Nonlinear Three-Dimensional Modeling of Bentonite Slurry Tunneling

By

M. M. Eid1, A. A. Ahmed2, H. M. Helmy3 and S. M. El-Sayed4 Ain Shams University, Faculty of Engineering

Abstract

The Egyptian tunneling activities have augmented in the last two decades

for several purposes such as construction of subways, sewers and road tunnels. The preponderance of the Egyptian tunnels are constructed through soft alluvial soils under high ground water pressures in which tunneling can trigger substantial ground deformations. The prevailing subsurface conditions limited the construction methods to full face tunneling machines; otherwise tunneling cannot be proceeding. The Bentonite Slurry Shields proved to be successful in many Egyptian tunneling projects.

In the present study, a three-dimensional finite element model is

developed to update the different sophisticated measures employed in the Bentonite Slurry technique to minimize the ground displacements associated with tunneling operation. The proposed numerical model is used to evaluate two case studies of tunnel projects constructed in Cairo namely, Greater Cairo Metro and the intersection of Al-Azhar Twin Road Tunnels and the CWO sewer at Port Said Street. The later case study is a typical three-dimensional problem; otherwise the output will be unrealistic. The results of the numerical modeling of the two case studies are then compared with the field measurements compiles during tunneling activities in order to verify the results of the proposed numerical model. Keywords: Bentonite Slurry Tunneling; Three-dimensional Analysis; Nonlinear

Finite Element; Gap Parameter; Tailskin Grouting; Gap Element; Field Measurements.

1 Professor of Structural Engineering and Head of the Geotechnical Division. 2 Associate Professor of Structural Engineering. 3 Assistant Professor of Structural Engineering. 4 Assistant Lecturer of Structural Engineering.

1. Introduction:

Tunnel modeling is an intricate nonlinear three-dimensional problem. The

key sources of nonlinearly in tunneling analysis are illustrated in Fig. (1) and summarized as following:

• The nonlinear soil constitutive behavior, which depends mainly on the stress path, confining pressure and rate of loading;

• The distribution of the marginal yield zones around the tunnel; • The pressurized excavation boundaries and ground support measures; • The radial and axial ground loss and the over-cutting gap; • The tailskin grouting and the hardening of grouting material with time; • The unloading forces developed during ground excavation; • TBM advancement and lining installation; • The mutual interaction between the excavated tunnel and the surrounding

underground pre-erected pipelines and tunnels. Tunneling analysis, using two-dimensional plane strain or axisymmetric

models, has been considerably employed in research and in design. The displacement field is approximated in plane strain models by neglecting the non-radial deformations while the stress and displacement field is approximated into symmetric fields in axisymmetric models. Ahmed [1] used the incremental non-linear FEM combined with the Convergent-Confinement approach of lining analysis to update the ground-lining interaction. Esmail [9] used Rowe and Cake Gap Parameter technique [15] with some modifications to allow the simulation of the tunnel construction stages. Little literature is available in which soft ground tunneling is idealized using three-dimensional models due to the required high computational cost especially when employing the nonlinear soil models.

2. Idealization of Problem:

The soil, shield and liner are modeled using three-dimensional hexahedral

elements. The soil nonlinear behavior is identified by variable modulii dependent on the confining pressure and the stress path. The soil constitutive relationship is expressed in an incremental form to account for the path-dependency. Using the incremental form of the constitutive matrix [Det], the tangential element stiffness matrix [Ket] can be written as [13]:

[ ] [ ] [ ][ ]∫=element

eett

eet )Volume(dBDBK …… (1)

where the [Be] is the element strain-nodal displacement matrix. The loading modulus (Et) and the unloading-reloading modulus (Eur) are presented by the following exponential forms [5]:

( )( ) n

a

3

2

3

31fat psin2cosC2

sin1R1KpE

σ

φσ+φφ−σ−σ

−= …… (2)

n

a

3aurur p

pKE

σ= …… (3)

where Rf is the ratio between the ultimate and the failure deviator stresses, pa is the atmospheric pressure, n is the stiffness exponent, K is the loading stiffness coefficient, Kur is unloading-reloading stiffness coefficient, σ1 & σ3 are the major and the minor principal stresses and C & φ are the soil shear parameters. During the finite element analysis, it is not possible to pre-determine the regions subjected to loading or unloading in order to conclude whether the loading modulus or unloading modulus should be used. Since the loading modulus is lower than the unloading modulus as explained by the Equations (2) and (3), the use of the loading modulus can lead to numerical divergence when unloading occurs. Using the unloading-reloading modulus during the first iteration of every loading step will underestimate the displacement in the first iteration if loading occurs but the correct modulus will be used in subsequent iterations according to a parameter called the stress level [6] depending on deviator stress, the shear parameters and the confining pressure as follows:

4

a

3

3

31

psincosC)(SL σ

⋅φσ+φ

σ−σ= …… (4)

…

The stress level (SL) is calculated for each gauss point and compared to the maximum value reached during the loading history at the same gauss point (SLmax). The modulus (E) depends on the parameter SL as following:

• If ( maxSLSL ≥ ), loading is taking place and the used modulus E=Et • If ( maxSL75.0SL ≤ ), unloading is taking place and used modulus E=Eur • If ( maxmax SL75.0SLSL >> ), neutral loading is taking place and the modulus

E is calculated by interpolation between E and Eur as shown in Fig. (2). The shield-soil interface is modeled using a hyperbolic gap element [4].

The liner-grout-soil interface is modeled by introducing grout elements with incremental hardening strength parameters and initial hydrostatic pressure equal to the grouting pressure [8] as shown in Figs (3) and (4); the normal stiffness is considered a constant of very high value for the contact and of trivial value for the open gap. The tangential shear stiffness (kt) of the gap is defined by:

ns

a

n

2

n

sfiwit ptan

R1Akk

σ

δσ

τ−γ= …… (5) …

where ki is the stiffness coefficient, γw is the water unit weight σn is the stress normal to the interface surface, Ai is the contact area and Rsf & ns are defined similarly to the soil hyperbolic model parameters.

2.1. Ground Excavation and Lining Installation Incremental Modeling: Tunnel excavation is modeled by removing a cluster of ground elements

from the finite element meshing; conversely, lining elements are new elements that are added to the mesh; this algorithm is equivalent of the Stress Reversal Approach [1]. The required changes in the mesh are applied to reconstruct the residual vector {R} resulting from the difference between the applied force and the straining forces and the tangential stiffness matrix [Kt]. The residual vector and the stiffness matrix are calculated at the beginning of each iteration (Newton-Raphson), i.e. the (i+1)th iteration is described by the following equation:

[ ] { } { }RUK tt1i

tt1it

tti

∆++

∆+

+∆+ =& { } [ ] { }∑ ∫

=

∆+∆+ σ−=elements of No.

1e elemente

tti

Te

tt )Volume(dBF …… (6)

where {F} is the nodal forces. The left subscript denotes the iteration process and the left superscript donates a sequential time index. If the iteration superscript is zero, the matrix or vector is calculated at the end of the previous time step. The stress increment can be calculated from the strain {ε} using the following integration:

{ } { } { } { } [ ] { }{ }

{ }

∫ε

ε

∆+∆++

∆+∆++

∆++

∆+

ε+σ=σ+σ=σtt1i

tti

dDettti

tt1i

tti

tt1i & …… (7)

Numerical integration is used to evaluate the integral in the stress calculations. Employing a predictor-corrector method (Modified Euler scheme) as following:

{ } { } [ ] { } { } [ ] [ ] { }UBD21D

21 tt

1ieettti

tti

tt1iet

tti

tti

tt2/1i

&&∆+

+∆+∆+∆+

+∆+∆+∆+

+ +σ=ε+σ≅σ …… (8)

then [ ]ettt2/1i D∆+

+ using the predicated stress { }σ∆++

tt2/1i . The stress can be calculated

using { } { } [ ] [ ] { }UBD tt

1ieettt2/1i

tti

tt1i

&∆+

+∆+

+∆+∆+

+ +σ≅σ …… (9)

2.2. Modeling of Grouting Measures in Tunneling:

Grouting of sandy soils to increase the strength and stiffness of such soils is a common measure in tunneling projects to minimize the tunneling effect on adjacent structures. Bell [3] showed that the change in the angle of friction (φ) of sandy soil caused by grouting is generally insignificant. The effect of grouting can be recognized as increasing the soil stiffness and cohesion. Tan and Clough [16] propose a scale of the effect of grouting on sandy soil in tunneling project. They divided the grouting quality into four distinct categories; namely: weak, medium, strong and very strong as shown in Table (1). The cohesion parameter of the grouted soil can be estimated (assuming no change in the frictional angle of the stabilized soil) using the following equation:

φ

+=

245tan2

qco

ungrouted

…… (10)

where qun is the unconfined compressive strength of grouted soil. The effect of grouting on the soil stiffness is expressed by the ratio SR, which is defined in Table (1), as following

KSRKgrouted ⋅= …… (11) where Kgrouted is the strength parameter for grouted soil and K is the strength parameter of the ungrouted soil. 3. Case Studies: The model was used to analyze the tunneling status in the Greater Cairo Metro Project (Line 2-Phase 1A) and Al Ahzar Twin Road Tunnels at the site of the intersection with Cairo Wastewater Spinal Sewer (CWO). The two projects are the most giant tunneling activities in Cairo in which the Bentonite Slurry Technique was used. The analysis was performed using small PC that has a Pentium II 300 MHz processor with 32 MB RAM. 3.1. The Greater Cairo Metro 2nd Line – Phase 1A:

The Greater Cairo Metro Second Line is a double deck circular bored

tunnel having an excavated diameter of 9.35 m. Two identical bentonite slurry shields built by Herrenknecht of Germany were selected to drive the tunnel. Two test sections, south of El-Khalafawy station (Lot 12) and south of Rod El-Farag station (Lot 16), were instrumented during the construction [7] and the results were presented by Hamza Associates [11]. Soil strata at the location of these Lots are shown in Fig. (5-a) and the geotechnical properties are summarized in Table (2). The finite element mesh used in the analysis is shown in Fig. (5-b). The tunneling activities been idealized in 21 incremental steps, the mesh at the end of the steps is shown in Fig. (5-b). The technical data of the employed TBM recommended the total ground loss as 0.5%. The measured insitu ground surface settlements were used to compute the volume of ground surface settlement trough, which is converted to a volume of ground loss around the TBM. Hamza Associates [11] reported the total volume of about 0.24%ground loss. The face loss was estimated to be about 0.09%, i.e. the loss along perimeter of the TBM is about 0.15%. The grouting pressure is assumed to be 3.25 bar. The face pressure is assumed to be 2.0 bars.

Figs. (6) & (7) demonstrate the surficial deformation field at Lot 12. The

figures show a fair agreement between the predicted surface settlement and the measured settlement troughs. The maximum settlement is about 11 mm. The trough extends 25m ahead of the TBM face and 45 m behind the TBM face with a width of about 18 m. The model predicates some heave beyond the settlement trough with a maximum value of 1.5 mm. The vertical subsurface deformation for a point at a depth of 12.5 m is shown in Fig. (8). The monitoring report

described the constant settlement profile above the crown contradicting the well-known observational formulae [2].

Figs. (9) & (10) show the surficial vertical deformation for Lot 16. The

maximum settlement is about 18 mm. The settlement at the face is 7 mm (i.e. 40% of the maximum settlement). The trough extends to a distance of 25 m ahead of the tunnel and increases after the passing of the TBM to a distance of 45 m similar to Lot 12. The actual settlement trough is wider than the predicated one. The settlement trough extends to a distance of 20 meters. The results show a good agreement between the predicated and measured values.

3.2. Al-Ahzar Twin Road Tunnels - CWO Crossing:

The proposed three-dimensional model is used to analyze the tunneling at

the intersection of Al-Azhar Road Twin Tunnels (excavated diameter 9.35m and spaced 18.7 m apart) and the CWO sewer (5 m external diameter) at Port Said Street. The specific crossing is especially important because tunneling is designed to pass underneath the CWO sewer with a minimum distance of 4 m. The precautionary measures to minimize the tunneling effect on the existing CWO sewer comprise reinforcing of the ground underneath the sewer with grout injection in form of two walls and carrying out heavy instrumentation plan during the TBM passage [10]. According to the Hamza Associates [12], the major soil units for zone of the intersection of Al-Azhar and CWO tunnels are as described in Table (2) and shown in Fig. (11-a). The finite elements mesh used in the analysis is shown in Fig. (11-b). The assumed radial loss was set to 0.14% similar to the tunneling conditions in Greater Cairo Metro.

The effect of the construction of Al-Azhar Road Tunnels on the CWO

tunnel for the untreated ground is shown in Fig. (11.b). The vertical settlement, the compressive stress and the tensile stresses are estimated to be 13.7 mm, 15.6 kg/cm2 and 11.6 kg/cm2 respectively. The settlement of the zone far from the CWO crossing shows a fair agreement with the measured trough during driving of the north tunnel as shown in Fig. (12). The settlement trough above the CWO has less maximum values but on the other hands it spreads in a larger distance than the trough far from the crossing. The maximum value of the settlement during driving of the north tunnel is about 4.2 mm but increases to about 9 mm after the south tunnel is completed. Introducing the grouting effect reduces the internal stresses and the deformation furthermore as shown in Fig. (13). The compression stresses apparently approaches a limit that cannot be affected by higher stabilization category other than strong grouting; however, the tensile stress and the settlement reduced monotonically with increasing the grouting category but with a declining rate. The maximum settlement, the compressive stress and the tensile stresses can be reduced to 8.54 mm, 12.8 kg/cm2 and 6.2

kg/cm2 respectively for very strong grouting category. It should be noted that at high grouting categories, the maximum tensile stress is found to occur at the crown; conversely, at low grouting categories it occurs at the invert. The grouting measure proved to be successful by reducing the settlement by 38% and tensile stress by 47%. Compression stress can only be reduced by 22%. 4. Conclusion:

Comparing the results of the proposed numerical three-dimensional

idealization of the Bentonite Slurry Tunneling with the field measurements compiled during the construction of two major tunnel projects constructed in Cairo indicated the capability of such sophisticated modeling to develop realistic pattern of ground subsidence associated with tunneling. Practicing the proposed numerical model to the Greater Cairo Metro and Al-Azhar tunnels intersection with CWO tunnel confirmed precious results of the proposed numerical model. The results implied that, simulating the details of tunneling operation through the modeling formulation is considered as the basis for optimum idealization. Adapting the main factors affecting the pressurized Bentonite Slurry Tunneling such as; unloading forces due to excavation, ground nonlinearly, interface condition, engineering properties of shield, rate of advance, machine overcutting, face pressure, yielding zones and the tail grouting is badly needed for realistic updating of the ground-tunneling interaction.

Furthermore, the three-dimensional tunneling analysis is considered as the

entirely capable arrangement to simulate very sophisticated problems such as the intersection of different tunnels that cannot be preceded by means of two-dimensional analysis or empirical approach superposition. Consequently, the deformations and the internal forces developed in underground pipelines and sewers due to tunneling can be estimated. The results of the intersection of AlAzhar Road Tunnels and CWO show that grouting proved to be a salutary process to control the deformation and the internal forces (especially tensile stresses) developed in underground structures due to tunneling.

5. Reference

1. Ahmed, A. A., 1991, “Interaction of Tunnel Lining and Ground”, Ph. D. Thesis, Ain Shams University, Cairo, Egypt.

2. Attwell, P. B. and Yeates, J., 1984, “Tunneling in Soil Ground; Movements and Their Effects on Structures”, Blackie and Son Ltd., Glasgow, UK.

3. Bell, F. G., 1993, “Engineering Treatment of Soils”, E & FN SPON, London, UK.

4. Dessouki, A. K., 1985, “Stability of Soil-Steel Structures”, Ph. D. Thesis, University of Windsor, Ontario, Canada.

5. Duncan, J. M. and Chang, C. Y., 1970, “Nonlinear Analysis of Stresses and Strains in Soils”, Journal of Soil Mech. And Found. Div., ASCE, Vol. 96, No. SM5.

6. Duncan, J. M., Seed, R. B., Wong, K. S. and Ozawa, Y., 1984, “FEADAM84: A Computer Program for Finite Element Analysis of Dams”, Virginia Polytechnic Inst. And State Univ., Dept. of Civil Engineering, USA.

7. El-Nahhas, F. M., 1999, “Soft Ground Tunnelling In Egypt: Geotechnical Challenges and Expectations”, Tunnelling and Underground Space Technology, Vol. 14, No. 3, pp. 245-256.

8. El-Sayed, S. M., “Elasto-plastic Three Dimensional Analysis of Shielded Tunnels, with Special Application on Greater Cairo Metro”, Ph. D. Thesis, Ain Shams University, Cairo, Egypt, (In Progress).

9. Esmail, K. A., 1997, “Numerical Modeling of Deformation around Closed Face Tunneling”, Ph. D. Thesis, Ain Shams University, Cairo, Egypt.

10. Ezzeldine, O. Y., 1999 “Tunneling at the CWO Crossing, Results of Montoring”, El Azhar Road Tunnels Project, Detailed Design, NAT, Egypt.

11. Hamza Associate, 1995, “Greater Cairo Metro: Phase (2) Tunnel Monitoring”, Comprehensive Report, NAT, Egypt.

12. Hamza Associates, 1998, “Al Azhar Road Tunnel; Port Said, Al Azhar & El Mosky Street”, Geotechnical Report, NAT, Egypt.

13. Owen, D. R. and Hinton, E. H., 1980, “Finite Element in Plasticity: Theory and Application”, Pineridge Press Ltd., Swansea, UK.

14. Richards, D. P., Ramond, P. and Herrenkenecht, M., 1997, “Slurry Shield Tunnels on the Cairo Metro”, General Report, RETC, Las Vegas, USA.

15. Rowe, R. K., Lo, K. Y. and Kack, G. J., 1983, “A Method of Estimating Surface Settlement above Tunnels Constructed in Soft Grounds”, Can. Geotech. J., Vol. 20, pp. 11-22.

16. Tan, D. Y. and Clough G. W., 1980, “Ground Control for Shallow Tunnels by Soil Grouting”, J. of Geotech. Eng., ASCE, Vol. 106, No. GT9, pp. 1037-1057.

ملخص

رى خالل العقدين األخيرين ألغراض عديدة منها مترو انفاق تزايد إنشاء االنفاق فى القاهرة الكباألنفاق فى تربة نهرية هذه أنشئت غالبية القاهرة الكبرى وأنفاق الصرف الصحى و أنفاق السيارات ولقد

ونظرًا لطبيعة . ضعيفة و تحت ضاغط مائى آبير حيث يمكن أن تتسبب فى العديد من االزاحات االرضيةنات المستخدمة آانت ذات تدعيم وجهى آامل و لقد اثبتت ماآينات الحفر التى تستخدم التربة فان الماآي

مستحلب البنونيت آفاءة آبيرة فى مشروعات االنفاق المصرية و فى هذا البحث نقدم نموذج تحليلى عددى ل االزاحات مبنى على طريقة العناصر المحددة ثالثية االبعاد مع االخذ فى االعتبار الطرق المتبعة لتقلي

االرضية فى ماآينات مستحلب البنتونيت و السلوك الالخطى للتربة و لقد طبق هذا النموذج فى دراسة .مشروعين من مشروعات االنفاق بالقاهرة و قورنت نتائجه مع القياسات الحقلية للتحقق منه

Table (1) Grouting effect on the sandy soil parameters for tunneling projects [16] Unconfined compressive strength for

different relative density (t/m2) Grouting designation Loose Medium Dense

Ratio of stiffness of grouted to ungrouted soil

(SR) Weak

Medium Strong

Very Strong

0.87 2.18 4.35 6.96

1.81 4.57 9.14 14.6

3.84 9.57 19.1 30.6

1.50 2.25 3.50 5.00

Table (2) Soil properties for Greater Cairo Metro 2nd Line-Phase 1A (Lot 12 and Lot 16)

Stratum FILL CLAY – SILT Silty SAND Dense SAND φ 15 0 30 37

C (kg/cm2) 0 0.8 0 0 γ (t/m3) 1.7 1.8 1.9 2.0

ko 1.0 0.74 0.50 0.40 K 150 225 325 600 n 0.6 0.55 0.5 0.5 Rf 0.70 0.75 0.8 0.8

Poisson’s ratio 0.4 0.4 0.35 0.3 Table (3) Soil properties for the CWO-Al Azhar Tunnels Crossing

Stratum FILL CLAY – SILT Silty SAND Dense SAND Gravelly SAND φ 23 0 30 35 41

C (kg/cm2) 0.2 1.0 0 0 0 γ (t/m3) 1.65 1.8 1.90 1.95 2.0

ko 1.00 0.74 0.50 0.43 0.35 K 150 200 325 475 750 N 0.6 0.55 0.5 0.5 0.5 Rf 0.73 0.75 0.8 0.8 0.8

Poisson’s ratio 0.4 0.4 0.35 0.3 0.3

Figure (1) Elements of nonlinearity in tunnel modeling

Underground utilities

Yielded zone

Launch Shaft

Figure (2) Effect of stress path on soil stiffness [6].

Figure (3) Interface modeling

Overcut

Shield elements

Gap elements

Soil elements

(a) Shield/soil interface modeling

Liner elements

Soil elements

Grouting elements (initially under hydrostatic grouting pressure)

(b) Liner/grouting/soil interface modeling

Tail gap

Shield/Liner

Enfolding ground

SLmax 0.75 SLmax

Et

Eur

SL

E

ε1

σ 1−

σ 3

Et

Eur

Figure (4) The interface element

Figure (5) Greater Cairo Metro Phase Line 2- Phase 1A (a) Subsurface Conditions

(b) initial mesh for Lot 16 (c) the mesh after 21 increments

(b) (c)

Local axes and convergent gap

Normal stiffness

Tangential stiffness

(a)

17.8

Figure (6) Surficial longitudinal settlement trough at Lot 12

Figure (7) Surficial cross settlement trough at Lot 12

Figure (8) Subsurface longitudinal settlement trough at depth of 12.5 m (Lot 12)

Figure (9) Surficial longitudinal settlement trough at Lot 16

Figure (10) Surficial cross settlement trough at Lot 16

Figure (11) CWO- Al Azhar Tunnels intersection: (a) subsurface conditions (b) the mesh

(c) the deformed shape of the CWO sewer for untreated grounds (1000:1)

(b) (c)

(a)

Figure (12) Surficial settlement trough of the untreated ground

Ungrou

tedWea

k

MediumStrong

V. strong

Grouting Category

0

2

4

6

8

10

12

14

16

Stress (kg/sq. cm)

Compression stress Tensile stress

(a)

Ungrou

tedWea

k

Medium

Strong

V. stro

ng

Grouting Category

0

2

4

6

8

10

12

14

16

Settl

emen

t (m

m)

(b)

Figure (13) Effect of grouting on the CWO sewer (a) the maximum internal stresses (b) the maximum settlement