Chapter 3 Case Histories
3.1 Case A
3.1.1 Project overview
Case A locates at Da-an District of Taipei City, and details of project can be found in Hsieh et al. (2017). Case A project is a 17-story office building with 4 levels of basement. The excavation zone is a polygon with a maximum length and width of 40 m and 38 m, respectively. The excavation was carried out using the bottom-up method in 6 excavation stages, and the excavation depth was 17.1 m.
Since the excavation site is located in Taipei, the subsurface consists mostly of clayey soil. The soil stratigraphy of the site consists of eight soil layers underlain by a dense gravel layer at a depth of 56.1 m. The top layer is a 3.5-m thick clay layer. The second layer is a 5.8-m silty sand with a SPT-N value of 8. The third layer is a 14.9-m thick clay layer. The undrained shear strength (𝑠𝑢 ) of the third layer is considered to increase with the effective overburden pressure (𝜎𝑣′), and a ratio of 0.18 is used between
𝑠𝑢 and 𝜎𝑣′ , i.e., 𝑠𝑢 = 0.18𝜎𝑣′ . The ratio is called the undrained shear strength ratio (𝑠𝑢/𝜎𝑣′). The fourth layer is a 6.2-m thick clay with 𝑠𝑢/𝜎𝑣′ = 0.22. The fifth layer is a 2.4-m thick silty sand with a SPT-N value of 9. The sixth layer is a 12.6-m thick clay with
𝑠𝑢/𝜎𝑣′ = 0.25. The seventh layer is a 3-m clay with 𝑠𝑢/𝜎𝑣′ = 0.25. The eighth layer is a 7.7-m clay with 𝑠𝑢/𝜎𝑣′ = 0.28 . Underlain the soft soil layer is a very dense layer comprises mainly of sandy gravel with a SPT-N value of more than 100. The simplified
soil profile and soil parameters are presented in Table 3.1 and Table 3.2, respectively. The ground water level was at 2 m below the ground surface.
The diaphragm wall was 0.8 m in thickness and 34 m in depth together with five levels of H-steel bracing as the retaining system. The typical horizontal spacing of H-steel bracing is 6 m, and each level of bracing was preloaded to 50% of its allowable axial capacity. The horizontal bracings were installed stage by stage in a bottom-up excavation scheme and pre-stressed to design values immediately after installation. Auxiliary measure in the form of cross walls were adopted to reduce the wall deflection. Depth of the cross wall extended from GL. 0 m to GL. -34 m. The cross walls above the excavation surface would be removed by step-by-step excavation. There were six inclinometer casings installed in the perimeter diaphragm wall to monitor the wall deflection for each excavation stage. The layout of 4 cross walls and 6 inclinometer casings are shown in Figure 3.1. The excavation sequence of Case A is shown in Figure 3.2, including the sizes and preloads of horizontal struts.
3.1.2 PLAXIS simulation
1. Boundary condition
For the domain of the analysis model, there are two methods to calculate the domain size in the finite element software PLAXIS 3D. One is that the boundary of the domain in x-direction and y-direction extended seven times of the excavation depth suggested by
Khoiri and Ou (2013). As shown in Figure 3.3, a full model was established, including the whole analysis domain and the excavation model. In Case A, the domain size is 400 m by 400 m, it is about eleven times of the excavation depth.
2. Soil parameters
The Mohr-Coulomb Model was used in the numerical analyses with the parameters listed in Table 3.1 and Table 3.2. An effective stress analysis under drained condition was used for sand layer, while a total stress analysis under undrained condition (Undrained C) was used for clay layer. The undrained condition in Mohr-Coulomb Model has three types, A, B and C, which are used for the undrained or short-term material. Undrained A is performed by the material behavior in which stiffness and strength are defined in terms of effective properties, while Undrained B is performed by the material in which stiffness is defined in terms of effective properties and strength is defined as undrained shear strength. Undrained C is performed by the material behavior in which stiffness and strength are defined in terms of undrained properties. In the drained condition, the material parameters for the Mohr-Coulomb Model are the effective Young’s modulus (𝐸′), effective Poisson ratio (𝜈′), effective cohesion (𝑐′) and effective friction angle (𝜙′). The effective Young’s modulus of sand layer was determined by the following empirical equation, which was suggested by Hsiung (2009).
𝐸′ = 2000𝑁 (kPa)
where N is the blow count of standard penetration test (SPT). For Undrained C of undrained condition, the parameters required are the undrained Young’s modulus (𝐸𝑢), undrained Poisson ratio (𝜈𝑢), undrained shear strength (𝑠𝑢) and friction angle (𝜙𝑢 = 0).
The undrained Young’s modulus of clay layer was obtained by the following empirical equation reported by Bowles (1996), Lim et al. (2010), Likitlersuang et al. (2013), Khoiri and Ou (2013).
𝐸𝑢 = 500𝑠𝑢 (kPa)
3. Structural parameters
Table 3.3 and Table 3.4 list the input parameters of the diaphragm wall, cross wall and floor slabs. Diaphragm wall, cross wall and floor slabs are regarded as plate elements in PLAXIS 3D. The Young’s modulus of diaphragm wall, cross wall and floor slabs are estimated as suggested by ACI code or Construction and Planning Agency, MOI (2011):
𝐸 = 4700√𝑓𝑐′ (MPa)
𝐸 = 15000√𝑓𝑐′ (kgf/cm2)
where 𝑓𝑐′ is the compressive strength of the concrete.
Table 3.5 shows the input parameters of the H-steel bracing. In the numerical analyses, the H-steel bracings are regarded as node-to-node anchor elements. According to the AISC standard or Construction and Planning Agency, MOI (2011), the Young’s modulus of the H-steel is 2.04 × 106 (kgf/cm2).
3.1.3 Comparison of results
In Case A, there are a total of four cross walls within the excavation zone. It is obvious that the wall deflection would be larger than the excavation with cross walls if the cross walls are ignored in numerical analysis. Situations with and without cross walls are both analyzed by the numerical code PLAXIS 3D. Figure 3.4 summarizes all results including field observations, numerical results with and without cross walls. The red and blue curves respectively represent the wall displacements with and without the effect of cross walls, and the blue curve exhibits larger wall deflection than the others. The diaphragm wall deflection would be pronouncedly refrained if the cross walls are implemented in the numerical model. The effect of cross walls on the suppression of wall deflection is obvious once the two numerical results are compared.
Table 3.6 and Figure 3.5 compare the maximum wall displacements including field data, two numerical results and the predictions by Clough’s chart. The predictions from Clough’s chart overestimate the wall displacements compared with the field performance and numerical results. Essentially, the numerical results without cross wall should be similar to the estimated results by Clough’s chart. However, there is an obvious difference between these two results. The difference could be attributed to the three-dimensional effect in the excavation zone, which could not be reflected by Clough’s chart.