Advanced finite element analysis of a complex deep excavation case history in Shanghai

Abstract

The construction of the North Square Shopping Center of the Shanghai South Railway Station is a large scale complex top-down deep excavation project. The excavation is adjacent to several current and newly planned Metro lines, and influenced by a neighboring Exchange Station excavation. The highly irregular geometry of this excavation greatly increases the complexity in 3D Finite Element modeling. The advanced numerical modeling described in this paper includes detailed structural and geotechnical behavior. Important features are considered in the analysis, e.g., 1) the small-strain stiffness of the soil, 2) the construction joints in the diaphragm wall, 3) the shrinkage in the concrete floor slabs and beams, 4) the complex construction sequences, and 5) the shape effect of the deep excavation. The numerical results agree well with the field data, and some valuable conclusions are generated.

Keywords

advanced finite element analysis / deep excavations / case history / small-strain stiffness

Introduction

Deep excavation is a very complex soil-structure interaction problem. Its mechanism, however, could be studied by Finite Element analysis which is an effective tool to simulate detailed structures and complex construction sequences. In addition, the reliable material behavior could be straightforwardly considered in the analysis.

A number of deep excavation case histories have been reported all over the world, but detailed Finite Element analyses of those cases are rarely seen in the publications. Several researchers [1-5] have conducted simplified 2D or 3D analyses, and shown useful results. However, some important features are not included in their analyses, e.g., irregular geometries, detailed retaining structures, complex construction sequences, thermal effect of concrete structure components.

Advanced numerical analyses should consider accurate model for structural and geotechnical behavior, e.g., 1) detailed structures; 2) correct construction sequence; 3) reliable material models and input parameters.

The excavation of North Square Shopping Centre of Shanghai South Railway Station is a large scale complex deep excavation project using top-down construction method [6,7]. The construction started in 2005 and last for 2 years. It has several distinctive features: 1) Close to adjacent infrastructure, 2) irregular geometry, 3) large openings in floor slabs, 4) complex construction sequence, 5) affected by the neighboring excavation. It is, therefore, an ideal case history to investigate those features through advanced finite element analysis. The excavation was carefully monitored during the construction process, with well documented field date available which can be used for calibration of the numerical analyses.

A 3D Finite Element model was created in ABAQUS 6.11, a commercial finite element software for general purposes, to investigate the excavation behavior. A number of important features are considered in the analysis, e.g., 1) the small-strain stiffness nonlinearity of the soil, 2) the construction joints in the diaphragm wall, 3) the shrinkage in the concrete floor slabs and beams, 4) the complex construction sequences, and 5) the shape effect of the deep excavation. The numerical result is compared with the field data, and some valuable conclusions are generated.

Case history description

General description

The North Square Shopping Centre, as shown in Fig. 1, is part of the Shanghai South Railway Station project which is designed to increase the transportation capacity of the existing passenger terminals. The new station combines the subway, light rail transit system, public transportation, elevated freeway, and passenger station systematically. The excavation is 12.5 m deep, and covers an area of around 40,000 m². The main structure has two basement levels, with a pile-raft foundation. Three current or new Metro Lines are close to the excavation, which requires a high standard of construction.

Soil properties

The subsoil of Shanghai is composed of Quaternary sediments of the Yangtze River estuary which consist of clay, loam, silt and sand, the different deposits being the final result of the variation from an estuarine to fluviatile sedimentation process [8].

The site is underlain by typical Shanghai alluvial soft clay which is normally consolidated, with high water content, high compressibility, low shear strength, and low ground bearing capacity. The geological profile and soil properties from the site investigation report are shown in Fig. 2. However, it is noted that such information is not sufficient for derivation of the input parameters for the advanced soil model used in this paper, e.g., small-strain stiffness nonlinearity of the soil. Therefore, further data are collected from publications about Shanghai clay which is described later in this paper.

Retaining system

The retaining structure of the excavation in cross section A-A (see Fig. 1) is shown in Fig. 3. It has two levels of floor slabs, supported by horizontal beams and vertical piles and columns. There is a slope on the top level of the floor slab close to the main station. The diaphragm wall is 0.8 m thick, 28 m deep. The wall panels are between 4 to 6 m wide, with joints. The steel lattice columns are embedded into the bored piles (ø700 mm). The length of the column-pile is 54 m. After the final stage of excavation, a concrete bottom slab (1m thick) is cast in place.

The concrete floor slabs are supported by concrete grid beams, as shown in Fig. 4. Large openings are designed in the floor slabs to transfer the excavated soils and improve the lighting and ventilation conditions. This, however, also weakens the stiffness of the supporting system. The influence of the opening accesses on the excavation behavior is not going to be discussed in this paper, but will appear in other publications of the authors.

Construction sequence

The construction sequence of the excavation is described in Table 1. The numerical analysis follows closely to this sequence. The influence of construction sequences on the excavation behavior is not discussed in this paper.

Instrumentations

The excavation was carefully monitored during the construction process to understand its performance and make sure its safety. The items measured, as shown in Fig. 1, include the wall deflection, the ground surface settlement outside the excavation, the sublayer soil lateral movement outside the excavation, the vertical displacement at the top of the diaphragm wall, and vertical displacement of the piles and columns. The field data was initially collected and analyzed by Xu [7].

FEM model description and input parameters

FEM model description

The geometry of this deep excavation is extremely irregular and the construction sequence is sophisticated. A fully 3D FEM model, therefore, was created using ABAQUS 6.11 to investigate the performance of this large scale complex deep excavation. The model considers the detailed retaining structures (e.g., the diaphragm wall, piles, columns, beams, floor slabs), adjacent Exchange Station excavations, zoned construction sequence, berms, slop and opening accesses in the floor slabs, and the construction joints in the diaphragm wall.

The mesh of the model is shown in Fig. 5. The depth of the model is 80 m. The soil is represented by 8-noded hexahedral elements with reduced integration (C3D8R), due to the large size of the model and limitation of computational resources. Quadratic elements might be more accurate in theory compared to linear elements, but the running time and computational resources will increase significantly because of the increased number of nodes and integration points. In addition, the difference between the computed results could be neglected based on some initial sensitivity studies of this problem. Four vertical sides are roller boundaries. The bottom is fixed.

The diaphragm wall, as shown in Fig. 6, is modeled with 8-noded hexahedral element with reduced integration (C3D8R). Two layers of elements are generated along the thickness. Shell element is also suitable to model the diaphragm wall, but it should be noticed that the computed wall deflection and ground movement are larger from shell element wall compared to the solid element wall [5,9,10]. Interface properties between the soil and diaphragm wall were not considered in this analysis due to the complexity of its mechanism and associated numerical problems in the computation. Therefore, rough condition was assumed at the interface between the soil and the diaphragm wall.

Details of the supporting system are shown in Fig. 7. The floor slabs are modeled with 4-noded shell elements (S4). The beams and piles are modeled with 2-noded beam elements (B31). Tie constraints are used to model the connection between piles, beams and floor slabs. Opening accesses are considered in the model. The piles are embedded into the soil. The interface property between the pile and soil is not considered in this analysis. The floor slabs are also tied with the diaphragm wall at the retained level for simplicity, although in reality the connection between floor slabs and the diaphragm wall might not be rigid because rotation might be allowed and gap might exist.

Input material properties

The soil

The soil is represented by a multi-yield surface soil model [11] which is developed in Oxford to consider the small-strain stiffness nonlinearity of the soil. This multiple yield surface model is formulated within the framework of work-hardening plasticity theory. It takes into account the nonlinear behavior of soil at small strains, and also includes effects such as hysteresis and dependence of stiffness on recent history. Nonlinearity of the small-strain response is achieved using a number of nested yield surfaces of the same shape as the outer fixed surface, as shown in Fig. 8. Totally ten yield surfaces are used in this paper, in balance between the accuracy and computational efficiency.

A previous use of this nested yield surface model in tunnelling installation is described in Burd et al. [12]. For the current analysis, this model has been implemented into ABAQUS via the subroutine UMAT [13]. This model is expressed with total stress, and used in undrained conditions. Therefore, the pore pressure is not included in the analysis. The input parameters include the undrained shear strength S_u, shear stiffness G, the bulk stiffness K\approx \mathrm{50}G, and a set of ratio parameters for the inner nested yield surfaces which are derived from the S-shaped small-strain stiffness curve.

The undrained shear strength S_u, expressed as Eq. (1), increases linearly with ground depth z.

(1)s_{\mathrm{u}}=(\mathrm{20}+\mathrm{2}z)\mathrm{k}\mathrm{P}\mathrm{a}\mathrm{.}

The stiffness at very small strain G₀, expressed as Eq. (2), also increases linearly with depth.

(2)G_{\mathrm{0}}=(\mathrm{20}+\mathrm{2}z)\mathrm{M}\mathrm{P}\mathrm{a}\mathrm{.}

The small strain stiffness parameters for the advanced soil model are derived from Eq. (3).

(3){\displaystyle \frac{G}{G_{\mathrm{0}}}}={\displaystyle \frac{\mathrm{1}}{\mathrm{1}+\mathrm{9.2}{\left({\displaystyle \frac{\gamma }{\mathrm{0.475}\%}}\right)}^{\mathrm{1.34}}}}.

where G is the shear stiffness, γ is shear strain.

The above equations are derived from laboratory experiment and in situ test data collected from publications about Shanghai clay. The detailed derivation process is not included in this paper but is shown other publications of the authors.

Based on Eq. (3), a normalized curve is plotted in Fig. 9, in which both the shear stiffness G and shear strain \gammaare normalized because it is believed that this expression has advantages in physical meaning.

The diaphragm wall

The diaphragm wall is modeled as an anisotropic linear elastic material to consider the construction joints between wall panels. The elastic stiffness value is adopted as the design value for concrete, E = 30 GPa, v = 0.2. The anisotropic stiffness ratio between the out-of-plane and in-plane stiffness E_out/E_in = 0.1 is used based on the previous back analysis of some deep excavation case histories.

The beams and floor slabs

The concrete beams and slabs are modeled as linear elastic materials. The thermal effect is included to consider the concrete shrinkage during the curing process, E = 30 GPa, v = 0.2, α = 10^-5 °C. In the bottom-up area and the exchange station area, the struts are steel pipes with the steel elastic properties E = 210 GPa, v = 0.3.

Results

There are a large amount of data from both field measurement and numerical analysis. To present the data in a systematic way, only selected results from the final stage of the excavation are shown below. The results include the wall deflections, ground surface settlement outside the excavation, and sublayer soil lateral displacement outside the excavation. The computed results are compared with the field data.

Wall deflection

The wall deflections at two most dangerous points, I-6 and I-25 (see Fig. 1), are shown in Fig. 10.

The largest wall deflections from the numerical result agree well with the field data, although they happen at a slightly higher level. Moreover, the wall deflection at the wall top is larger than the field data, and it might be that the shrinkage of the top concrete slab is large in the numerical analysis. The wall deflection at point I-25 has relatively large discrepancy between the computed result and field data, and it is worth doing more analysis to investigate the reason.

Ground settlement

The predicted ground settlement pattern along BC (see Fig. 1), as shown in Fig. 11, agrees well with the field data. However, the numerical result predicts slightly larger ground settlement close to the Exchange Station (B), and smaller result on the other side (C).This might be caused by the complex shape of the excavation.

Soil deflection

The sublayer soil lateral movement at IT10 (see Fig. 1), as shown in Fig. 12, is smaller than the adjacent wall deflection at I-25. The numerical result indicates larger movement than the field data. This might be because the soil behavior is more difficult to predict. Another reason could be that the point selected from the model is closer to the wall due to the mesh generation.

Contour display

The ground vertical displacement contour is shown in Fig. 13. The ground settles outside the excavation and the settlement concentrates behind the center of the wall, whereas inside the excavation the ground moves upwards due to stress relief. This trend is captured because the small-strain nonlinearity of the soil is considered in the analysis.

The deflection pattern of the diaphragm wall is shown in Fig. 14. It can be seen that the spatial distribution of the displacement. The displacement is larger at the wall center, while smaller at the wall corner. The 3D effect is quite obvious.

The displacement pattern of the retaining system is shown in Fig. 15. Although the displacement of the retaining system is not the main focus of the field measurement and such data are normally not available, the numerical analysis could provide such information which is the advantage of the numerical analysis.

Conclusions

The advanced FE analysis captures this complex deep excavation behavior well. This is attributed to the detailed structural and geotechnical analysis, including, 1) small-strain stiffness of the soil and reliable soil properties, 2) joints in the diaphragm wall, 3) the thermal shrinkage of the concrete floor slabs, iv) the opening accesses in the floor slabs, and v) the construction sequences.

Discrepancies exist between numerical results and field data, and this might be caused by the complexity and uncertainty of 1) the construction activities of the project, 2) the soil behavior, 3) the structure performance. The numerical analysis could not consider all those factors. Once more reliable analytical procedures and material models are adopted; the accuracy of numerical analysis would be improved.

More useful results and conclusions from this case study are beyond the scope of this paper.

References

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