Finite Element Numerical Simulation of Three-Dimensional Seepage Control for Deep Foundation Pit Dewatering

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2008,20(5):596-602

FINITE ELEMENT NUMERICAL SIMULATION OF THREEDIMENSIONAL SEEPAGE CONTROL FOR DEEP FOUNDATION PIT DEWATERING* LUO Zu-jiang, ZHANG Ying-ying, WU Yong-xia College of Civil Engineering, Hohai University, Nanjing 210098, China, E-mail:[email protected]

(Received October 17, 2007, Revised March 2, 2008)

Abstract: For deep foundation pit dewatering in the Yangtze River Delta, it is easy to make a dramatic decrease of the underground water level surrounding the dewatering area and cause land subsidence and geologic disasters. In this work, a three-dimensional finite element simulation method was applied in the forth subway of Dongjiadu tunnel repair foundation pit dewatering in Shanghai. In order to control the decrease of the underground water level around the foundation pit, the foundation pit dewatering method was used to design the optimization project of dewatering ,which was simulated under these conditions that the aquifers deposited layer by layer, the bottom of the aquifers went deep to 144.45 m, the retaining wall of foundation pit shield went deep to 65 m, the filters of the extraction wells were located between 44 m to 59 m, the water level in the deep foundation pit was decreased by 34 m, and the maximum decrease of water level outside the foundation pit was 3 m. It is shown that the optimization project and the practical case are consistent with each other. Accordingly, the three-dimensional finite element numerical simulation is the basic theory of optimization design of engineering structures of dewatering in deep foundation pit in such areas. Key words˖Yangtze River Delta, land subsidence, deep foundation pit dewatering, seepage control

1. Introduction  The Yangtze River Delta is one of the most economically developed areas in China. In recent years, with the rapid development of the national economy and the continuous expansion of urban construction, the development of underground space has received more and more attention. Quaternary loose sediments with great thickness distributes in the Yangtze River Delta, in which form a few pore-confined aquifers with large thickness. The aquifers are divided by the clays with weak permeability, but there is close hydraulic relation among these aquifers. Because the thickness of the aquifer is large, the burial depth of the impervious base is deep, the water level is high, and the quantity is abundant, it is difficult for the retaining wall of 

* Project supported by the Major Scientific Research Project Foundation of Shanghai (Grant No. 04dz12003). Biography: LUO Zu-jiang (1964-), Male, Ph. D., Professor

foundation pit shield to reach the base, and the foundation pit dewatering is exceedingly easy to make a dramatic decrease of the underground water level surrounding the dewatering area and cause land subsidence and geologic disasters, even major security incidents if not handled properly[1,2]. Therefore, based on the characteristics of three-dimensional geological body, it has become a top priority to design rationally the entire engineering structures of dewatering if economic and technological conditions are available, so that the demand of the decrease of the underground water level in deep foundation pit can be met and meanwhile the decrease of the underground water level around foundation pit is incapable of causing land subsidence and geologic disasters. The forth subway of Dongjiadu tunnel repair foundation pit dewatering in Shanghai was used as an example, this work aims to elaborate the theories and methods of three-dimensional finite element simulation[3] of deep foundation pit dewatering based on the control of land subsidence in such areas. According to the numerical

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simulation of different engineering structures of dewatering, the optimal program of dewatering is determined, and the practice has proved that this program is correct and reliable and can control effectively the land subsidence around the foundation pit. Accordingly, three-dimensional finite element numerical simulation is the basic theory for designing engineering structures of deep foundation pit dewatering in such areas.

k zz

wH cos  n, z wz

*2

= q ( x, y , z , t )

 x, y , z  * 2 (c) Free surface boundary conditions :

H  x, y, z, t = Z  x, y, t 2. Mathematical model of groundwater seepage flow 2.1 Governing equation By taking the direction of the main infiltration corresponds with the coordinate axis direction in anisotropic porous medium, the governing equation for three-dimensional transient flow is[4]

w wH w wH w wH ( k xx ) + ( k yy ) + ( k zz )+ wx wx wy wy wz wz wH W = SS wt

 x, y , z  :

(1)

where S S is the specific storativity, k xx , k yy , k zz are the permeability coefficient in the principal directions of anisotropy medium respectively, H is the water level at the pointat  x, y, z the instant t , W is the source and sink terms , t is time, : is the computational domain. 2.2 Initial and boundary conditions The initial and boundary conditions for the unsteady seepage in porous medium are given as follows. (1) Initial conditions:

H ( x, y , z , t )

t =0

= H 0 ( x, y , z , t 0 )

 x, y , z  :

(2)

(2) Boundary conditions: (a) The first kind of boundary condition:

H ( x, y , z , t )

*1

(b) The second kind of boundary condition:

k xx

wH wH cos  n, x + k yy cos  n, y + wx wy

k

wH wn

*3

=P

 x, y, z  * 3

wH nz wt

(5) (6)

where H 0 ( x, y , z , t0 ) is the initial water-level at the point ( x, y , z ) , H 1 ( x, y , z , t ) is the known water-level at the boundary, q ( x, y, z , t ) is the recharge capacity per unit area for the second kind of the boundary conditions, cos  n, x , cos  n, y and

cos  n, z are the directional cosines for the normal of the body surface, P is the saturation deficiency (free surface rise) or the specific yield (free surface drops), nz is the third component of the outward normal vector n = ^nx , n y , nz ` at the free surface, * 1 , * 2

and * 3 are the first kind of the boundary, the second kind of the boundary and the free-water table boundary respectively. 3. Numerical simulation with finite element method 3.1 Finite element equation The three-dimensional computational domain is divided into n units, and the interpolation function of the eight-node isoparametric element is utilized. According to the variational principles, the corresponding functional of the differential Eq.(1) is taken as zero, and time is applied in implicit difference. Then the finite element equation in the seepage domain is

1 1 ª º «¬ K + 't  S + G »¼ H t + 't = F + 't  S + G H t

= H 1 ( x, y , z , t )

 x, y , z  * 1

(4)

(3)

(7) where K is the general seepage matrix, S is the water storage matrix, G is the recharge matrix, F is the water quantity matrix, H is the water level vector of node to be calculated, 't is the time step. Let

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A= K +

1 1  S + G , B = F +  S + G Ht , 't 't

then Eq.(7) can be taken as

AH t + 't = B

(8)

where A is called the total stiffness matrix, and B is called the constant term. 3.2 Treatment of the first kind and free surface boundary conditions In this article, the authors utilize the method of improved cut-off negative pressure[5,6], and select the improving element conduction matrix adjustment method[7,8] to deal with the free surface boundary conditions. The results prove to be satisfactory. It is able to deal with the first kind of boundary conditions by using “putting large number” method, namely the principal diagonal elements of total stiffness matrix which sticks to known water head are put a large number, and then the corresponding elements on the right sides of equations are multiplied by the lager number[8]. 3.3 Solution In this work, the Preconditioned Conjugate Gradient (PCG) method[9,10] is used to solve the above finite element equations. The basic ideas are that the coefficient matrix of symmetric positive definite equations is pretreated in order to reduce the condition number of equivalence, and then the conjugate gradient method is used to enhance the convergence rate and to overcome the numerical instability[11,12]. The computation is translated to computer program with the Visual Fortran 90[13,14]. With the program, the computation was completed by PIV 3.0.

dewatering. The confined aquifers of high head are buried below the base of foundation pit, which are classified as the upper Pleistocene confined aquifers ǿ and ǿǿ, middle Pleistocene confined aquifer ǿǿǿ respectively. The three confined aquifers are connected with each other, and the static water level excavation is approximately –5 m. In order to ensure the smooth progress of the excavation, the water level in the foundation pit must be decreased to below the base of the foundation pit. To ensure the security of surrounding buildings, especially the security of the Linjiang Garden Building, the decrease of the underground water level around the foundation pit should be incapable of causing land subsidence and geologic disasters[15].

Fig.1 Plane distribution of the foundation pit

Fig.2 Finite element meshes

4. Engineering applications 4.1 Engineering situation The forth subway of Dongjiadu tunnel repair foundation is located in the east of the South Zhongshan Road and in the south of Dongjiadu Ferry. The restoration project is located in the west of the Huangpu River and the 22-storey Linjiang Garden Building is in its north, and the ground elevation is about 3.5 m. The excavation is approximately 39.8 m in depth, the excavating scale on the plane is 236 m in length and 19 m-23 m in width and the distribution of the foundation is a circular arch,with the radius 350 m. Figure 1 shows the plane distribution of the foundation pit. The retaining wall of foundation pit shield is designed with a thickness of 1.2 m, and the weak phreatic aquifer is distributed below the miscellaneous fill in the upper part of the foundation. The groundwater level is from 0.5 m to1.2 m, and it is not rich in water quantity and not easy to cause

4.2 Spatial discretization and boundary conditions To overcome the capriciousness of results caused by the uncertainty of the boundary, according to the principle that boundary of constant head should be far away from the source and sink term, this calculation takes furthest border points in the east, west, south and north of the entire foundation as starting points by using a trial-and-error procedure, and expands outward about 400 m in each direction, namely the actual plane size is 1060 m2×870 m2 , all around are treated as boundary of constant head, and the sea level of the foundation center is taken as the origin of coordinates. According to the hydrogeologic characteristics of the study area and in order to meet the requirements of the retaining wall of foundation pit shield and the filters of pump wells, quaternary loose sediments entirely is divided into 10 layers vertically, and partition in the horizontal direction

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becomes sparse gradually from the foundation center to the outward, which can be seen in Fig.2. The finite element mesh is subdivided into a total of 16280 nodes and 13980 units.

Fig.3

head tends to be in accordance with those of the observed head. Therefore, this model can be used to simulate and forecast.

Schematic of the wells distribution in parameterregulating model

4.3 Identification and verification of model The water level descending period of six pump wells labeled as W23, W24, W25, W26, W27 and W28 was selected for the model identification, which was from 21:15 on January 24, 2006 to 19:38 on January 29, 2006, and the recovery period was for the model confirmation, which was from 19:38 on January 29, 2006 to 14:06 on February 1, 2006 when pumping water was stopped. The whole process was divided into five stress periods, and every one was also divided into several steps. Other layers except Layers1, 2 and 10 had water lever observation wells used for fitting, the filters of water level observation holes outside the foundation pit, namely Q11, Q9, Q7, Q5, Q3 and Q1 were located in the Layers 3, 4, 5(6), 7, 8 and 9 of the model separately, and the filters of water level observation holes W17, W19, W21, W22, B5 and B6 in the foundation were located in the Layers 5(6). Figure 3 shows the plane distribution drawing of pump wells and observation wells. Based on the water level fitting of the twelve observation holes mentioned above, the hydrogeologic parameters of various aquifer are obtained. Layers 5 and 6 where the pump well filters are set are in the same parameter zone, which is divided into seven parameter zones respectively, the Layers 4 and 8 are divided into two parameter zones respectively, and the Layer 7 is into four, while others are in a parameter zone respectively. The parameter values of every parameter zone can be seen in detail in Table 1. The fitting precision for groundwater table of the observation holes W17 in the foundation pit and Q11 outside the foundation pit is shown in Fig.4. The hydrogeologic parameters zoning map of Layer 5 is shown in Fig.5. According to the fitting results, the general changes of the calculated

Fig.4 Water level fitting map of observation points

Fig.5 Hydrological parameters zoning map for Layer 5

Fig.6 Distribution map of wells in the optimization program of dewatering

4.4 Model forecast According to the above mathematical model after identification and verification, the optimum design of dewatering of the forth subway of Dongjiadu tunnel repair foundation pit in Shanghai was performed. In view of economy and technique, the final optimization program of dewatering was obtained by simulation

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Table 1 Hydrological parameters zoning of every layer in the model Layer number

Zone number

Kxx (m/d)

Kyx (m/d)

Kzz (m/d)

SS (m-1)

ȝ

1

1

1×10-5

1×10-5

1×10-6

1×10-9

0.0005

2

2

1×10-5

1×10-5

1×10-6

1×10-9

0.0005

3

3

6

6

0.6

3×10-6

0.15

4

8

8

0.8

5×10-6

0.15

11

7

7

0.7

8×10-5

0.15

5

9

9

0.9

3×10-4

0.15

12

3

3

0.3

7×10-5

0.15

13

1

1

0.06

9×10-5

0.15

14

1.5

1.5

0.08

1×10-4

0.15

15

2

2

0.07

1.5×10-4

0.15

16

11

11

1.1

1×10-4

0.15

17

20

20

2

7×10-4

0.15

7

7

7

0.7

5×10-6

0.15

18

1

1

0.06

1×10-4

0.15

19

9

9

0.9

2×10-4

0.15

20

15

15

1.5

2×10-4

0.15

8

9

9

0.9

8×10-5

0.15

21

6

6

0.6

8×10-5

0.15

9

9

7

7

2

5×10-6

0.15

10

10

10

10

0.8

8×10-6

0.15

Continuous wall

6

1×10-10

1×10-10

1×10-11

1×10-15

1×10-11

4

5(6)

7

8

and comparison analysis for different programs, which shows that a total of 25 wells will be required, the distribution of wells can be seen in Fig.6, and the pump discharge of each well can be seen in Table 2. The filters of the pump wells are set between 44 m to 59 m, the retaining wall of foundation pit shield goes deep to 65 m (see Fig.7). After 30 d of dewatering, the water level in foundation pit will fall down to below  38.8 m (42.25 m in the burial depth), so that the demand of dewatering can be met, and the maximum

decrease of water level outside the foundation pit will be 3 m, which is incapable of causing destructive land subsidence based on the existing experience in Shanghai. Figure 8 shows the plane water level isogram map of the bottom of the foundation pit (Layer 4 in the model) after 30 d of dewatering, and Fig.9 gives the section water level isogram map at the center of the foundation pit in the Y direction after 30 d of dewatering. By the verification of follow-up project, it is

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Table 2 Pump discharge of each well in the optimization program of dewatering Pump well number

Pumping quantity of single well (m3/d)

Pump well number

Pumping quantity of single well (m3/d)

P1

 150

P14

 300

P2

 150

P15

 300

P3

 150

P16

 300

P4

 100

P17

 300

P5

 90

P18

 300

P6

 90

P19

 300

P7

 105

P20

 300

P8

 320

P21

 300

P9

 320

P22

 300

P10

 310

P23

 300

P11

 330

P24

 300

P12

 310

P25

 300

P13

 330 shown that the above optimization program and the practical case are consistent with each other, so it is effective to control the land subsidence and geologic disasters around the foundation pit. According to observation by the follow-up project, the maximum land subsidence outside the foundation pit is only 3.5 mm, which guarantee the security of the Linjiang Garden Building effectively.

Fig.8 Plane water level isogram map of the bottom of the foundation (Layer 4 in the model)after 30 d of dewatering (unit: m) Fig.7 The schematic of dewatering engineering structures

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Fig.9

The section water level isogram map of the center of the foundation pit in the Y direction after 30 d of dewatering (unit: m)

5. Conclusions (1) The three-dimensional finite element numerical simulation method has a good quality to portray the geologic body, and can be used to simulate and analyze complex quaternary loose sediments with great thickness and the engineering structures of dewatering in deep foundation pit, and can serve as the basic theory of optimization design of engineering structures of dewatering in deep foundation pit in such areas. (2) Improving element conduction matrix adjustment method has been used to deal with the free-water table boundary condition, which could improve the stability of the model. (3) If it can deal well with the relation between the diaphragm wall of basic pit maintenance and the location of the filters of the pump wells, the foundation pit dewatering method can be used to meet the demand of foundation pit dewatering, and can effectively control land subsidence around the foundation pit in the area of complex quaternary loose sediments with great thickness.

[6]

[7] [8]

[9]

[10]

[11]

[12]

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