Soil Mechanics and Foundation Engineering, Vol. 36, No. 1, 1999 SOIL MECHANICS

COMPUTATIONAL STUDIES OF TRENCH-ENCLOSING SHEET PILING PHYSICAL TEST FOR THE COMPUTER PIg)GRAM GEO-MIGG

Yu. K. Zaretskii, V. N. Vorob'ev and E. D. Toimbetov

UDC 624.131

This paper cites an example o f the formulation o f a physical test for computer programs. Results o f calculations performed in accordance with the computer program GEO-MIGG are presented for a trench-enclosing sheet piling.

1. Introduction A number of organizations use the applied software package G E O - M I G G as a computational base of design solutions for structures, which are intended for different purposes and which interact with soil masses. The finite-element method and a mathematical model reflecting the elasto-viscoplastic behavior of a saturated soil subject to static and seismic effects in a complex stress state and under an arbitrary load path are implemented in this package [1, 2]. The model makes it possible to use this software package for practical engineering problems with consideration given to the building sequence and procedure used on the structures. Retaining designs are frequently used, for example, when structures are built above and below the ground in a dense urban setting. Here, additional constraints are set forth for new construction. New construction should not cause existing buildings to settle or be displaced by more than the allowable values. Considering that existing buildings and structures have already experienced deformations during their own construction and service, these criteria are quite harsh. In this connection, estimation of the validity and accuracy of the calculation, which predicts the joint behavior of the retaining-structure/soil-mass system and which evaluates the displacements of neighboring buildings and structures, acquires special significance in the design of enclosing structures. In practice, the accuracy of the prediction made on the basis of the computer program by the finiteelement method can be determined by one of two means when convergence requirements are observed. The first consists in the fact that a similar problem with a known analytical solution is analyzed using the same finite elements and shape functions. Considering the nonlinear deformability of the soil and the procedure and sequence used to build the structures, however, this method is unacceptable for this class of problems. The second method consists in the compilation of computed estimates and results of the physical experiment that most completely reflects the behavioral characteristics of the building-design/soil mass system. In our study, we set forth the results of this compilation for the applied software package GEOMIGG. In 1994 on the initiative of Professor Gudekhus (University of Karlsruhe, Germany), a large-scale experiment consisting in the determination of the interaction between an enclosing sheet piling and the soil mass in the base and Translated from Osnovaniya, Fundamenty i Mekhanika Gruntov, No. 1, pp. 2-7, January-February, 1999. 0038-0741/99/3601-0001522.00 9

Kluwer Academic/Plenum Publishers

+I.00 m

VK 3 0.00 m Bracing system .,.

I,...

'"

........

I

l?. V

--

Pl

Q

,

.Steel sheet piling I

9

P2

Inclinometer

PI ].!

l-a5

J't"

:..,. ~.9 k~ -0.80 m

_~5.00

m

5.s0m

z". ... ~.~

y_ .2 ..-7..

..v_'6.00m ,.~ . 9

0 S c a l e -

lm

~m ,

;

Sm '

"-,

v-

f-~i

o.

Fig. I. Determination of displacements of retaining wall and settlements of soil mass. I) Soil pressure; • stresses in sheet piling; e ) horizontal displacements; i ) force in bracing system.

sides of a trench 5 m deep was proposed as a "physical test" [3]. In that case, the participants in this unusual competition were supplied with all data on the geotechnical properties of the soils, including laboratory and field determinations. Later, it was proposed that the participants fill-out several forms in which results of calculations were entered, and submit them to the University of Karlsruhe. The authors of the test compared the results obtained with experimental data and assessed the validity and accuracy of the computational investigations. In 1995, we received a response from the university of Karlsruhe in which, among other things, it was indicated that: "It must be pointed out that your solution is one of the most successful, with the exception of the bending-moment prediction. The bending moment should be zero in the extreme lower section of the wall. We believe that rotation of this section is permitted in the computational scheme that we employed."

2. Initial Data of Large-Scale Experiment The formulation of the experiment and the sequence with which it was conducted are described in [3]. The diagram in Fig, 1 shows how this experiment was conducted; the diagram represents a segment of a trench for protective sheet piling fitted with strain gages. The field studies of the interaction between the enclosing sheet piling and soil mass in the base and sides of the experimental trench were performed in the following sequence (Fig. 1) in accordance with the steps:

O"

xlO 2 MPa -45.0

- 40.0

-35.0

-30.0

9---*-

20.0

e----

15.0

-30.0

-20.0

-10.0

1

I

I

0 ._ .r~O.-~

____;

/

20

30.0

40

~ , ai

t

J

50.0 O" x l O 2

el~%

MPa

Fig. 2. Chart of triaxial tests of gravelly sand with Pd = 1.56 g/cm 3. O) Experiment [3]; A) computed from model.

0. Installation of enclosing sheet piling 6 m high in the soil mass. 1. Excavation of the trench to a depth of 4 m with the intermediate installation of a support at a depth of 1.25 m from the top of the piling. 2. Excavation of the trench to a depth of 5 m. 3. Surcharging of the free surface of the region under consideration by a uniformly distributed load q = 10 kN/m. 4. Gradual weakening of the support coupling at a depth of 1.25 m from the top of the piling. To verify the computer program, the authors of the test submitted all materials relative to determination of the physicomechanical characteristics of the soils in the bed, including the results of odometric, shear, and triaxial tests, and plate and pressiometer experiments [3]. We processed the laboratory-test data (triaxial) and obtained the parameters of the mathematical model of the soil, which were required to perform the computational investigations. The chart of the triaxial testing of a gravelly soil under a kinematic load, and the chart calculated in accordance with the mathematical model adopted for the soil are shown in Fig. 2 as an example. Their satisfactory correspondence provides the basis for use of the approximations obtained in the calculations. A uniformly distributed load with an intensity of 150 kN/m was applied to the upper boundary of the computational region and subsequently removed to assess the natural stress state of the soil bed under its own weight, and the degree of its recompaction (unfortunately, the OCR coefficient was not given in the initial data). This procedure models to a certain degree the geological process of the "approach" and "retreat" of a

S, mm

P, xl02 MPa

0.00

20.00

40.00

0 . 0 0 ~=._.~

i

t

60.00 ,, m

80.00

100.00

J

I

-o.ooL \\

Fig. 3. Diagram showing curve of plate settlement versus load 1) plate tests [3]; 2) calculation; broken line represents calculation with allowance for translational motion of load surface [1].

glacier. The correctness of the choice of a temporary "surcharge" on the foundation bed and values of the parameters of the mathematical model were later confirmed by comparing data derived from plate tests with the computed values. In the initial data submitted to us, a plate with an area of 706.5 cm ~ (d = 30 cm), which was placed on the surface of the bed, was loaded in steps of 0.18 MPa each to a total value of 1.08 MPa with subsequent unloading. During deformation, the displacements in the bed of the plate were measured at each load step. A diagram illustrating the experimental relationship between the settlement of the plate and load in shown in Fig. 3 in which the computational relationship between the plate's settlement and the applied load is also indicated. In the calculations, complete "adherence" was assumed at the contact between the plate and soil. Agreement between the experimental and computed "plate-settlement/load" curves suggests basically the correctness of the selection of the parameters for the mathematical model of the soil and the degree of bed recompaction.

3. C o m p u t a t i o n a l

Investigations o f T r e n c h - E n c l o s i n g

Sheet Piling

The computational investigations of the interaction between sheet piling enclosing an experimental trench and the soil mass were conducted in a sequence strictly reflecting the sequence of the large-scale experiment conducted by yon Wolffersdorff [3]. The plastic-strain increments are determined in conformity with the model adopted by summing the strain increments over all regular segments r of surface f,

o~6, 4

(1)

where d&" are certain scalar parameters, tro are the stress components, and de~ are the plastic-strain increments. The analytical description of the regular segments of the load surface in the soil model adopted assumes the form

f , = T ~ - c , - / c , a v,

(3)

where the values of c, and k r are given by expressions presented in detail in [1, 2]. The c, and k r values depend on three hardening functions, whose arguments are Odequist parameters. The concept according to which failure occurs over certain slip areas in accordance with the "dry-friction" law

rj = c +k a j

(4)

is adopted for the soil model in question, where c* and k" are strength parameters, and ~ and ~ are the tangential and normal stresses on an area with a normal 9 in the space of principle stresses "r~ > x2 > ~3- The value of the strength parameters are given by relationships dependent on the accumulated shear strains ~ ' [4]

C" =afCf +(1--O~f)Cres; k* =otfk] +(1-otf )kr*es; t~f

[(~* I)'~P)'~ when ~vp > ~t*

(5)

Here, cf and kf, and c~s and k~s are, respectively, parameters of the peak and residual strengths. The calculated parameters of the model are defined on the basis of test data derived under an axisymmetric stress or plane strain state. Zaretskii [2] cites a procedure for determining the hardening functions and calculating the parameters of these functions for plane strain from results of stabilometer tests. The computational algorithm, which is based on use of the above-indicated soil model, is given in [1]. If the material manifests properties of nonlinear deformability, and the equations of state are solved in terms of strains, the equations of equilibrium of a finite element assume the final form [ 1, 5] on the assumption that decomposition of the total-strain increment into the elastic and plastic components is additive. In that case, the computational process for the set of finite elements is constructed in accordance with the method of initial deformations with corrections made to the equilibrium equations in each step of the solution. The computational procedure described makes it possible to calculate the soil pressure on the enclosing walls of the trench with allowance for the following factors: the sequences with which the trench is excavated and the structure being built; the stiffness and displacement of the wall; and, the contact friction along the wall. The concept of the contact elements proposed in [6] was used to account for the effect of contact friction between the enclosing wall and soil. In our study, the above-mentioned procedure was modified in an appropriate manner to account for nonlinear deformation along the contact surface. The relationship between the forces (~'s and tr) acting on the contact, and their relative displacements (o9) is represented as

9~ = k ~ ,

k~ =

P P. z. = k.w.,

(6)

c~ -cr ~tg6; (1 -B~)o~ + B, tos

(7)

Displacements

~

E

E

E

E

E

~

O.OO

Horizontal displacements of wall

p = I0 kNlm 2

ooo I o.5o m E-

I I

.................................

1.25 m I

I

..............................4! ...................................

2.~m l_ ~.-~o,m L a.oo m I ~.~o m I,,

I

~.~o m ~.oo m 5.so m ..oo m

l' [t f

1.1 I I

................................

9. : :

I o l l o

....................................

t~

..... :..........................

....................................

................................ ii ....................................

I [ ~,."//////~//f//////,4 ~ l I /{21Z .21ZIZ}X21122i Difference in displacements

I

1

Fig. 4. Step 4. Weakening of support coupling.

where k f and k~ are the specific stiffnesses in the normal and tangential directions, respectively, c~* and 5* are strength characteristics for the contact, B is a parameter of the model, as defined from shear tests, and m~* is the limiting displacement in the tangential direction. The reaction of a contact element in the normal direction was assumed linear with respect to the normal displacements with a restriction placed on the rupture strength of the contact. The computational algorithm, which is based on use of contact elements, is described in [7], where values are also given for the parameters used in the calculations in the "subpeak" state in terms of strength. Diagrams of the normal pressures of the soil against the wall, the displacements of the wall, and the bending moments of the curved axis of the wall were plotted from the results of the computational investigations of the stress-strain state of the "sheet-piling/soil-mass" system. According to conditions established for the international test, the computational results should have been presented on forms of the type shown in Fig. 4. A comparative analysis of all four load steps (steps 1-4) with results of the field experiments was performed at the University of Karlsruhe. The distribution of the lateral soil pressure over the height of the wall for the stepwise excavation of the trench is shown in Fig. 5. 6

Step 3

Step 4

0.0-

0.0"

-1.0-

-1.0-

-2.0 -

-2.oi

3o!

o

~ -3.0ID

o

.4.0-

-5.0

-6.0

t

i

-g0.0 -60.0

"~ -40.0

~

]

-20.0

0.0

20.0

40.0

Soil pressure, kN/m 2

60.0

j 80.0

"7 100.0

-6.0 -60.0

~ -40.0

~ -20.0

0.0

20.0

~ 40.0

60.0

Soil pressure, kN/m 2

Fig. 5. Diagram showing soil pressure against retaining sheet piling. .) Experiment [3] (E n = 1210 kN m2);<>) calculation with E I = 1210 kN m2; x) calculation with E 1 = 2032 kN mL

The magnitude and character of the distribution of the soil pressure against the enclosing walls are slightly dependent on its stiffness (within the limits of the stiffness values selected for the calculation). Maximum pressure values are realized near the intermediate support with a subsequent decrease in the span section. Qualitatively, the computational results and experimental data are in good agreement. It must be pointed out here that in contrast to the field experiments, the computational investigations were conducted under plane deformation in connection with the fact that the support reaction with respect to the median section is possibly exaggerated. It is interesting to trace the displacement of the wall as related to the stages of trench excavation. As is apparent from Fig. 6, the maximum displacements are observed in the median section of the span. Note that the stiffness of the wall affects only the displacements, especially in the span section. During soil excavation, the wall is displaced in the direction of the trench. This process is observed to a lesser degree in the embedded portion of the wall. Comparison of the computed and experimental results indicates their qualitative agreement. The greatest discrepancies are observed in the embedded part of the wall. The results of the investigations of the bending moments of the curved axis of the wall are of greatest interest for the design of enclosing walls. It should be pointed out that the previously observed (see the reference made in the text of the letter submitted by the authors of the test) significant discrepancy in the results between the computed prediction of the moment diagram and data derived from the physical test was the result of a simple error that we had permitted. The bending moments are determined either proceeding from the diagram of the pressure against the wall, or by double differentiation of the displacement curve of the axis of the wall. The discrepancy should not be significant, therefore, if the displacement curves are close. We calculated the bending moment by dou-

Displacement diagram of retaining sheet piling

Bending-moment diagram of curved axis of wall

0.0-

0.0-

-I.0 -

-1,0-

E -2.0-

-2.0 o

0

o

o1>

-3.0 -

r

x"

-3,0 -

0

o

o

-4.0-

-4.0-

\\ -5.0

-

-6.0 -30.0

-5.0

|

I

-20.0

-10.0

Displacement, mm

W

i

0.0

10.O

rlll/lll/ll//'ff~/

-6.0 =810

! -4.0

vi\

0.0

41o

si0

Bending moment, kN/m 2

Fig. 6. Step 3 excavation of trench to 5 m with external load of q = 10 kN/m. 9 , O, x) See Fig. 5. ble differentiation of the displacement curve (without laying down the condition of absolute fixity for the "'base" of the wall), and obtained the results reflected in Fig. 6. As is apparent from Fig. 6, the pattern of the bending-moment diagram during stepwise trench excavation varies little, and the results of the experiments and calculations are qualitatively in rather satisfactory agreement. A regular increase in the absolute values of the bending moments, especially in the span section of the wall, is observed as the latter's stiffness increases. Analysis of the computational investigations of the interaction between an enclosing sheet piling and bed soils and their comparison with results of field tests indicated the need to account for the stiffness characteristics of the wall, the strength properties and elastoplastic deformations of the soil, and the procedure and sequence of work production. REFERENCES .

2. 3. 4. 5.

,

7.

Yu. K. Zaretskii, Lectures on Modern Soil Mechanics [in Russian], Izdatel'stvo Rostovskogo Gosudarstvennogo Universiteta, Rostov-na-Donu (1989). Yu. K. Zaretskii and V. N. Lombardo, Statics and Dynamics of Earth Dams [in Russian], Energoatomizdat, Moscow (1983). P. A. Von Woifferstorff, "Feldversuch an einer spunwand in sandboden. Institut fur bodenmechanik und felsmechanik," Geotechnik, No. 13, 44-46 (1994). Yu. A. Zaretskii, "Long-term strength and viscoplasticity of clayey soils," Osn., Fundam., Mekh. Gruntov, No. 2, 2-6 (1995). V. N. Vorob'ev, "'Prediction of the creep strains of slopes as beds for pressure conduits at pumped-storage power plants", Author's Abstract of Dissertation for Candidate of Technical Sciences, Moscow (1990). R. E. Goodman, R. L. Tailor, and T. L. Brekke, "Model for the mechanics of jointed rock," J. Soil Mech. Found Div., Am. Soc. Civ. Eng., 94, No. 3, 637-659 (1968). E. D. Toimbetov, "Soil pressure against enclosing walls of trenches", Author's Abstract of Dissertation for Candidate of Technical Sciences, Moscow (1994).