences in
the calculation models (i.e., the way in which the upper
tier is treated) adopted in the two design approaches may
also be responsible for the discrepancies. Also found is
that required reinforcement lengths are usually governed
by the global slope stability requirement rather than the
external stability calculations, thus demonstrating the global
stability analysis should be part of design calculations in
addition to the internal and external stability checks. It
is shown that when considering the global stability
requirement, the required reinforcement lengths for the
upper tiers are much longer than those based on the
10T L=6.0M
10T L=6.0M
10T L=6.0M
8T L=7.0M
8T L=7.0M
8T L=4.0M
8T L=6.0M
8T L=5.0M
8T L=5.0M
6T L=4.0M
6T L=5.0M
6T L=4.0M
6T L=4.0M
2500
1:0.12
800
3400
5000
87
q=1.0 ton/m2
PG 6T H=0.2 L=6.0M
PG 10T H=0.8 L=6.0M
PG 10T H=1.4 L=6.0M
PG 10T H=2.0 L=6.0M
PG 6T H=2.6 L=8.0M
PG 6T H=3.2 L=8.0M
PG 6T H=4.0 L=8.0MPG 6T H=4.8 L=8.0M
PG 6T H=0.2 L=6.0M
PG 6T H=1.0 L=6.0M
PG 6T H=1.6 L=6.0M
PG 6T H=2.4 L=5.0M
PG 6T H=3.2 L=5.0M
PG 6T H=4.0 L=5.0M
PG 6T H=4.8 L=5.0M
5000
500
5100
400
2500
q=13.0kN/m2
q=100.0kN/m2
속채움 잡석구간
유공관 150φ
(a) Wall A (FS=1.20) (b) Wall B (FS=1.20)
L1 TYPE3 H=0.6M L=10.0ML1 TYPE3 H=1.2M L=10.0ML1 TYPE3 H=1.8M L=10.0ML1 TYPE2 H=2.4M L=10.0ML1 TYPE2 H=3.0M L=10.0ML1 TYPE2 H=3.6M L=10.0ML2 TYPE2 H=4.2M L=10.0ML2 TYPE2 H=4.8M L=10.0ML2 TYPE2 H=5.6M L=12.0M
L2 TYPE1 H=6.4M L=12.0M
L2 TYPE1 H=7.2M L=12.0M
L3 TYPE1 H=7.8/8.0/8.2M L=12.0ML1 TYPE1 H=0.6M L=7.0ML1 TYPE1 H=1.2M L=7.0ML1 TYPE1 H=1.8M L=7.0M
L1 TYPE1 H=3.8M L=7.0M
L1 TYPE1 H=3.0M L=7.0ML1 TYPE1 H=2.4M L=7.0M
1
8
18
400
4000
8000
2000
30050
0
2800
1240
0
6000 500 6850
650
2000
2000
4650
G.L
F.L
2000
L1 TYPE H=1.6M L=3.0M
L1 TYPE H=0.6M L=3.0M
L1 TYPE H=0.6M L=2.0M
L1 TYPE H=1.6M L=2.0M
(c) Wall C (FS=1.20) (d) Wall D (FS=1.26)
Note) All numbers are in ‘mm’ unless otherwise indicated.
Fig. 8. Reinforcement distributions to meet global stability requirement
32 Jour. of the KGS, Vol. 24, No. 9, September 2008
current design guidelines in which the upper tier is treated
as an independent wall. These results warrant that a global
stability based design approach needs to be developed for
geosynthetic reinforced segmental retaining walls in tiered
configuration.
Acknowledgements
This work was supported by Grant No. R01-2004-000-
10953-0 from the Basic Research Program of the Korea
Science & Engineering Foundation and by Korea Ministry
of Construction and Transportation under Grant No.
C06A0300-01511.The financial supports are gratefully
acknowledged.
References
1. Collin, J. (1997), “Design Manual for Segmental Retaining Walls”,2nd Ed. 1997, National Concrete Masonry Association (NCMA),Virginia, USA.
2. Elias, V. and Christopher, B.R. (1997), “Mechanically StabilizedEarth Walls and Reinforced Soil Slopes, Design and ConstructionGuidelines”, FHWA Demonstration Project 82, FHWA, Washington,DC, FHWA-SA-96-071.
3. Lee, K.Z.Z. and Wu, J.T.H. (2004), “A synthesis of case historieson GRS bridge-supporting strucutres with flexible facing”, Geotextileand Geomembranes, 22(4), 181-204.
4. Leshchinsky, D. (1999), Putting Technology to Work: MSEW andReSlope for Reinforced Soil-Structure Design. Geotechnical FabricsReport, Vol.18, pp.34-39.
5. Leshchinsky, D. and Han, J. (2004), “Geosynthetic ReinforcedMultitiered Walls”, J. of Geotech. and Geoenvir. Engrg, ASCE,Vol.230, No.12, pp.1225-1235.
6. Yoo, C. (2003), “Instrumentation of Geosynthetic ReinforcedSegmental Retaining Wall in a Tiered Configuration”, InternalReport, Sungkyunkwan University.
7. Yoo, C. and Kim, J.S. (2002), Behavior of Soil-ReinforcedSegmental Retaining Walls in Tiered Arrangement. Journal ofKorean Geotechical Society, KSGE, Vol.18, No.3, pp.61-72.
8. Yoo, C. and Jung, H.S. (2004), “Measured behavior of a geosynthetic-reinforced segmental retaining wall in a tiered configuration”,Geotextiles and Geomembranes, Vol.22, No.5, pp. 359-376.
9. Yoo, C. and Kim, S.B. (2006), “A Comparative Study on Designof Geosynthetic Reinforced Modular Block Wall in TieredArrangement”, Proceedings of 8th International Conference onGeosynthetics, Yokohama, Japan, in-print.
10. Yoo, C., Jung, H.Y., and Song, A.R. (2005), “Numerical Investigationon Behavior of Geosynthetic Reinforced Modular Block Walls ina Tiered Arrangement”, Journal of Korean Geotechnical Society,21(10):1-12.
11. Yoo, C. and Song, A.R. (2006), “Effect of foundation yielding onperformance of two-tier geosynthetic reinforced segmental retainingwalls A numerical investigation”,– Geosynthetics International,20(30): 110-120.
12. Griffiths, D.V. and Lane, P.A. (1999), “Slope stability analysis byfinite elements”, Géotechnique 49, No.3, 387-403.
13. Rocscience Inc. (2005), Phase2 v6.0 Two dimensional finite elementslope stability analysis.
14. Zienkiewicz, O.C. and Taylor, R.L. (1989), “The finite elementmethod”, Vol.1, 4th edition. London, New York, McGraw-Hill.
(received on Jul. 24, 2008, accepted on Sep. 26, 2008)
Prediction and Assessment on Consolidation Settlement for Soft Ground by Hydraulic Fill 33
Prediction and Assessment on Consolidation Settlement forSoft Ground by Hydraulic Fill
준설매립 연약지반에 대한 압밀침하 예측 및 평가
Jeon, Je-Sung1전 제 성
Koo, Ja-Kap2구 자 갑
Oh, Jeong-Tae3오 정 태
요 지
본연구에서는해안준설매립지반에대한연약지반개량사례를이용하여연직배수공법적용시의현장계측및압밀침
하해석을실시하였다 대상현장은원지반위에대략 의준설매립을통해조성된부지로서고함수비및고압축성의. 10m
해성점토로구성되어있다 년동안의현장계측결과 당초설계시의예측침하량에비해매우큰압밀침하가발생하였. 1 ,
고 이 조건에서의 향후 침하거동을 예측하기 위한 추가 압밀침하 해석 및 계측결과를 이용한 역해석을 실시하였다, .
상부시공 영향 등에 의해 준설매립지반에는 과다한 전단변형이 발생하였으며 이에 대한 현장 계측결과의 평가 및,
보정을실시하였다 압밀해석및원지반조건을평가하기위해실내시험결과를이용한물질함수분석을실시하였으며. ,
최종적으로부지인도후의잔류침하량및최종지반고를만족시키기위한추가성토고를산정하였다 추가성토이후의.
현장 계측결과와 당초 예측했던 압밀침하 거동을 비교하였으며 이를 통해 당초 예측내용에 대한 검증을 수행할 수,
있었다.
Abstract
This paper describes the performance of ground improvement project using prefabricated vertical drains of condition,
in which approximately 10 m dredged fill overlies original soft foundation layer in the coastal area composed of soft
marine clay with high water content and high compressibility. From field monitoring results, excessive ground settlement
compared with predicted settlement in design stage developed during the following one year. In order to predict the
final consolidation behavior, recalculation of consolidation settlements and back analysis using observed settlements were
conducted. Field monitoring results of surface settlements were evaluated, and then corrected because large shear
deformation occurred by construction events in the early stages of consolidation. To predict the consolidation behavior,
material functions and in-situ conditions from laboratory consolidation test were re-analyzed. Using these results, height
of additional embankment is estimated to satisfy residual settlement limit and maintain an adequate ground elevation.
The recalculated time-settlement curve has been compared with field monitoring results after additional surcharge was
applied. It might be used for verification of recalculated results.
Keywords : Consolidation analysis, Consolidation settlement, Dredged fill, Marine clay, Settlement monitoring
1 Member, Principal Researcher, KIWE, Korea Water Resources Corporation, [email protected], Corresponding Author2 Member, Prof., Dept. of Civil Eng., Hankyong National University3 Member, Construction Team Manager., Yeosu Regional Office, Korea Water Resources Corporation
Jour. of the KGS, Vol. 24, No. 9. September 2008, pp. 33 40~
34 Jour. of the KGS, Vol. 24, No. 9, September 2008
1. Introduction
Increasing national necessity for expansion of industrial
site together with a general decrease in the number of
available areas have created the need for landfills using
fine-grained material dredged from the coastal area near.
For the construction of national industrial complexes, a
large scale reclamation and ground improvement project
involving about 20 million square m of soft ground
improvement has been under way on the south coast area
in Korea.
Land reclamation on the foreshore of existing coastlines
often overlies soft clays which require soil improvement
to ensure stability during and after construction and to
reduce or eliminate undesirable short and long term
settlement (Choa et al., 2001). The project is the case of
landfills on soft marine clay in the coastal area of Yeosu,
southern Korea, and involves ground improvement using
prefabricated vertical drains and surcharge. The consoli-
dation settlement of not only the surface reclamation layer
but also the original soft clay layer underneath has been
continuously measured since the beginning of the work.
The predicted results in design stage using various labora-
tory data are compared with the observed ones considering
construction effects, such as heaving and displacement,
caused by additional works near. From the field monitoring
results, excessive ground settlement has been developed
and compared with the value in design stage. This is a
serious issue for this project, in which the transfer date
of final improved is limited for further construction of
industrial facilities. In this study, the magnitude and the
rate of the consolidation settlement were reassessed by
back analysis of the observed settlement, and results from
laboratory consolidation test.
2. Improving Soft Ground
2.1 The Site and Ground Condition
The site for the study is located in the Yeosu national
industrial complexes project in Korea. The project com-
prises land reclamation and ground improvement works
to allow for the future construction of advanced chemical
and heavy industry complex. Land reclamation works
which involved the hydraulic placement up to 20 m of
soft marine clay for the formation of 7.8 km2 land has
been conducted from 1996 to 2003 on the original soft
ground. The ground consists of upper dredged fill which
contained very soft marine clay, up to 10 m in thickness,
having high compressibility and high moisture content and
lower original clay layer of 3-10 m thickness. The areas
for project were divided into 4 sections, and each section
was divided into appropriate blocks for efficient con-
struction. For block 3 in section 1, ground improvement
by vertical drain in combination with up to 3.5 m
thickness of surcharge commenced from September, 2006
is in progress after hydraulic filling of 8,300×103 m3 of
slurry completed in Dec. 2003.
2.2 Vertical Drains with Preloading
The use of prefabricated vertical drain with preloading
was considered in this project to accelerate the rate of
consolidation and to minimize future settlement of the
treated area under future load.
Construction procedure for improving soft ground is
shown in Fig. 2. Geotextile of PET mat was spread out
on the soft ground to get construction capability caused
by very low shear strength. With the same reason, rubble
mat of 0.8 m height was spread out using conveyer system.
Generally, the ground improvement works are carried out
in such a way that a specified degree of primary con-
solidation is attained within the desired time by improving
The South Sea
SEC. 1SEC. 2SEC. 3
Block 3The South Sea
SEC. 1SEC. 2SEC. 3
Block 3
Fig. 1. The site of national industrial complexes project
Prediction and Assessment on Consolidation Settlement for Soft Ground by Hydraulic Fill 35
the soil drainage system. It should be required to satisfy
final ground level pre-designed for industrial facilities
after site transfer, and to limit residual consolidation set-
tlement within 10~30 cm in this project. It corresponds
to requirement of site transfer to client companies which
have plans to construct industrial facilities. The main
variables in design stage are the magnitude of preloading,
the spacing of vertical drains, the duration of preloading,
and the consolidation parameters of soft marine clay.
Prefabricated vertical drains in a width 10 cm were
installed at 0.8~1.5 m square spacing depending on the
duration of the preloading period. Preloading was subse-
quently placed to the design height of 2.35~3.5 m for 8~12
month after surcharge placement. In design stage, the
consolidation settlement that the requirements for site
transfer can be satisfied was expected to develop during
8~12 month. However, there was a great difference be-
tween the design value and estimated results from the field
monitoring.
2.3 Field Monitoring
In order to monitor the performance of ground
improvement and to verify the original design for
improving soft ground, several geotechnical instruments
were installed to monitor the degree of consolidation and
final settlement. The surface settlement plates were install-
ed just before the installation of vertical drain on the
geotextile to ensure construction capability. The multilevel
settlement gauges and piezometers were installed at various
levels in order to monitor the settlement of various sub-
layers and pore pressure dissipation.
Surface settlement and pore pressure were monitored
at close intervals of 1~3 days during the first three months,
and at the wider intervals of 7~10 days during the later
part of monitoring. Fig. 3 shows the surface settlement
results of P1-2-4, P1-2-5, and P1-2-6 together with the
construction activities. These three surface settlement
plates were installed in a typical zone with a space of
25 m in order to verify each result by cross review. As
shown in Fig. 3, surface settlement of each point shows
big differences due to construction events in which large
shear deformation may occur by installation of PVD and
continuous embankment in the early stages of consolidation.
However, from results after 33 days of PVD installation,
PET Mat-2(15TON)
Embankment-1 ( Rubble Mat for horizontal drainage) 0.80m(0.3+0.5m)
PET Mat-1(20TON)
Embankment-2
Installation of PVD
0.70m(0.4+0.3m)
0.85m
Embankment-3
(a) Spread PET Mat-1 (20T) (b) Rubble Mat-1, 0.8 m
(c) Spread PET Mat-2 (15T) (d) Embankment-2, 0.7 m
(e) Installation of PVD (f) Embankment-3, 0.85 m
Fig. 2. Construction procedure for improving soft ground
-100
0
100
200
300
400
5000 50 100 150 200 250 300 350 400
Elapsed Time (day)
Set
tlem
ent
(cm
)
P1-2-4
P1-2-5
P1-2-6
2006.09.11Instruments installation
06.09.14~09.18Embankment 1Final H=0.8m
06.11.02Installation of
PVD
06.11.20Embankment 3Final H=2.35m
06.09.30~10.16Embankment 2Final H=1.5m
Fig. 3. Monitoring results of surface settlement for zone-1
36 Jour. of the KGS, Vol. 24, No. 9, September 2008
surface settlements of three points show a good agreement
as shown in Fig. 4. It is important to note that settlement
up to the present has developed over 4.5 m although
ultimate consolidation settlement in design stage was
predicted as about 3.0 m at zone-1. These disagreements
between predicted consolidation settlement in design and
monitored results made big trouble for this project, in
which the transfer date of final improved site is limited
for further construction of industrial facilities.
Fig. 5 shows results of consolidation settlements on
surface with surcharge period of 250 days for zone-2.
Monitoring period of zone-2 after installation of PVD and
continuous embankment is under 3 months. For zone-2,
field monitoring results of surface settlement could not
be used for the prediction of consolidation behavior and
ultimate settlement.
3. Characteristics of the Marine Clay
3.1 Sampling Methods
The most important thing when unexpected excessive
settlement developed was to take a proper step for pre-
dicting ultimate consolidation settlement. It was required
to investigate consolidation parameters and material func-
tion by laboratory (Yoo, 2007) and in situ tests.
Undisturbed samples were taken from lower original
clay layer of 3-10 m thickness. All samples were carefully
sealed on site immediately after sampling. The fresh sam-
ples were carefully wire trimmed into specimens for testing
in the laboratory. For the upper dredged fill up to 10 m,
retrieval of undisturbed sample was impossible because
fill material of marine clay was in the state of slurry with
high moisture content up to 150%. Disturbed clays were
taken from field and remolded samples for laboratory tests
were made by large consolidation apparatus under certain
effective stress.
3.2 Soil Properties
In accordance with KS standards, natural unit weight,
specific gravity, grain size distribution, and Atterberg
limits of marine clay at Yeosu were determined as shown
in Table 1. For upper layer of dredged fill, test results
of disturbed sample taken from in-situ show that average
values of the specific gravity, liquid limit and plasticity
index are 2.72, 86.3% and 56.5, respectively. Maximum
natural water content which is determined by disturbed
clay of SPT sampler is 117.9%. For lower layer of original
0
100
200
300
4000 30 60 90 120 150 180 210 240 270 300
Elapsed Time (day)
Set
tlem
ent
(cm
)
P1-2-4
P1-2-5
P1-2-6
Zero reading time : 2006.12.05
- 33 days have elapsed since installation of PVD
- 15 days have elapsed since final embankment
Fig. 4. Monitoring results after zero reading for zone-1
-200
-150
-100
-50
0
50
1000 50 100 150 200 250 300
Elapsed Time (day)
Set
tlem
ent
(cm
)
P2-28
P2-29
P2-30
07.01.05Instrument installation
(P2-29)
06.12.15Instrument installation
(P2-28)
07.01.17Instrument installation
(P2-30)
Final EmbankmentH = 3.0m
Fig. 5. Monitoring results of surface settlement for zone-2
(a) preparation of clay slurry (b) setup consolidation apparatus
(c) consolidation (d) sampling for laboratory tests
Fig. 6. Remolded sample of disturbed clays taken from dredged
fill (Yoo, 2007)
Prediction and Assessment on Consolidation Settlement for Soft Ground by Hydraulic Fill 37
marine clay, laboratory tests were conducted using undis-
turbed sample.
3.3 Consolidation Parameters
The preconsolidation pressure, the compression index,
vertical coefficient of consolidation and permeability were
determined by conventional oedometer tests as well as
150 mm diameter CRS (Constant Rate of Strain) tests using
both undisturbed and remolded samples. With the use of
vertical drain, the horizontal coefficient of consolidation
becomes one of the most important consolidation pa-
rameters. Laboratory tests with 60 mm, 100 mm, 150 mm
diameter were also performed to measure coefficient of
consolidation in horizontal direction, . In-situ test,
conepenetrometer dissipation tests (CPTu) were used to
measure as well as pore water pressure. Results of
consolidation parameters are shown in Table 2.
3.4 Material Function
The most important parameters governing the primary
consolidation calculations are the void ratio-effective stress
and void ratio-coefficient of permeability relationships
obtained from laboratory consolidation tests (Stark et al.,
2005).
Cargill (1985) and Poindexter (1988) describe the rec-
ommended laboratory testing procedure to obtain these
relationships. These relationships may be used to assess
initial effective stress at each sub-layer for consolidation
calculation and coefficient of consolidation at each effec-
tive stress. Defining these relationships from low effective
stress level requires two different laboratory consolidation
tests of self-weight consolidation and conventional oedo-
meter. Stark et al. (2005) used results of self-weight con-
solidation test to find the void ratio-effective stress and
void ratio-permeability relationships at effective stresses
less than about 0.96 kPa. Also, results of conventional
oedometer test were used to find the void ratio-effective
stress and void ratio-permeability relationships at effective
stresses greater than about 0.96 kPa. In this research, con-
ventional oedometer, Rowe cell and CRS tests were per-
formed for these relationships.
Fig. 7 presents the void ratio-effective stress and void
ratio-permeability relationship measured using self-weight
Table 1. Soil properties of marine clay
Soil properties
Upper dredged fill layer
(remolded sample except for
water content)
Lower original clay layer
(undisturbed soil)
Min. Max. Min. Max.
Natural water content (%) 88.1 117.9 65.1 82.5
Passing No.200 sieve (%) 95.8 99.9 97.9 99.1
Specific gravity 2.71 2.73 2.70 2.73
Liquid limits (%) 76.3 96.2 54.5 88.9
Plasticity index 50.8 62.2 31.9 60.3
USCS CH CH
Table 2. Consolidation parameters of marine clay
Soil properties
Upper dredged fill layer
(remolded sample)
Lower original clay layer
(undisturbed soil)
Min. Max. Min. Max.
Initial void ratio, eo 2.3 2.9 1.6 2.3
Compression index, cc 0.83 1.22 0.79 1.07
Vertical coefficient of consolidation,
cv(cm2/s)
5.0E-04 9.2E-04 3.0E-04 3.5E-04
Horizontal coefficient of consolidation,
ch(cm2/s)
6.0E-04 9.7E-04 4.6E-04 6.5E-04
38 Jour. of the KGS, Vol. 24, No. 9, September 2008
consolidation and typical oedomenter tests for 19 dredged
material types from 17 placement sites (Stark et al., 2005)
Fig. 8 presents material function for void ratio-effective
stress and void ratio-permeability from Lab. tests in this
study. For void ratio-effective stress relationship, material
function shows a good agreement with empirical rela-
tionship of high void ratio, e > 2.3. A series of results
that describe effective stress and permeability with void
ratio less than 2.3 show difference of a considerable margin.
4. Prediction of Consolidation
As mentioned above, settlement after 350 days has de-
veloped over 4.5 m although ultimate consolidation set-
tlement in design stage was predicted as about 3.0 m at
zone-1. These disagreements between predicted consoli-
dation settlement in design and monitored results made
big trouble for this project, in which the transfer date of
final improved site is limited for further construction of
industrial facilities. In this particular situation, overriding
concern was to predict the consolidation settlement with
time including magnitude of ultimate settlement.
In conventional consolidation theory, strains are assumed
to be small or in a mathematical sense, infinitesimal
(Gibson et al., 1981; Mesri et al., 1974).
This is a background to use constant coefficient of
compressibility, and the coefficient of volume compress-
ibility, when calculating consolidation settlement. Pri-
mary consolidation settlements in design stage of this
project were calculated by . However, this method has
limitations for considering large strain problem associated
with a great change of effective stress because of its
nonlinear stress-strain relationship (Gibson et al., 1981;
Terzaghi et al., 1996).
The primary consolidation settlements of upper dredged
fill and original clay layer were recalculated using com-
0
2
4
6
8
10
12
14
1.0E-03 1.0E-02 1.0E-01 1.0E+00 1.0E+01 1.0E+02 1.0E+03
Effective Stress(kPa)
Voi
d R
atio
New Haven(PI=68) Port Authority(PI=65)
Lower Passaic(PI=63) Port Elizabeth(PI=49)
Stamford(PI=46) Red Hook(PI=43)
Duwamish(PI=39) PI=40 (relationship)
PI=50 (relationship) PI=60 (relationship)
PI=70 (relationship)
PI=40PI=50 PI=60
PI=70
0
2
4
6
8
10
12
14
1.0E-10 1.0E-09 1.0E-08 1.0E-07 1.0E-06 1.0E-05 1.0E-04
Permeability(m/s)
Voi
d R
atio
New Haven(PI=68)
Port Authority(PI=65)
Lower Passaic(PI=63)
Port Elizabeth(PI=49)
Stamford(PI=46)
Red Hook(PI=43)
Duwamish(PI=39)
PI=40 (relationship)
PI=50 (relationship)
PI=60 (relationship)
PI=70 (relationship)
PI=70
PI=60
PI=50
PI=40
Fig. 7. Void ratio-effective stress and void ratio-permeability
relationship for inorganic clays of high plasticity (Stark et
al., 2005)
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
0.0001 0.001 0.01 0.1 1 10 100Vertical effective stress (kgf/cm2)
Voi
d r
atio
, e
Zone-1 (No.1) Zone-1 (No.2)
Zone-2 (No.1) Zone-2 (No.2)
Zone-2 (No.3) Zone-2 (No.4)
Zone-2 (CRS)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
1.0E-9 1.0E-8 1.0E-7 1.0E-6 1.0E-5 1.0E-4
Permeability, k (cm/sec)
Voi
d ra
tio,
e
Zone-1 (No.1) Zone-1 (No.2)
Zone-2 (No.1) Zone-2 (No.2)
Zone-2 (No.3) Zone-2 (No.4)
Zone-2 (CRS)
Fig. 8. Void ratio-effective stress and void ratio-permeability
relationship from Lab. tests
Prediction and Assessment on Consolidation Settlement for Soft Ground by Hydraulic Fill 39
pression index, . Initial effective stresses of sub-layers
were estimated from both void ratio-effective stress rela-
tionship and natural water content-void ratio relationship.
The magnitude of settlement was calculated on several
subdivided layers in order to be able to predict the ultimate
settlement accurately. The and values basically were
derived from material function of laboratory tests, and
different values were applied to calculation by effective
stress level.
Field monitoring results gave a good agreement with
time-settlement relationship although it shows fluctuation
in initial part caused by shear deformation with upper
construction activities. At first, consolidation settlement
with time was recalculated using material function from
Lab. tests. There were a some differences between recal-
culated value and real field monitoring results during 350
days. The back analysis was conducted by modifying
material function until recalculated curve fits to field
monitoring results. The recalculated and monitored
surface settlements for zone-1 are shown in Fig. 9.
Major contract terms for site transfer in this project are
that residual settlement after site transfer should be less
than 10 cm, and final ground elevation should be the same
as the original design value. For satisfying ground elevation
in design stage, additional surcharge was required to
compensate excess ground settlement.
However, additional surcharge may act as an external
load, and this may give rise to more settlement. In
instances when it appears that too much consolidation
settlement is likely to occur, it may be desirable to apply
some additional surcharge loading in order to eliminate
or reduce the post-construction settlement. It was important
to estimate how much additional surcharge was required
to satisfy all contract terms for site transfer. Essential facts
related with estimation of settlement, such as settlement
history, final ground elevation, date of site transfer, load
condition after completion, and allowable residual
settlement, were considered carefully. Fig. 10 shows the
consolidation settlement with time in case of applying
additional surcharge at time elapse of 429 days. The
additional surcharge with the height of 3.2 m was applied
for satisfying residual settlement limit and final ground
level.
The recalculated time-settlement curve shown in Fig. 9
has been compared with field monitoring results from 85
to 350 days. Fig. 11 includes some monitored results after
additional surcharge with the height of 3.2 m was applied.
It might be used for verification of recalculated results.
0.0
1.0
2.0
3.0
4.0
5.0
6.00 50 100 150 200 250 300 350 400
Elapsed Time (day)
Set
tlem
ent
(m)
Prediction of settlement
Monitoring relusts - Part1
Field monitoring resultsfor assessment
2006.09.11 2006.12.20 2007.03.30 2007.07.08 2007.10.16 2008.01.24 2008.05.03
2006.11.02Installation of PVD
Fig. 9. Recalculated and monitored time-settlement curve for
zone-1
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.00 100 200 300 400 500 600 700
Elapsed Time (day)
Set
tlem
ent
(m)
No additional surchargeSurcharge h=1.0mSurcharge h=2.0mSurcharge h=3.0m
Embankment H=2.35m
Additional Surcharge
Fig. 10. Prediction of time-settlement for each surcharge height
0.0
1.0
2.0
3.0
4.0
5.0
6.00 100 200 300 400 500 600 700
Elapsed Time (day)
Set
tlem
ent
(m)
Prediction of settlement
Monitoring relusts - Part1
Monitoring relusts - Part2
2006.11.02Installation of PVD
Field monitoring resultsfor assessment
Field monitoring resultsfor verification
2006.09.11 2006.12.20 2007.03.30 2007.07.08 2007.10.16 2008.01.24 2008.05.03
Fig. 11. Additional field monitored time-settlement curve for
zone-1
40 Jour. of the KGS, Vol. 24, No. 9, September 2008
5. Conclusion
The project of landfills on soft marine clay including
ground improvement using prefabricated vertical drains
and surcharge was carried out on the foreshore of southern
Korea where a significant thickness of highly compressible
soils existed on the seabed. Ground improvement works
were required for both upper dredged fill layer and lower
seabed soils. Excessive settlements, which could not be
expected in design stage have been developed. It was
required to reassess monitoring results because it showed
large fluctuations in magnitude of settlement due to shear
deformation. The material functions related to consolidation
and permeability characteristics of the marine clay were
investigated from laboratory and in situ tests. Application
of different consolidation parameter by effective stress
level from material function gives a good result for
prediction of settlements with time for very soft marine
clay.
The primary consolidation settlements with time of
upper dredged fill and original clay layer were recal-
culated, and the back analysis was conducted by modifying
material function until recalculated curve fits to field mon-
itoring results. Method of additional surcharge loading
was adapted as a technical measure to reduce the post
construction settlement, and speed up consolidation
process before site transfer. Amount of additional surcharge
loading was evaluated carefully in consideration of final
ground elevation, date of site transfer, and allowable
residual settlement.
References
1. Arulrajah, A, Nikraz, H, and Bo, M.W. (2004), “Observational methodof assessing improvement of marine clay”, Ground Improvement,Vol.8, No.4, pp.151-169.
2. Cargill, K.W. (1984), “Prediction of Consolidation of Very Soft Soil”,J of Geotechnical Engineering, ASCE, Vol.110, No.6, pp.775-795.
3. Cargill, K.W. (1985), Mathematical model of the consolidation/desiccation processes in dredged material, Technical Rep. D-85-4,U.S. Army Engineering Waterways Experiment Station.
4. Choa, V, Bo, M.W., and Chu, J (2001), “Soil improvement worksfor Changi East Reclamation Project”, Ground Improvement, Vol.5,No.4, pp.141-153.
5. Chu, J, Bo, M.W., Chang, M.F., and Choa, V (2002), “Consolidationand Permeability Properties of Singapore Marine Clay”, J Geotech-nical and Geoenvironmental Engineering, Vol.128, No.9, pp.724-732.
6. Cousens, T.W., and Stewart, D.I. (2003), “Behavior of a trialembankment on hydraulically placed pfa”, Engineering Geology,Vol.70, pp.293-303.
7. Gibson, R.E., Schiffman, R.L. and Cargill K.W. (1981), “The Theoryof One-dimensional Consolidation of Saturated Clays II. FiniteNonlinear Consolidation of Thick Homomgeneous Layers”, CanadianGeotechnical Journal, Vol.18, pp.280-293.
8. Hansbo, S. (1981), “Consolidation of fine-grained soils by prefab-ricated drains”, 10th Int Conf Soil Mechanics and Found Engineering,Stockholm, Sweden, Vol.3, pp.677-682.
9. Mesri, G., and Rokhsar, A. (1974), “Theory of Consolidation forClays”, Journal of the Geotechnical Engineering Division, ASCE,Vol.100, No.GT8, pp.889-904.
10. Poindexter, M.E. (1988), Behavior of subaqueous sediment mounds:Effect on dredged material disposal site capacity, Ph.D. Thesis,Texas A&M Univ., College Station, Tex.
11. Stark, T.D., Choi, H., and Schroeder, P.R. (2005), “Settlement ofDredged and Contaminated Material Placement Areas. II: PrimaryConsolidation, Secondary Compression, and Desiccation of DredgedFill Input Parameters”, J Waterway, port, coastal, and ocean engi-neering, Vol.131, No.2, pp.52-61.
12. Tan, S.A. (1993). “Ultimate Settlement by Hyperbolic Plot for Clayswith Vertical Drains”, J Geotechnical Engineering, Vol.119, No.5,pp.950-956.
13. Terzaghi, K, Peck, R.B., and Mesri, G. (1996), Soil Mechanics inEngineering Practice, 3nd Edition, John Wiley & Sons, New York,pp.71-121.
14. Yoo, N.J. (2007), Consolidation Characteristics of Dredged FillMaterial Including Centrifuge Test, Research Rep., KSCE, pp.1-117.
(received on Aug. 22, 2008, accepted on Sep. 17, 2008)
A Graphical Method for Evaluation of Stages in Shrinkage Cracking Using S-shape Curve Model 41
A Graphical Method for Evaluation of Stages in Shrinkage CrackingUsing S-shape Curve Model
형 곡선 모델을 적용한 수축 균열 단계 평가S
Min, Tuk-Ki1민 덕 기
Vo Dai Nhat2보 다이 낫
요 지
본 연구에서는 수축균열 단계를 나타낼 수 있는 도해적인 방법을 제안하였다 우선 발생된 균열들을 균열.폭의크기순서대로나열하여균열분포를구하였다 다음에균열폭을정규화하여 에서 사이의값으로나타내었. 0 1다 마지막으로 와 와 이 제안한바 있는 형 곡선. Brooks Corey(1964), Fredlund Xing(1994), van Genuchten(1980) S모델에 실험 결과를 적용시켰다 분석 결과 의 식이 와 식보다 정확도가 크게 높은. van Genuchten Brooks Corey것으로 나타났으며 와 식보다도 높게 나타나 의 식을 적용하였다 결과적으로 수축, Fredlund Xing van Genuchten .균열의 단계는 정규화된 균열폭 분포가 개의 직선부로 나누이는 도해적인 방법으로 나타낼 수 있었다 제안된3 .방법의적용성을보기위해시료의두께에변화를주며시험을실시하였다 측정된데이터를제안된모델에적용하.여본 결과높은 상관성을보여 주었다 따라서수축 균열은 초기수축단계 이차수축단계그리고잔류수축단계의. ,단계로 모사할 수 있었다 또한 각 단계에서의 균열 폭의 범위를 제시하였다3 . .
Abstract
The aim of this study is to present a graphical method in order to evaluate stages in shrinkage cracking. Firstly,the distribution of crack openings is established by sorting the openings of individual cracks in the soil crackingsystem. Secondly, it is normalized in a range of 0 to 1 to obtain the normalized crack opening distribution. Thirdly,three S-shape curve models introduced by Brooks and Corey (1964), Fredlund and Xing (1994) and van Genuchten(1980) are chosen to fit the normalized crack opening distribution using a curve fitting method. The accuracy offitting which is described through fitting parameters by the van Genuchten equation is much higher than that bythe Brooks and Corey equation and slightly higher than that by the Fredlund and Xing equation; thus the vanGenuchten model is used. Finally, the stages of shrinkage cracking are graphically evaluated by drawing three separatestraight lines corresponding to three linear parts of the fitted normalized crack opening distribution. The proposedmethod is tested with different sample thicknesses. The measured data are fitted by the selected model with thefairly high regression coefficient and small root mean square error. The results show graphically that shrinkagecracking comprises three stages; namely, primary, secondary and residual stages. Subsequently, the ranges of evaluatedcrack opening for each of these stages are presented.
Keywords : Curve fitting method, Fitting parameters, Graphical method, Normalized crack opening distribution,
Shrinkage cracking stages, S-shape curve
1 Member, Prof. Dept. of Civil & Environ. Engrg., Univ. of Ulsan., [email protected], Corresponding Author2 Researcher, Dept. of Civil & Environ. Engrg., Univ. of Ulsan
Jour. of the KGS, Vol. 24, No. 9. September 2008, pp. 41 48~ Technical Note
42 Jour. of the KGS, Vol. 24, No. 9, September 2008
1. Introduction
Soil cracking has been the subject of investigation formany years since it is a natural phenomenon andfrequently observed in many natural and man-madestructures such as buildings, dams, etc. Analysis methodsfor soil cracking during drying have been introduced anddeveloped based on (i) elasticity theory, (ii) transitionbetween tensile and shear failure, and (iii) linear elasticfracture mechanics (Morris et al., 1993). A numerical andphenomenological study has been based on the linearhygro-elasticity (Hu et al., 2006). Several theoreticalproblems and challenges have been summarized andintroduced by Fredlund (2006). Subsequently, manyresearchers have attempted to study the criteria ofshrinkage cracking (Horgan and Young, 2000; Kodikaraet al., 2000; Konrad and Ayad, 1997; Lecocq andVandewalle, 2003; Mal et al., 2005; Min and Vo-Dai,2007; Peng et al., 2006; Tay et al., 2001; Velde, 1999;Velde, 2001; Vogel et al., 2005; Wijeyesekera andPapadopoulou, 2001; Yesiller et al., 2000). As waterevaporates from the soil surface, the tensile stressdevelops in the soil system. The soil tends to crack whenthe tensile stress exceeds the tensile strength. Theyreported that cracking of clay generally depends onexperiment conditions such as base material, soil density,the desiccation rate, and thickness of the sample.Conditions that govern the characteristics of soil crackingmay be categorized as two separate terms: extrinsic andintrinsic conditions (Wijeyesekera and Papadopoulou,2001). Extrinsic conditions include fundamentally thetemperature, relative humidity, and wind velocity whereasmoisture condition, structure of material, degree ofpacking, physical and chemical composition, etc. belongto intrinsic conditions.
Furthermore, soil cracking also influenced soil structure
and behavior (Kodikara et al., 1999); volumetric shrinkage
strain, compaction water content and hydraulic con-
ductivity (Albrecht and Benson, 2001); and water infiltration
(Liu et al., 2004). The results showed that cracking led
to a considerable increase of hydraulic conductivity.
However, the development of soil cracking has been
known as a complex process consisting of several stages.
Thus it is important to understand the behavior of soil
in the cracking process characterized by how many stages
it includes. There are many different ways to describe
evaluation of stages in soil cracking. In this study, we
propose a graphical method to evaluate the stages of
shrinkage cracking for Kaolinite clay using a S-shape
curve equation based on the normalized distribution of
crack opening. The proposed method is examined with
several sample thicknesses. The results obtained by the
proposed method provide the ranges of crack opening
values for each of stages in the shrinkage cracking
process.
2. Fundamentals of Shrinkage Cracking
Evaporation appears from the soil surface. Con-sequently, the mass of the soil for motion will bedecreased by a loss of water as drying continues. Theevaporation rate is affected by conditions such astemperature, relative humidity, and wind velocity and soon. The flux of soil water upward to the soil surface ismainly controlled by the hydraulic properties of the soilsuch as unsaturated hydraulic conductivity, water potentialgradient, and thermal gradient in soil. The evaporationrate computed from the water loss is determined by boththe external conditions and the internal properties of thesoil system.
Shrinkage cracking is one of the most common typesof cracking found in the earth structures. As water is lostfrom the soil surface, tensile forces are established in thedrying surface layer and soil also loses its ability to relievethese tensile forces. These stresses are finally relieved bythe occurrence of cracks that grow up at the surface ofthe soil. As the drying process develops continuously,cracks are formed successively. An individual crackpropagates until it contacts with the other cracks or theborders of the container. Consequently, a network ofcracks is established.
3. Graphical Method
3.1 Establishment of Crack Opening Distribution
In a network of cracks, for simplicity, a crack is defined
A Graphical Method for Evaluation of Stages in Shrinkage Cracking Using S-shape Curve Model 43
by a set of pixels limited by two ends (diamond symbols)
as illustrated in Fig. 1 for a sample thickness of 0.01 m
as an example. The openings of individual cracks are
automatically calculated by applying a program written
in Matlab.
Due to the occurrence of cracks, the shrinkage potential
in the soil system will be reduced. Consequently, we
assume that this leads to a decrease of crack opening with
an increase of drying time. That means the later crack
will give smaller opening than the previous one. The
assumptions are appropriately verified with the results of
crack opening reported by Lecocq and Vandewalle (2003)
and Mal et al. (2005). Therefore, the values of crack
openings (presented in Fig. 1) are sorted as shown in Fig.
2 by a dot line. In this figure, the abscissa is crack opening
and the ordinate is number of crack.
3.2 Normalization of Crack Opening Distribution
Recently, S-shape curve models have been used widely
to describe the relationships between soil parameters such
as soil suction and volumetric water content, degree of
saturation and hydraulic conductivity (Jian and Jian-lin,
2005; Kamiya et al., 2006; Sharma et al., 2002; Sharma
and Mohamed, 2003; Sillers and Fredlund, 2002;
Sriboonlue et al., 2006; Zhang and Chen, 2005). Each
models is characterized by its parameters determined by
experiment.
The crack opening distribution is normalized in a range
of 0 to 1 as shown in Fig. 3 by dot line. The equations
for normalizing are given as follows:
minmax
min
minmax
min
WWWWW
NNNN
N
normalized
normalized
−−
=
−−
=
(1)
where and are minimum and maximum crack
openings corresponding to the minimum and maximum
number of crack and , respectively. is the
measured opening corresponding to the number of crack, .
3.3 Comparison of Three S-shape Curve Models
Based on the normalized distribution of crack opening
given in Fig. 3, three S-shape curve models are used and
compared to select the best model to fit the measured
data. They are given as follows:Fig. 1. Illustration of the individual cracks limited by two diamond‐
ends in case of 0.01 m in thickness as an example
0
30
60
90
120
0.0 0.5 1.0 1.5 2.0 2.5 3.0Cr ack opening [mm ]
Num
ber o
f cra
ck
Fig. 2. The distribution of crack opening for individual cracks
presented in Figure 1
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.2 0.4 0.6 0.8 1.0(W-Wmin) /(Wmax-Wmi n)
(N-N
min)/(
N max
-Nm
in)
Fig. 3. The normalized distribution of crack opening obtained from
Figure 2
44 Jour. of the KGS, Vol. 24, No. 9, September 2008
Brooks and Corey (1964) y = a - bxm (2)
Fredlund and Xing (1994)mn
axe
y
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛⎟⎟⎠
⎞⎜⎜⎝
⎛⎟⎠⎞
⎜⎝⎛+
=
ln
1
(3)
van Genuchten (1980) ( )( )mnaxy
+=
1
1(4)
where a, b, n, and m are fitting parameters determined
through the curve fitting method.
These models are used to fit the measured data by using
the curve fitting method. The results are illustrated in Fig.
4. The normalized experiment data are denoted by dot
points (by the dash dot line for the Brooks and Corey
model, the dash line for the Fredlund and Xing model,
and the solid line for the van Genuchten model). The
Brooks and Corey model show worse fitting than the
others. The fitting parameters infer that van Genuchten
model is the best one consisting of the lowest values of
the sum of squares due to error (SSE, i.e. 0.0484) and
root mean squared error (RMSE, i.e. 0.0207), and the
highest value of R-square (i.e. 0.9950). They are summarized
in Table 1. Therefore, van Genuchten model is selected
for fitting the experiment data in this study.
3.4 Evaluation of Shrinkage Cracking Stages
According to the S-shape normalized distribution of
crack opening fitted by the van Genuchten model in Fig.
4 (solid line), we propose a graphical method for
estimating the stages in shrinkage cracking. The method
is presented in Fig. 5. Three regions from the S-shape
curve (solid line) are outlined separately by drawing three
straight components (dot lines). The first component is
determined by drawing a line tangent to the top curve
through the maximum value on the ordinate; the second
one is constituted by drawing a line tangent to the curve
through the point of maximum slope; and the third one
is a line tangent to the bottom part of the S-shape curve
through the minimum value on the ordinate. The first and
third straight components intersect the second one at two
separate points. These two transition points evaluate the
stages of cracking process described by the S-shape
equation. Three shrinkage cracking stages are illustrated
in Fig. 5. They are outlined by dash dot lines: namely,
primary, secondary and residual stages.
From these stages of shrinkage cracking, the corres-
ponding ranges of crack opening can be estimated by
projecting two transition points to the abscissa drawn by
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.2 0.4 0.6 0.8 1.0(W-Wmi n)/(Wmax-Wmin)
(N-N
min
)/(N m
ax-N
min
)
Normalized data
Brooks and Corey
Fredlund and Xing
Van Genuchten
Fig. 4. The normalized distribution of crack opening (dot points)
fitted by three S shape curve models of Brooks and Corey‐(dash dot), Fredlund and Xing (dash line), and van
Genuchten (solid line)
Table 1. Fitting parameters for three S shape curve models‐Fitting Model
parameterBrooks
and Corey
Fredlund
and Xing
van
Genuchten
SSE 0.4307 0.0543 0.0484
R square‐ 0.9554 0.9944 0.9950
RMSE 0.0617 0.0219 0.0207
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.2 0.4 0.6 0.8 1.0(W-Wmin)/(Wmax-Wmin)
(N-N
min
)/(N
max
-Nm
in)
Secondarystage
Residualstage
Primarystage
Fig. 5. Graphical method for evaluation of shrinkage cracking stages
by drawing three straight components corresponding to
three linear parts of the normalized crack opening
distribution fitted by van Genuchten equation
A Graphical Method for Evaluation of Stages in Shrinkage Cracking Using S-shape Curve Model 45
the arrows as shown in Fig. 5.
4. Soil Material Properties
For the laboratory measurements, Kaolinite clay is
used. The properties of Kaolinite are as follows: liquid
limit, LL = 42.07%; plastic limit, PL = 25.40%; plasticity
index, PI = 16.67%; specific gravity, Gs = 2.646; coefficient
of uniformity, Cu = 40.75; and coefficient of curvature, Cc= 2.33.
The experiments were performed in a rectangular steel
tray. Firstly, the soil was carefully mixed with water and
stirred for half an hour to make a paste. An initial water
content of the mixture was about 65%, 1.5 times higher
than the liquid limit. Secondly, the mixture was poured
in the tray and uniformly spread to make the surface flat.
We vary the thickness of sample with 0.005, 0.006, 0.007,
0.008, 0.009, 0.01, 0.015 and 0.02 m. Finally, the
specimen was balanced and allowed to dry naturally in
laboratory at room conditions. The drying process
continued for several days. When cracking processing
finished completely, images of the specimens were
captured by a digital camera. Image analysis with an
application of the control point selection technique is used
to analyze the images. The proper region of image is
selected to compute the opening of cracks by using a
numerical program written in Matlab.
5. Experimental Results
5.1 Shrinkage Cracking Stages Evaluated by the
Graphical Method
Fig. 6 presents the images of eight sample thicknessestested. Applying the proposed method for these images
resulted in the crack opening distributions as shown inFig. 7. The experiment data are plotted by dot lines; thenormalized values are denoted by dash dot lines; and
continuous lines present the fitted values correspondingto the normalized ones. The resulted fitting parametersare summarized in Table 2.
As seen in Table 2, for all the cases of sample thickness,the regression coefficients are extremely high, more than0.99; except in the case of 0.02 m (only 0.9724).
Correspondingly, the values of RMSE are really small,that is, less than 5% including the case of 0.02 m thicksample. This concludes that the proposed model is properly
adopted for describing the distribution of crack opening.As shown in Fig. 7, the distributions of measured crack
opening represent proximately S-shape curves with the
fairly high regression coefficients as well as low RMSEsshown in Table 2. By applying the graphical methodpresented in this paper to each of the crack opening
distributions, the ranges of shrinkage cracking stages -namely primary, secondary and residual - are tabulatedin Table 3 for both the normalized and real ranges of
crack opening.
0.5 0.6 0.7 0.8
2.01.51.00.9
Fig. 6. Images of soil cracking with different sample thicknesses (cm)
46 Jour. of the KGS, Vol. 24, No. 9, September 2008
5.2 Additional Considerations
As reported by Kodikara et al. (2000), the measure-
ments of soil cracking depend on the sample thickness.
An observation of images with different sample thicknesses
as shown in Fig. 6 indicates that the number of cracks
and that of crack opening are dependent on the sample
thickness. In detail, the variations of crack opening with
0
100
200
300
400
0.0 0.5 1.0 1 .5 2 .0C rack o pen ing [m m ]
Num
ber o
f cra
ck
0.0
0 .2
0 .4
0 .6
0 .8
1 .00.0 0 .2 0.4 0 .6 0.8 1 .0
(W- Wmi n)/(W max -Wm in)
(N-N
min)/(
N max
-Nm
in)
D = 0.5 cm
0
100
200
300
0.0 0.5 1.0 1.5 2.0C rack o pen ing [m m ]
Num
ber o
f cra
ck
0.0
0.2
0.4
0.6
0.8
1.00.0 0.2 0.4 0.6 0.8 1.0
(W- Wmi n)/(W ma x-W min)
(N-N
min)/(
N max
-Nm
in)
D = 0.6 cm
0
50
100
150
200
250
0.0 0 .5 1.0 1.5 2.0 2.5C rack o pen ing [m m ]
Num
ber o
f cra
ck
0 .0
0 .2
0 .4
0 .6
0 .8
1 .00.0 0 .2 0.4 0.6 0.8 1.0
(W- Wmi n)/(W ma x-W min)
(N-N
min)/(
N max
-Nm
in)
D = 0.7 cm
0
50
100
150
200
0.0 0.5 1.0 1.5 2 .0 2 .5 3.0C rack o pen ing [m m ]
Num
ber o
f cra
ck0 .0
0 .2
0 .4
0 .6
0 .8
1 .00.0 0 .2 0.4 0 .6 0.8 1.0
(W- Wm in)/(W ma x-W min)
(N-N
min)/(
N ma
x-Nm
in)
D = 0.8 cm
0
50
100
150
200
0.0 0.5 1.0 1 .5 2 .0 2 .5 3.0C rack o pen ing [m m ]
Num
ber o
f cra
ck
0.0
0 .2
0 .4
0 .6
0 .8
1 .00.0 0 .2 0.4 0.6 0.8 1.0
(W- Wm in)/(W ma x-W min)
(N-N
min)/(
N ma
x-Nm
in)
D = 0.9 cm
0
30
60
90
120
0.0 0.5 1.0 1 .5 2 .0 2.5 3.0C rack o pen ing [m m ]
Num
ber o
f cra
ck
0.0
0.2
0.4
0.6
0.8
1.00.0 0 .2 0.4 0.6 0.8 1.0
(W- Wm in)/( Wma x-W min)
(N-N
min)/(
N ma
x-Nm
in)
D = 1.0 cm
0
20
40
60
80
0 .0 1.0 2.0 3 .0 4.0C rack o pen ing [m m ]
Num
ber o
f cra
ck
0.0
0.2
0.4
0.6
0.8
1.00 .0 0.2 0.4 0 .6 0.8 1.0
(W- Wmi n)/(W max -Wm in)
(N-N
min)/(
N ma
x-Nm
in)
D = 1 .5 cm
0
10
20
30
40
50
0 .0 1.0 2.0 3 .0 4.0 5.0C rack o pen ing [m m ]
Num
ber o
f cra
ck
0.0
0.2
0.4
0.6
0.8
1.00 .0 0.2 0.4 0 .6 0.8 1.0
(W- Wmi n)/(W ma x-W min)
(N-N
min)/(
N max
-Nm
in)
D = 2 .0 cm
Fig. 7. Crack opening distributions for several different sample thicknesses: the dot lines are experiment data, the dash dot lines are
normalized values, and the continuous lines are the evaluated values using the van Genuchten S shape equation based on the‐normalized values
A Graphical Method for Evaluation of Stages in Shrinkage Cracking Using S-shape Curve Model 47
sample thickness for the cases of maximum and minimum
crack openings are shown in Fig. 8.
In case of the maximum, crack opening varies increasingly
with an increase of sample thickness. That is because of
higher shrinkage potential of larger thickness sample. This
variation of crack opening can be described proximately
by power law as presented in Fig. 8 with solid line.
It is verified that as cracks appear, the shrinkage
potential of the soil system decreases. Hence, the opening
of the generated cracks is smaller than that of the previous
cracks. Particularly, the minimum crack openings in the
cases of sample thickness appear to be the same as shown
in Fig. 8. It can be explained that the minimum values
of crack openings are obtained as the shrinkage potential
of the soil system reaches to zero. Therefore, the minimum
crack openings appeared to be independent of the sample
thickness. Consequently, the minimum crack openings
become much smaller than the maximum crack openings
as the sample thickness increases as given in Fig. 8.
Similarly, it is expected that there is a fitted relationship
between the number of crack and sample thickness as
thickness increases. The result is given in Fig. 9 by power
law with the fairly high regression coefficient, more than
0.99. However, the number of cracks decreases drastically
from 0.005 to 0.01 m in thickness but it decreases slowly
from 0.01 to 0.01 m in thickness. This implies that with
enough relative thin samples, the number of cracks
decreases considerably compared with the relative thicker
samples.
Table 2. Fitting parameters in the cases of sample thickness
Fitting Thickness (cm)
parameter 0.5 0.6 0.7 0.8 0.9 1.0 1.5 2.0
a 0.7071 2.03 1.059 0.0646 0.0729 0.2224 0.1399 0.054
m 15.63 2.12 5.726 545.7 338.5 402.1 310.1 861.9
n 2.195 2.188 2.093 1.67 1.679 2.803 2.214 1.944
R square‐ 0.9951 0.9949 0.9975 0.9966 0.9963 0.9950 0.9955 0.9724
RMSE 0.0203 0.0207 0.0144 0.0171 0.0177 0.0207 0.0198 0.0494
Table 3. Ranges of crack opening for shrinkage cracking stages in the cases of sample thickness (cm)
Cracking stageThickness (cm)
0.5 0.6 0.7 0.8 0.9 1.0 1.5 2.0
PrimaryNormalized 0.58~1.00 0.52~1.00 0.58~1.00 0.50~1.00 0.61~1.00 0.68~1.00 0.67~1.00 0.70~1.00
Crack opening [mm] 1.15~1.63 1.14~1.78 1.55~2.36 1.60~2.62 1.85~2.75 2.15~2.94 2.61~3.64 3.32~4.49
SecondaryNormalized 0.10~0.58 0.08~0.52 0.11~0.58 0.08~0.50 0.07~0.61 0.23~0.68 0.18~0.67 0.16~0.70
Crack opening [mm] 0.59~1.15 0.56~1.14 0.65~1.55 0.74~1.60 0.60~1.85 1.04~2.15 1.08~2.61 1.21~3.32
ResidualNormalized 0.00~0.10 0.00~0.08 0.00~0.11 0.00~0.08 0.00~0.07 0.00~0.23 0.00~0.18 0.00~0.16
Crack opening [mm] 0.47~0.59 0.46~0.56 0.44~0.65 0.58~0.74 0.43~0.60 0.48~1.04 0.52~1.08 0.58~1.21
0.0
1.0
2.0
3.0
4.0
5.0
0 5 10 15 20 25Thickness [mm]
Cra
ck o
peni
ng [m
m]
Max
M in
Fig. 8. The variations of crack opening with sample thickness in
the cases of max and min values
R2 = 0 .9919
0
100
200
300
400
0 5 10 15 20 25Thickness [mm]
Tota
l num
ber o
f cra
ck
Fig. 9. The variation of total number of crack with sample thickness
48 Jour. of the KGS, Vol. 24, No. 9, September 2008
6. Summary
A graphical method for evaluation of shrinkage
cracking stages based on the normalized crack opening
distribution represented as S-shape curve is presented. The
experimental data tested with different sample thicknesses
are fitted by van Genuchten model, which shows good
correlation with the fairly high regression coefficient and
low RMSE. Three stages in shrinkage cracking - primary,
secondary and residual stages - are evaluated graphically
by drawing three separately straight lines corresponding
to three linear parts of the fitted normalized crack opening
distribution. Consequently, the corresponding ranges of
crack opening for each of stages are represented for the
studied soil.
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(received on Jan. 8, 2008, accepted on Aug. 13, 2008)