Unanswered Questions in Unsaturated Soil Mechanics-2013

SCIENCE CHINA Technological Sciences

© Science China Press and Springer-Verlag Berlin Heidelberg 2013 tech.scichina.com www.springerlink.com

*Corresponding author (email: [email protected])

• RESEARCH PAPER • May 2013 Vol.56 No.5: 1257–1272

doi: 10.1007/s11431-013-5202-9

Unanswered questions in unsaturated soil mechanics

SHENG DaiChao1, 2, ZHANG Sheng1* & YU ZhiWu1

1 School of Civil Engineering, Central South University, Changsha 410075, China; 2 The University of Newcastle, NSW 2308, Australia

Received January 5, 2013; accepted February 22, 2013; published online April 4, 2013

The last two to three decades have seen significant advances in the mechanics of unsaturated soils. It is now widely recog- nized that the fundamental principles in soil mechanics must cover both saturated and unsaturated soils. Nevertheless, there is still a great deal of uncertainties in the geotechnical community about how soil mechanics principles well-established for satu-rated soils can be extended to unsaturated soils. There is even wide skepticism about the necessity of such extension in engi-neering practice. This paper discusses some common pitfalls related to the fundamental principles that govern the volume change, shear strength and hydromechanical behaviour of unsaturated soils. It also attempts to address the issue of engineering relevance of unsaturated soil mechanics.

unsaturated soils, constitutive modeling, volume change, shear strength, engineering applications

Citation: Sheng D C, Zang S, Yu Z W. Unanswered questions in unsaturated soil mechanics. Sci China Tech Sci, 2013, 56: 12571272, doi: 10.1007/s11431-013- 5202-9

1 Introduction

Research on unsaturated soil behaviour probably dates back to 1920s [1], but it was not until 1950s that significant re-search effort has been devoted to the geotechnical aspects of unsaturated soils [2–9]. Some early Chinese contributions towards understanding unsaturated soil behaviour include, for example, the classification of liquid and gas status in unsaturated soils by Yu & Chen [10], and the stress-strain- strength behaviour of unsaturated soils by Lu et al. [11], Chen et al. [12, 13], Shen [14] and Li et al. [15]. Some early Japanese contributions include the theoretical work of Karube et al. [16] and Kohgo et al. [17, 18]. The subject of unsaturated soil mechanics has particularly flourished since 1990s, much attributed to the inspirational work of Alonso et al. [19] and Fredlund et al. [20]. Indeed, the most signifi-cant developments in theoretical soil mechanics during the

last three decades or so have probably occurred in the area of unsaturated soil mechanics. Today the subject is still one of the most active and prolific research areas in soil me-chanics and geotechnical engineering.

Even though the last two to three decades have seen sig-nificant advances in unsaturated soil mechanics, there is still a great deal of uncertainties in the geotechnical community about how well-established soil mechanics principles for saturated soils can be extended to unsaturated soils. There is even wide reservation about the necessity of such extension in engineering practice. In particular, some basic questions are often raised on the fundamental principles that govern the hydromechanical behaviour of unsaturated soils and on the engineering relevance:

(1) Reconstituted soil versus compacted soil. What are the main differences in the hydromechanical behaviour of these soils? What are the implications of different pore size distributions (PSD), in constitutive modelling of unsaturated soils? Can a reconstituted soil become collapsible?

(2) Relationship between volume change, yield stress and

1258 Sheng D C, et al. Sci China Tech Sci May (2013) Vol.56 No.5

shear strength. Can the constitutive equations for volume change, yield stress and shear strength be defined separa- tely? Does the loading-collapse yield surface have to recov-er the apparent tensile strength surface? Do we need the suction-increase surface to capture possible plastic volume change when a soil is dried to a historically high suction? What are the implications of stress state variables in defin-ing volume change and shear strength equations?

(3) Implications of using a Bishop effective stress. Can we use a Bishop-type effective stress in modelling unsatu-rated soil behaviour and what are the implications?

(4) Engineering relevance. What is the relevance of the unsaturated soil mechanics in engineering practice? Is a design based on the saturated soil mechanics always con-servative? Considering the difficulty and uncertainty in measuring or monitoring in-situ suctions, the applicability of the unsaturated soil mechanics to engineering practice has also been questioned.

These questions represent some of the most fundamental issues in unsaturated soil mechanics. There are currently no unified answers to these questions. This paper only repre-sents the authors’ own understanding of these issues. It is our intention that the paper can serve as a springboard lead-ing to more in-depth discussion and perhaps more insightful understanding of the fundamental issues of unsaturated soil mechanics.

2 Natural, reconstituted versus compacted soils

Soil is a porous material. The pores in a soil can be filled with different fluids. The term of unsaturated soil refers to the state where the pores are filled partly with liquid water and partly with air. A soil can become unsaturated with wa-ter in different ways. In field, soils above the ground water table are naturally unsaturated. Engineered soils such as those compacted fills used in road and railway embank-ments are usually unsaturated. In laboratory, three types of unsaturated soil samples are commonly used: (1) samples statically or dynamically compacted from dry soil powders mixed at specified water contents, (2) samples reconstituted from slurry (at moisture contents in excess of the liquid lim-it) and then dried to unsaturated states, and (3) undisturbed samples that are naturally unsaturated. The first type of samples (compacted soils) is far more common than the second and third types of samples (reconstituted soils and natural soils). One reason for this is that it is much easier to desaturate a compacted sample than reconstituted sample. The second type sample is commonly used for saturated soil testing in laboratory, but not so common for unsaturated soil testing. Undisturbed samples are difficult to obtain and ex-tremely difficult to duplicate. Because laboratory experi-ments often require a fair amount of repeated tests on the same sample, the use of undisturbed samples is very limited. As a consequence, principles of unsaturated soil mechanics

and constitutive models for unsaturated soils are almost exclusively based on experimental data for compacted soils [21]. The key question is then: Can we extend these princi-ples or models to other types of unsaturated soils? The an-swer to this question also affects the applicability of un-saturated soil mechanics to engineering practice. After all, we want to apply our unsaturated soil mechanics to various unsaturated soils, not just compacted soils. As pointed out by Gens et al. [22] and Sheng [21], all soils can be unsatu-rated with water and partial saturation is only the state of soil, not a new soil.

To answer the question, we need to understand the main differences between the different types of soil samples. The most important difference is perhaps the microstructural differences. Compacted soil samples can be prepared dry of optimum or wet of optimum. Reconstituted samples can be air-dried, heat-dried, freeze-dried or osmotically-dried. Dif-ferent sample preparation methods usually result in different soil microstructures. For example, soils compacted dry of optimum tend to have a double-porosity microstructure, meaning that the pore size distribution curve exhibits two or more peaks (Figure 1(b)). In these soils, there usually exist

Figure 1 Pore size characteristics of decomposed granitic soil compacted (after Li & Zhang [23]). (a) SEM of decomposed granitic soil compacted dry of optimum; (b) pore size distribution of decomposed granitic soil.

Sheng D C, et al. Sci China Tech Sci May (2013) Vol.56 No.5 1259

two types of pores: large inter-aggregates pores which are collapsible upon wetting and small intra-aggregates pore which are more stable (Figure 1(a)). Some naturally un-saturated soils such as loess and tropical residual soils can also have a double-porosity microstructure, as shown in Figure 2(a) for a gneiss residual soil [24]. On the other hand, soils air-dried from slurry usually exhibit a unimodal pore size distribution, at least at low stresses (Figure 2(b)).

Unsaturated soils with a bimodal pore size distribution are usually collapsible at certain stress ranges. Wetting of such a soil can collapse the inter-aggregates pores and result in a unimodal pore size distribution when the soil becomes saturated, as shown in Figure 1(b). In an elastoplastic con-stitutive model such as the Barcelona Basic Model (BBM) developed by Alonso et al. [19], a collapsible soil is typi-cally characterised by a loading-collapse (LC) yield surface where the yield stress increases with increasing suction. Suction refers to the matric suction, which is the difference between pore air pressure and pore water pressure. The LC

Figure 2 Pore size characteristics of (a) natural residual soil and (b) reconstituted soil. (a) Pore size distribution of a natural residual soil (Futai & Almeida [24]); (b) pore size distribution of a soil reconstituted from slurry (Tarantino [25]).

yield surface in BBM evolves with stress and/or suction changes. As shown in Figure 3, the compacted soil at point A is unsaturated (provided that suction is greater than the air entry suction) and has a bimodal pore size distribution. At point B the soil is saturated and can have a unimodal pore size distribution. Experimental data seem to support such an evolution of pore structure (Figure 1(b)). The wetting path A B causes the LC yield surface to evolve from LCA to LCB, as the interaggregate pores collapse and the soil vol-ume decreases. However, drying the unimodal soil at point B to point A and then compressing it to point C, i.e. stress path B A C , should regenerate the bimodal pore size distribution, because the soil at point C is collapsible again according to BBM [19]. Some experimental data also sup-port such a development of soil collapsibility [26]. In other words, the pore size distribution can evolve with stress and hydraulic paths or stress and suction history. Most constitu-tive models in the literature are based on data for compacted soils and hence predict an evolution of the LC yield surface as shown in Figure 3.

The question is: does this kind of yield surface evolution apply to reconstituted soils as well? A soil air-dried from slurry is characterised by a yield surface where the yield stress decreases with increasing suction (Point A in Figure 4). Since such a soil usually has a unimodal pore size dis-

Figure 3 Evolution of pore size distribution and LC yield surface (s: difference between air pressure and water pressure, p : net mean stress =

difference between total mean stress and air pressure).

Figure 4 Evolution of the yield surface for a reconstituted soil according to the SFG model [27].


tribution, wetting it under constant stress usually does not cause volume collapse. However, can such a soil become collapsible if it is compressed to high stresses? According to the SFG model [27], the yield surface for an air-dried soil can evolve into a LC yield surface if the soil is compressed to sufficiently high stresses (Figure 4), which means that compressing a unimodal reconstituted soil at unsaturated states can generate a ‘collapsible’ soil (stress path A C ). Is there experimental evidence for such an evolution? Un-fortunately there is very few data on reconstituted soils in the literature. Nevertheless, the classic reference by Jen-nings and Burland [6] seems to support such an evolution. Figure 5 is a re-plot from Jennings and Burland [6] for an air-dry silt. It is clear that the air-dry soil can become ‘col-lapsible’ if it is compressed to sufficiently high stresses. This collapsibility is purely due to the degradation of soil stiffness during wetting. In other words, the volume de-crease along stress path BAC is smaller than the volume decrease along path BD, because the saturated soil (BD) is more compressible than the unsaturated soil (AC). There-fore, wetting the soil from C to D will cause volume de-crease, or the so-called wetting-collapse. However, this col-lapse is not necessarily related to the microstructural change of the soil, rather to the overall stiffness change of the soil at different suction levels. Another set of data reported by Cunningham et al. [28] for a reconstituted silty clay also seems to suggest that compressing a soil at sufficiently high

suction can make the soil ‘collapsible’ (Figure 6). There- fore, the available data in the literature seem to support the evolution of the LC yield surface as suggested by the SFG model (Figure 4). However, experimental data on reconsti-tuted soils are generally too few to be conclusive on this specific characteristic.

In summary, the microstructure and particularly the pore size distribution of a soil are usually reflected in the yield surface and volume change behaviour of the constitutive model for the soil. As recently pointed out by Tarantino [25], the boundary between compacted and reconstituted soils is not always clear and the microstructure of a soil can change with stress and hydraulic paths. A bimodal pore size distribution can evolve to a unimodal pore size distribution under appropriate stress and hydraulic paths, and vice versa. Some existing constitutive models for unsaturated soils can potentially be applied to different types of unsaturated soils, at least as a first-order approximation.

3 Relationship between volume change, yield stress and shear strength

Two classical issues in geotechnical engineering are settle-ment and stability, respectively related to volume change and shear strength behaviour of geomaterials. Therefore, volume change and shear strength criteria represent the most

Figure 5 Oedometer curves for air-dry silt soaked at various constant applied pressures (after Jennings & Burland [6]).


Figure 6 Isotropic compression curves for a reconstituted silty clay at various suctions ([28]). Sat, saturation; comp, compression; iso, isotropic.

fundamental principles in soil mechanics. For saturated soils, these criteria are usually described in terms of effective stress. For unsaturated soils they are also functions of suc-tion and/or degree of saturation. Indeed, two fundamental issues in unsaturated soil mechanics are the volume change and shear strength behaviour associated with suction or wa-ter content changes. For fine-grained soils like clay and silt and for soft rocks like claystone and mudstone, increasing the degree of saturation can cause significant strength loss and volume change, and these changes of strength and volume are essentially responsible for the engineering problems such as rainfall induced landslides, foundation failures due to wetting-induced strength loss or excessive deformation, sinkholes caused by water infiltration or seep-age, settlement or instability of compacted fill embankments, etc.

One key feature in unsaturated soil behavior is that the volume change criterion is closely related to the yield stress-suction and shear strength-suction relationships [19, 29‒32]. The so-called LC yield surface which defines the yield stress-suction relationship is derived from the volume change equation, as done in the BBM [19] and in the SFG model [28]. The shear strength-suction relationship can also be derived from the volume change equation, as shown in ref. [30]. However, these relationships are often overlooked in the literature, leading to inconsistent constitutive equa-tions.

The volume change equation usually defines the volume change caused by a stress or suction change, and is used to derive the LC surface. The shear strength equation of an unsaturated soil is expressed through the apparent tensile strength function and the friction angle of the soil. The ap-parent tensile strength is usually a function of suction and this function can be derived from the volume change equa-tion. The apparent tensile strength surface in the stress-suction space also represents the zero shear surface, as the soil

has no shear strength when suction and stress change along this surface. For saturated soils where the effective stress principle holds, this surface follows the 135o line in the net mean stress – suction space, and the 90o (vertical) line in the effective mean stress – suction space. For unsaturated soils, an increment in suction does not usually have the same ef-fect on the soil shear strength as an equal increment in the mean stress, and hence the zero shear strength will drift away from 135o or 90o line. In fact, the existing effective stress definitions for unsaturated soils in the literature are essentially the definitions of this zero shear strength surface. The discussion below will show that the zero shear strength surface is also the initial yield surface of a soil that has a zero preconsolidation stress and that the LC yield surface must recover this zero shear strength surface if the precon-solidation stress is set to zero.

The relationship between the shear strength and the LC yield surface has often been overlooked in some existing models for unsaturated soils. In the BBM [19] and early models based on the BBM, the volume change equation has a singularity when the suction becomes zero. As a conse-quence, the LC yield surface becomes undefined when the preconsolidation stress at zero suction is zero, and hence the apparent tensile strength surface cannot be derived from the volume change equation. Therefore, a separate apparent tensile strength surface was introduced in the BBM. How- ever, it should be noted that this is solely due to the singu-larity in the BBM volume change equation. In later models based on the Bishop effective stress and in the SFG model, the volume change equation is continuously defined through saturated and unsaturated regions. As such, the apparent tensile strength surface is automatically recovered from the LC yield surface by setting the preconsolidation stress ( c0p

or c0p ) to zero at zero suction (Figures 7(a) and 7(b)).

Hence a separate function for the apparent tensile strength surface is not required. In fact, the original suction-increase (SI) yield surface in the BBM, which is a horizontal line in the p s space is used to capture the possible plastic

volume change when a soil is dried to a historically high suction. The SI yield surface is not needed if the volume change equation is properly defined, as shown in Figures 7(a) and 7(b). On the other hand, if the LC yield surface does not recover the apparent tensile strength surface (as shown in Figures 7(c) and 7(d)) when the preconsolidation stress ( c0p or c0p ) is set to zero, the yield stress and shear

strength functions would become non-unique. The LC yield surfaces shown in Figures 7(c) and 7(d) are also in conflict with the definition of yield surface, which are the contours of the hardening parameter in the stress space. Obviously, the hardening parameter (e.g., the plastic volumetric strain) cannot be constant along these LC yield surfaces. The hardening parameter at points B and C should have the ex-actly same value as point A in Figures 7(c) and 7(d), but plastic volumetric strain must occur in order to expand the


Figure 7 Evolution of yield surface for a reconstituted soil. s, Suction; p , net mean stress; p , effective mean stress; pc0, preconsolidation stress at zero

suction; ABC, stress path under constant net mean stress; CD, stress path under constant suction.

yield surface from B to C. Therefore, the LC yield surface must recover the apparent tensile strength surface when the preconsolidation stress at zero suction is set to zero, irre-spective of the stress space used.

It is sometimes observed that the shear strength of an unsaturated soil exhibits a peak value at an intermediate suction level (Figure 8(a)). Such a peak shear strength has implications in the volume change equation and in the yield surface as well. To capture peak shear strength, the equation that defines the volume change caused by suction changes should predict a minimum value at the intermediate suction (Figure 8(b)). As a consequence, the apparent tensile strength should also change (Figure 8(c)) accordingly.

The shear strength of an unsaturated soil is often consid-ered to be sufficiently defined by a single effective stress [33, 34]). However, this is only true when the friction angle of the soil does not change with suction. In this case, the two-stress-variable equation proposed by Fredlund et al. [35] is equivalent to the single-stress-variable equation based on an effective stress:

bn

b

n n

tan tan

tan tan tan ,tan

c s

c s c

(1)

where is the shear strength, c is the effective cohesion for saturated states, n and n are respectively the ef-

fective and net normal stress on the failure plane, and

is the friction angle of the soil. In eq. (1), the Bishop effective stress parameter () is set

to btan / tan . It is clear that the variable (s) cannot be

eliminated from eq. (1) if the friction angle of the soil ( )

Figure 8 Implications of peak shear strength at intermediate suctions.


depends on suction, no matter how the effective stress is defined. While there are experimental data supporting that the slope of the critical state line is independent of suction (e.g., refs. [36, 37]), there is perhaps equal amount of data supporting the opposite (e.g., refs. [24, 38, 39]). Therefore, there is no conclusive evidence that the shear strength of an unsaturated soil can be sufficiently defined by a single ef-fective stress.

4 Implications of using a Bishop effective stress

An important issue about constitutive modelling of unsatu-rated soils is the choice of the stress space where the con-stitutive model is built. Early models were usually estab-lished in the net stress and suction space (e.g. Alonso et al. [19]), while the second generation models have mostly used Bishop effective stress and suction (e.g., Wheeler et al. [40]; Sheng [21]; Tamagnini [41]). The more recent SFG model (Sheng et al. [27]) has reverted back to the net stress and suction space.

Net stress and suction are both independent and control-lable variables in laboratory tests. Therefore, it is straight forward to represent laboratory tests using models built in such a space. The definitions of net stress and suction are independent of material states and hence the stress space remains fixed. This is a significant advantage of the inde-pendent stress variables. As pointed out by Morgenstern [42], we normally link equilibrium considerations to defor-mations through constitutive behaviour and should not in-troduce constitutive behaviour into the stress state variables. However, models based on net stress and suction usually have difficulties in (1) handling the transition between satu-rated and unsaturated states, (2) handling the shear strength variation with suction, (3) showing the effects of degree of saturation and the coupling with hydraulic hysteresis. One exception is perhaps the more recent SFG model [27], which seems to have overcome most of the difficulties. These difficulties are indeed the main motivation for the shift to the Bishop effective stress in the second generation models.

The Bishop effective stress is not a controllable variable in laboratory tests. The effective stress definition usually involves material state variables such as the degree of satu-ration or air entry value, and hence the stress space changes as the material state changes. The constitutive behaviour of the material is embedded both in the constitutive equation and the effective stress definition, leading to less explicit physical meaning of the constitutive law. Nevertheless, models built in the Bishop effective stress space have many advantages, for example, the smooth transition between saturated and unsaturated states, coherent relationship be-tween volume change, shear strength and yield surface, easy incorporation of the effects of hydraulic hysteresis and the degree of saturation, a straightforward finite element im-

plementation. The above-mentioned advantages and shortcomings of

the two categories of models are relatively well known in the literature. However, there is one specific issue of using the Bishop effective stress, which is related to the volume change equation and is less known in the literature, as de-scribed below.

A general form of the effective stress can be

r( , ) ,p p s S s (2)

where p is the net mean stress, p is the effective mean

stress, is the Bishop effective stress parameter and treated either as a function of suction or as a function of suction and degree of saturation. Obviously, such a defini-tion of effective stress is very general and covers all the existing definitions we have used in the literature (perhaps not Vlahinić et al. [43]).

With such an effective stress, the volume change equa-tion for normally consolidated soils is usually assumed to take the following form:

( ) ( ) ln ,v N s s p (3)

where v is the specific volume of the soil, is the compres-sion index, and N is the specific volume when ln 0p or

the specific volume for a soil slurry (at the liquid limit). If the effective stress is indeed effective in controlling volume change, the specific volume (v) should remain constant un-der constant p , and hence N and should be independent

of suction. However, this is seldom true in reality. In the literature, N and are usually assumed to be functions of s. We will show below that a varying N can lead to incon-sistency with the yield surface evolution and cannot be recommended.

In all the models that are based on effective stress, the apparent tensile strength surface or the zero shear strength surface is assumed to be the vertical line that goes through zero effective mean stress, i.e.,

0.p (4)

In other words, the soil is assumed to have zero shear strength as long as the effective mean stress remains zero, or the soil has no apparent tensile strength in the effective stress space. This line must also represent the yield surface for a slurry soil that has never been consolidated. For a sat-urated soil that has a zero yield stress, i.e. a slurry, the size of the elastic zone remains zero as long as the effective mean stress remains zero, irrespective of the pore water pressure. When the soil becomes unsaturated, the yield sur-face will continue along the zero shear strength line, if the effective mean stress remains zero. To keep the effective mean stress zero, a tensile net mean stress has to be applied to balance out the suction increase. As a consequence, the size of the elastic zone remains zero, which also reflects the


effective stress principle. Furthermore, if the yield surface does not collapse to the zero shear strength line when

c0p =0 (the dashed LC curve in Figure 9(a)), there would be

plastic deformation for loading along the yield surface, and the shear strength as well as the yield stress would become non-uniquely defined.

Therefore, drying a slurry soil under zero effective mean stress is a neutral loading process, meaning that the stress point is always on the yield surface (path AB in Figure 9(a)). The elastic zone does not expand, which is different from the case of drying a slurry soil under zero net mean stress (Figure 7(b)). Such a loading process is also logical if there exists an effective stress. To keep the effective mean stress zero as the suction is increased, a tensile net mean stress has to be applied. This tensile net mean stress balanc-es out the effect of the suction increment, which is the es-sence of the effective stress principle.

As a consequence, drying a slurry soil under zero effec-tive mean stress implies that the soil is always on the nor-mal compression line (NCL). This is only possible: (1) if N remains constant or decreases with increasing suction (the dashed line in Figure 9(b)), or (2) if N increases with in-creasing s (the dotted line in Figure 9(b)).

Figure 9 Inconsistency of a varying N in the Bishop effective stress approach.

Case (1) would lead to the constraint that must de-crease with increasing suction, which suggests that the col-lapse strain increases with increasing stress level and the soil compressibility decreases with increasing suction. Such behaviour is not always supported by experimental data. Experimental data by, for example, Toll [38], Sharma [44], Sivakumar et al. [45] and Toll et al. [46] all indicate that the soil compressibility can increase with increasing suction (Figure 10). The data by, for example, Vilar et al. [47], Sun et al. [48, 49] and Vilar et al. [50] show that the collapse potential reaches a maximum at intermediate stress levels. Case (2) suggests that the soil volume increases when dry-ing under constant effective mean stress, which is not sup-ported by any experimental data.

A possible strategy to overcome the above limitation of the Bishop effective stress approach is to adopt a volume change equation of the following form:

r( ) ln ,v N S p (5)

where N is a constant, and is a function of degree of satu-ration (Sr).

Because the compression index () is a function of Sr, the normal compression line under a constant suction would not be a straight line unless the suction is zero (Figure 11(a)). Compressing an unsaturated soil under constant suction will generally lead to an increase in degree of saturation. If the compression index () is assumed to vary with degree of saturation according to Figure 11(b), the normal compres-sion line (NCL) for constant suction would take the form of Figure 11(a), which mimics the oedometer curves for a silty sand tested by Jennings and Burland [43].

The implication of using a saturation-dependent com-pression index is that the yield surface will also depend on Sr. In fact, the LC yield surface can be derived from eq. (5):

r

(1)( )

c c0 ,Sp p

(6)

where cp is the yield stress, c0p is the yield stress at

Figure 10 Variation of with degree of saturation (after Toll [38]).


Figure 11 Saturation-dependent compression index ( r( )S ) and its

implications.

saturation (Sr=1), and is the elastic compression index. Because of the non-unique relationship between Sr and s due to hydraulic hysteresis, the yield surface can no longer be plotted in the space of effective mean stress versus suc-tion. Instead, we have to use the degree of saturation as the additional axis of the stress space, and plot the yield surface in the space of effective mean stress versus degree of satu-ration (Figure 11(c)). Because neither the degree of satura-tion nor the effective stress is a controllable variable in la-boratory tests, it will be difficult to represent simple stress paths like constant net mean stress (ABC in Figure 11(c)) or

constant suction (CD in Figure 8(c)) in the rp S space.

Nevertheless, there are a few advantages of this approach: (1) the constraints on the compression index due to the use of the Bishop effect stress are avoided; (2) it is a natural outcome of eq. (5) that the collapsible volume reaches a maximum value at an intermediate stress level (Figure 11(a)); (3) according to such a model, it is possible to com-press an unsaturated soil to full saturation even if the suc-tion is kept constant.

The above approach was initially suggested by Sheng [27] and a complete model has recently been developed by Zhou et al. [51‒54]. The model by Zhou et al. shows very promising features in capturing unsaturated soil behaviour. The challenge of using this approach is that simple stress paths in laboratory tests become very complex and a com-plete mathematical model is always needed to interpret la-boratory tests, in addition to the other implications of the Bishop effective stress mentioned above.

Another issue related to the Bishop effective stress is that a closed loop of net stress and suction changes do not nec-essarily lead to a closed loop of effective stress changes (Figure 12), because of the material state dependency of the Bishop effective stress. For example, the effective mean stress change along path AB is usually different from that along path CD, because the degree of saturation has changed from A to C, even though the net mean stress is kept constant during both paths (Figure 12). Such an un-closed loop means that the model is stress-path dependent, even if the stress changes are inside the elastic zone. In a recent discussion by Zhang et al. [55] and Sheng et al. [30], it was found that models based on net stress were usually stress-path dependent in the elastic zone, but the discussion did not realise that models based on effective stress were also stress-path dependent. A model that exhibits stress-path dependent elastic behaviour is at variance with classical elastoplasticity theory and thermodynamics and should generally be avoided. However, an unsaturated soil model that exhibits stress-path independent elastic behaviour does not currently exist in the literature and is a remaining chal-lenge.

5 Engineering relevance

Whereas the unsaturated soil mechanics has been one of the

Figure 12 A closed loop in the net stress space and its corresponding open loop in the effective stress space.


most active and prolific research areas in soil mechanics during the last three decades or so, its theoretical develop-ment is not without questioning. For example, its engineer-ing relevance has often been questioned. One common per-ception is that, if we design for fully saturated soils using the classic soil mechanics principles, we are on the con-servative side, making the unsaturated soil mechanics re-dundant. Another common argument is that, since suction is difficult to measure and it varies significantly in-situ, it is not practical to apply the unsaturated soil mechanics princi-ples to engineering practice. We will show, through case studies, that such perceptions are not correct and unsaturat-ed soil mechanics is indeed very relevant in engineering practice and can play an essential role in some engineering problems.

5.1 Stability of unsaturated soil and rock slopes

The loss of shear strength due to the increase in degree of saturation in unsaturated soil slopes is one of the most common reasons for landslides, which result in millions of dollars of socioeconomic cost every year. The Thredbo landslide, for example, was a disastrous landslide that oc-curred at the ski resort of Thredbo, New South Wales, Aus-tralia in 1997 and resulted in a total of 18 deaths (Figure 13). The New South Wales Government subsequently spent $40 million in out-of-court settlement with 91 business and individuals. According to the Supreme Court verdict, the landslide was mainly caused by the leakage of main water pipeline which saturated the surrounding soil and in turn dramatically reduced soil shear strength. Another example is the Kwun Lung Lau landslide, which occurred in Hong Kong on 23 July, 1994 and resulted in five fatalities. This landslide was closely related to the saturation and weaken-ing of the soil mass after a heavy rainfall. Interestingly, however, rainfall had largely ceased for about 10 hours be-fore the failure. The ground was made of a rather permeable fill overlying partially weathered volcanic tuff. The forensic investigation concluded that the landslide was most likely to have been caused by the ingress of a large volume of water as a result of leakage from underground services (storm-water pipes and a sewer), bringing about an increase of de-gree of saturation and a reduction of the shear strength of the ground [57, 58]).

Another type of instability problems related to unsatu-rated soils is the slopes excavated in certain rocks such as claystone, mudstone, marl and siltstone. These types of ma-terials behave more like rock when they are dry and intact, but become mud or clay when wet or weathered. Excavation facilitates the formation of fissures and cracks in these ma-terials, and consequently facilitates the infiltration of liquid water or air moisture into them. Figure 14 shows the typical degradation process of claystone in water. Exposure to air moisture (humidity) can also significantly reduce the strength of claystone, as shown in Figure 15. Pineda [60] recent-

ly showed that the strength and stiffness of marls and clay-stones decreased significantly with increasing number of humidity change cycles (Figure 16). Chandler [61] and Berdugo [59] also showed the significant decrease of un-drained shear strength of claystones with water content (Figure 17). This loss of strength and stiffness, combined with the development of tensile cracks caused by excavation and cutting, can cause slope instability and landslide prob-lems (Figure 18). For example, landslides occurred along the F3 freeway between Sydney and Newcastle, due to the wetting of thin claystone layers and deep tensile cracks.

One key question about landslides of unsaturated soil slopes is: how can we incorporate the strength reduction due to saturation increase into the slope stability analysis? Much progress has been made in this respect. For example, Cai and Ugai [62] studied the dependency of the safety factor on the rainfall intensity and duration via a shear strength reduc-tion scheme. Griffiths and Lu [63] adopted an analytical

Figure 13 Thredbo landslide, NSW, Australia, 1997 (image from Geo-science Australia).

Figure 14 Degradation of claystone in water (Pineda et al. [56]). (a) t=0; (b) t=5 h; (c) t=46 h.

Figure 15 Degradation of claystone in moist air (Pineda et al. [56]). (a) t=0; (b) t=150 d.


Figure 16 Shear strength reduction due to cycles of humidity change (after Pineda et al. [56]).

Figure 17 Shear strength reduction of claystones with water content.

Figure 18 Landslide in claystone.

solution of the unsaturated flow problem to estimate the evolution of suction in the slope. The suction distribution was then integrated into elastoplastic finite element program, by defining Bishop’s effective stress, to calculate the slope stability. Huang and Jia [64] and Chen and Liu [65] have also shown how to incorporate the suction-dependent shear strength in stability analysis of unsaturated soil slopes.

The most fundamental elements for analyzing unsaturated soil slopes are (1) the unsaturated shear strength criterion, (2) the water retention function, (3) the permeability func-tion, and (4) the influx boundary condition at the ground surface. The unsaturated soil shear strength is usually writ-ten as a function of suction or a function of degree of satu-ration. There are a number of shear strength equations in the literature and Sheng et al. [21] provided a recent review of these equations and their performance against experimental data. To determine the suction and saturation redistribution inside soil slopes due to rainfall infiltration and evaporation, the water retention function and unsaturated permeability function are pivotally important. As mentioned in Section 5, water retention behaviour (suction and saturation relation) is affected by soil deformation or the soil initial density. In cases where deformation is significant, a coupled hydrome-chanical approach is preferred. The boundary condition at the ground surface is another important factor and its de-termination usually involves, unfortunately, a great deal of uncertainties. Fredlund and Stianson [66] have recently discussed how to use the existing weather station data to determine the influx boundary condition, a very promising step forward.

5.2 Foundations on expansive soils

Attwooll et al. [67] reported a structure damage case owing to heave of expansive soils. The building is a manufacturing facility that was completed in Loveland, Colorado 1993 on clay shale Pierre Formation.

Before construction, the site investigation had indicated that the subsurface materials are of expansive characteristics. Therefore, drilled shaft foundations with a structurally sup-ported basement underlain by a crawl space were adopted


for design. Significant heave (almost 23 cm) occurred at portions of

the building in the first 3 years. Some early remediation me- asures were applied, including replacement of the damaged concrete masonry unit partition walls, cosmetic repairs, re-moving the lawn and ponds, and installation of deep dewat-er ing wells. In spite of these efforts, heave continued pro-gressing across the building. In 2005, heave impacted over three-quarters of the building: maximum heave was about 30.5 cm and over half of the building had raised more than 6 cm.

The damages on the building had been primarily in the form of shear cracking of concrete masonry unit partition walls, drywall distress and racked door frames. In addition, damages also occurred to the drilled shafts caused by lateral displacement of ground as the bedrock had expanded, which was the most significant structural distress. At least 10 drilled shafts with 107 cm diameters had sheared at or near ground line and the relative displacement across the shear cracks was 5 cm or more (see Figure 19).

The main reason for heave leading to structure damage can be attributed to the soil expansion due to soil moisture rising. Moisture profile indicated that soil moisture at heave areas was much higher than non-heave areas, as shown in ref. [67]. Boring I-1 was drilled in the basement where the greatest heave occurred (22.9 cm), and boring I-2 was in the location where the heave was about 5 cm. Compared with non-heave area, the soil moisture raised up to 75% at I-1 and up to 25% at I-2 (see Figure 20).

Forensic investigation indicated that the main reasons leading to the rapid soil moisture raise included: (1) the ex-cavation was backfilled with river sand and gravel, which allowed infiltrating water to flow promptly to the bottom of the building; (2) The perched groundwater flowed to the pond on the west and towards the building to the east via high permeability backfills (sand and gravel).

5.3 Accumulated settlement in high-speed rail em-bankment due to seasonal wetting and drying

Cardoso et al. [68] presented an interesting case where sea-sonal drying and wetting caused undesirable accumulated settlement for a high speed railway embankment. The em-

Figure 19 Cracked drilled shaft (Attwooll et al. [67]).

Figure 20 Soil moisture profiles for heave and non-heave areas (after Attwooll et al. [67]).

bankment cross section is shown in Figure 21(a). The sub-grade soil is a non-plastic silty sand classified as SM ac-cording to the Unified Soil Classification System. The soil is considered to be an appropriate base material if it is properly compacted and drained.

The embankment cross section under seasonal drying and wetting was simulated using the finite element code CODE_ BRIGHT. The BBM (Alonso et al. [19]) was used to repre-sent the behaviour of subgrade soil. The accumulated set-tlement at point A (Figure 21(a)) is shown in Figure 21(b). While the seasonal fluctuations after the first 2 years are minimum, the initial settlement during the first 2 years can be significant, particularly for high-speed trains which are more sensitive to vertical displacements than traditional geotechnical structures.

Jiang and his co-workers [69, 70]) had paid much atten-tion to the calculation of settlement of high-speed rail em-bankments founded on unsaturated subgrades. They used a simplified consolidation theory of unsaturated soils and modified the unsaturated soil permeability according to soil-water characteristic curves. They also considered vari-ous ground improvement methods of the unsaturated sub-grades. Their calculations seem to be reasonably accurate when compared with field measurements.

5.4 Summary of engineering applications

The case studies discussed above only provide some glim-


Figure 21 Accumulated settlement in high speed rail embankment (after Cardoso et al. [68]).

pses of the rich literature on engineering applications of unsaturated soil mechanics (e.g. Alonso et al. [67], Bao [71, 72], Shen [73], Ng et al. [74], Gens [58], Williams [75], Kong et al. [76]). We should note that a geotechnical design based on the assumption of full saturation is not always conservative, particularly when deformation and servicea-bility are of main concern. For example, embankments and dams that are made of compacted materials can experience accumulated deformation under cyclic wetting and drying, which in turn affects their serviceability [67]. During the last three decades or so unsaturated soil mechanics has shown promising engineering relevance and significance in foundation engineering, slope stability, underground pipe-lines, retaining structures, dams, pavements and embank-ments, geo-environmental engineering, and mining engi-neering. The evergrowing number of international confer-ences on unsaturated soils is a testimony of its importance. There is currently at least one major international confer-ence on unsaturated soils every year (the International Con-ference on Unsaturated Soils-every four years, the Asian- Pacific Conference-every three or four years, the European Conference-every four years, and the new established Pan- American Conference), not to mention specific sessions dedicated to unsaturated soils in other geotechnical confer-

ences. Nevertheless, it should be noted that unsaturated soil mechanics is still at its early stage and there is still a signif-icant gap between the theory and practice. In-situ measure-ment of soil suction, a key variable in analyzing unsaturated soil problems, is still a challenging task, in spite of signifi-cant advancements in the last two decades [77]. The high capacity tensiometer developed at Imperial College (e.g. Ridley et al. [78], see Figure 22) was a welcome to the ge-otechnical community. Lourenço [79] proposed further modifications to the high capacity tensiometer. These ten-siometers are now commercially available and reasonably affordable. It is likely to see more practical use of these ten-siometers in geotechnical engineering.

As pointed out by Xie [80], unsaturated soil mechanics complements the classical saturated soil mechanics and is an integral part of modern soil mechanics. It plays an essen-tial role in problems involving expansive soils and collapsi-ble soils, whereas it is generally important for all types of soils. It is likely we will see further significant develop-ments in both theoretical and experimental unsaturated soil mechanics in next few decades. These developments will foster more engineering applications of unsaturated soil mechanics principles.

Figure 22 Imperial College suction probe and tensiometer (after Ridley et al. [78]).


6 Concluding remarks

In an attempt to answer those questions posed in the Intro-duction, the following remarks can be made:

1) It seems possible to use the same theoretical frame-work to model reconstituted soils and compacted soils. The pore size distribution evolves with stress and suction paths and can be modelled by the evolution of the loading col-lapse yield surface. However, much experimental evidence is needed before an affirmative conclusion can be drawn. In particular, we need more experimental data on the behav-iour of natural soils or soils reconstituted from slurry.

2) The volume change, yield stress and shear strength behaviour of an unsaturated soil are co-related to each other and it is not recommended to define these functions sepa-rately. Of all these functions, the volume change equation is the most fundamental one and it underpins the yield stress- suction and shear strength-suction relations.

3) The loading-collapse yield surface should recover the apparent tensile strength surface when the preconsolidation stress at zero suction is set to zero, to avoid non-uniqueness of the yield surface. The suction-increase yield surface used to capture the possible plastic volume change associated with drying is not truly needed, if the loading-collapse yield surface is properly defined.

4) The shear strength of an unsaturated soil can be de-fined by a single effective stress, if the friction angle of the soil does not change with suction. On the other hand, the volume change behaviour of unsaturated soils usually has to be expressed in two stress variables.

5) There are implications associated with using the Bishop effective stress. Because there is only one compres-sion index associated with both stress and suction changes in the volume change equation, this compression index is constrained to decrease with increasing suction. Such a con-straint is not always supported by experimental data. A pos-sible solution is to adopt a saturation-dependent compres-sion index and to form the constitutive equations in the stress-saturation space.

6) All the existing elastoplastic models for unsaturated soils have stress-path dependent elastic behaviour. It is still a challenging task to solve this theoretical problem.

The mechanics of unsaturated soils has strong engineer-ing relevance. Most geotechnical problems involve some variations of suction, water content or degree of saturation. These variations can cause significant volume change and strength variation, leading to undesirable deformation and stability problems. It is likely that we will see further de-velopments and more engineering applications of unsatu-rated soil mechanics in the next few decades.

This work was supported by the National Natural Science Foundation of China (Grant No. 51208519).

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