Chapter 3 Case Studies
3.1 Case A
Case A located in Kaohsiung, Taiwan, is a rectangular site with length of 70 m and width of 20 m. The depth of excavation is 16.8 m, implemented by the bottom-up construction method and retained by diaphragm wall with thickness of 0.9 m and 32 m deep. There are 5 stages of excavation and the diaphragm walls were propped by struts at 4 levels. The relative positions of each excavation surfaces, struts, and soil layers are shown in Fig. 3.1, while the soil profile are shown in Table 3.1. There were 4 inclinometers set in the middle of each side of diaphragm wall to monitor the wall deformation, as indicated in Fig. 3.2, and the measurements of inclinometer are shown in Fig. 3.3. Construction site information and in situ measured data in Case A were obtained from Dao (2015).
The raw measured inclinometer data are slopes of diaphragm wall at different depth, and the toes of diaphragm wall were usually adopted as the reference points of the measurements of inclinometers. As can be seen in the Fig.3.3, the deflections of toes are zeros. According to Hwang et al. (2007), the connecting points where the first or
second level of struts jointed the diaphragm wall are more stable than the toe, and they are more suitable to be the reference points of inclinometer measurements. Therefore, the correction method following by Hwang et al. was applied to Case A, shown in the Fig. 3.4.
As can be seen in Table 3.1, soil types of Case A are primarily sand except three thin clayey layers. It is concluded that sandy layers would dominate the behavior of wall deformation in Case A. The Mohr-Coulomb model was used and the parameters of the soil model are listed in Table 3.2 on the basis of Dao (2015). In the Table 3.2, the
where N is the blow number of standard penetration test (SPT). The undrained Young’s modulus of clay layer can be obtained by the following empirical equation as reported by Bowles (1996), Lim et al. (2010), Likitlersuang et al. (2013), Khoiri and Ou (2013).
u
u S
E 500
Three finite element analyses were carried out, including 1 three dimensional model and 2 two dimensional models for different sections, shown in Fig. 3.5. The sections of two dimensional simulations are shown in Fig. 3.5 b, c and d.
According to the displacement result of simulations shown in Fig. 3.6, apparently,
is, the length of diaphragm wall in out-of-plane direction was assumed to be infinite long, the width of excavation, which is the distance of the walls in section in Fig. 3.5 b and c., became one of most important factor affecting the amount of wall deflections.
3.2 Case B
Case B is located in Taipei, Taiwan, with an irregular site shape and was constructed by the top-down method. There are 6 stages of excavation propped struts or floor slabs at 5 level (Fig. 3.7 and Fig. 3.8), and the soil profile is shown in Table 3.3.
The longest side of Case B has a length of 50.5 m with a diaphragm wall thickness of 1 m and depth of 36 m. The excavation was 19.6 m deep. Case B is adjacent to Songshan-Xindan line and Zhonghe-Xinlu line of Taipei MRT system; therefore, the wall deflection was regulated by law strictly. According to “Regulation on Building Restrictions along MRT Facilities”, the excavations near the MRT system must not cause any deflection of tunnel over 20 mm and deformation of rails over 10 mm.
Therefore, Case B used much stiffer retaining system, including 16 wall piles to depth of 45 m, 4 buttress walls and 3 cross walls, as shown in Fig. 3.9.
The construction procedures of Case B are complicated. It was divided into two zones, MRT side and warehouse area (Fig. 3.9), with different excavation procedures shown in Fig. 3.7 and Fig. 3.8. There are 7 inclinometers set on each side of excavation (Fig. 3.9), where the measured deflections of the walls were shown in Fig. 3.10.
According to Hsieh et al. (2016), the diaphragm wall around SID 1 was co-constructed with four wall piles to bear the weight of superstructure, and the four inclined steel columns for the top-down construction method were designed. Therefore, it was observed that the diaphragm wall around SID 1 kept deflecting outward after the first stage of excavation.
In Case B, the Mohr-Coulomb model were used with the parameters listed in Table 3.4. All of the site information and in situ measured data in Case B were provided by Trinity Foundation and Engineering Consultants, Co. Ltd.
In additional to Plaxis 3D analysis, the one-dimensional elastoplastic foundation beams analysis software TORSA (Taiwan Originated Retaining Structure Analysis) was also used.
The results of wall deformations show in Fig. 3.11. The finite element model was simplified for accelerating computation in Case B, i.e. the co-construction of diaphragm wall and wall piles was set vertically, but it can still react to the three dimensional effect.
The measured data shown in Fig. 3.10 and Fig. 3.11 was not corrected due to lack of complete wall deformation data at each construction stage. Therefore, the inclinometer correcting method in Case A cannot be applied here. As mentioned earlier, the diaphragm wall deformed shape can be obtained by inclinometers, but its displacement depends on the reference point we selected. Therefore, the wall deformed curves were shifted to match the toe displacements for the result of TORSA and Plaxis 3D separately, as shown in Fig. 12 and Fig. 13. It can be seen that three dimensional finite element method still works better because the three dimensional effect was involved in
Fig. 3. 1 Cross section of retaining system and soil layers of Case A.
Fig. 3. 2 Plane view of monitoring equipment in Case A.
Fig. 3. 4 Corrected wall deformations obtained by inclinometers in Case A.
Fig. 3. 6 Wall deformations obtained by measurements and simulations in Case A.
Fig. 3. 8 Cross sections of warehouse district retaining system in Case B.
Fig. 3. 10 Wall deformations obtained by inclinometers in Case B.
Fig. 3. 12 Wall deformations shifted to match Plaxis result.
Table 3. 1 Soil profile of Case A.
Depth (m) Soil Type γt (kN/m3) SPT N φ’ (Deg) c (kPa)
0.0-2.0 CL 19.3 6-7 29 28
2.0-6.5 SM 20.9 5-11 32 -
6.5-8.0 CL 19.7 3-4 30 21
8.0-17.0 SM 20.6 5-17 32 -
17.0-23.5 SM 18.6 5-17 32 -
23.5-28.5 SM 19.6 5-17 33 -
28.5-30.5 CL 18.6 11-15 32 84
30.5-42.0 SM 19.6 18-26 34 -
42.0-60.0 SM 19.6 28-42 34 -
Table 3. 2 Soil parameters of Case A for Mohr-Coulomb model.
Depth (m) Soil Type γt (kN/m3) φ’ (Deg) c (kPa) E’ (MPa) υ’ ψ’ (Deg) K0 Su (kPa) Eu (MPa) υu
0.0-2.0 CL 19.3 - - - 28 14 0.495
2.0-6.5 SM 20.9 32 0.5 16 0.3 2 0.47 - - -
6.5-8.0 CL 19.7 - - - 21 10.5 0.495
8.0-17.0 SM 20.6 32 0.5 22 0.3 2 0.47 - - -
17.0-23.5 SM 18.6 32 0.5 22 0.3 2 0.47 - - -
23.5-28.5 SM 19.6 33 0.5 22 0.3 3 0.46 - - -
Table 3. 3 Soil profile of Case B.
Depth (m) Soil Type γt (kN/m3) SPT N φ’ (Deg) c (kPa)
0.0-7.9 CL 18.7 3-7 30 24.5-34.3
7.9-17.1 SM 19.4 11-24 32 -
17.1-20.3 CL 18.9 4-12 30 63.8
20.3-29.3 SM 19.2 10-38 33 -
29.3-39.5 CL/ML 18.6 9-23 32 117.7
39.2-41.4 SM 19.7 22-26 33 -
41.4- GW 21.1 50 38 -
Table 3. 4 Soil parameters of Case B for Mohr-Coulomb model.
Depth (m) Soil Type γt (kN/m3) φ’ (Deg) c (kPa) E’ (MPa) υ’ ψ’ (Deg) Su (kPa) Eu (MPa) υu
0.0-7.9 CL 18.7 30 0 - - - 24.5-34.3 19.6 0.495
7.9-17.1 SM 19.4 32 - 39.2 0.3 2 - - -
17.1-20.3 CL 18.9 30 0 - - - 63.8 34.3 0.495
20.3-29.3 SM 19.2 33 - 49.1 0.3 3 - - -
29.3-39.5 CL/ML 18.6 32 0 - - - 117.7 54.0 0.495
39.2-41.4 SM 19.7 33 - 61.3 0.3 3 - - -
Chapter 4 Geometry Study
Eight factors, including excavation depth, wall depth, thickness of wall, length and width of excavation, difference of water head between inside and outside of excavation, average horizontal and vertical spacing of struts play significant roles in system stiffness of a deep excavation when three dimensional effect is considered.
Except for the factors mentioned above, other factors remained constant during analyses. In all of the geometry study, only single-layered sandy stratum was used and the soil parameters were unchanging. The H beam with dimension of 300 mm 300 mm 10 mm 15 mm was used in each level of struts and pre-stressed to 490.5 kN (compression). The details of soil, wall, and struts parameters are listed in the Table 4.1.
According to Roboski (2004), the boundaries were set ±5He (five times the excavated depth) to eliminate the boundary effect. A denser mesh was used inside the excavation and looser on the outside, on the basis of Ou et al. (1996).
The setting value of each factor was explained in the following section.
4.1 The Geometry Parameters
4.1.1 Excavation Depth (H
e) and Wall Depth (H)
There are two groups, Groups A and B, for different He and H in geometry study.
According to normal depth of excavation for commercial building in Taiwan, excavation depths were set 20 m in Group A. A typical depth excavation for commercial building in Taiwan is around 20 m. The ratio of wall depth to excavation depth in a range usually depends on the soil type of excavation, i.e. 1.7 to 2.0 for sandy soil, 2.2 to 2.5 for clayey soil, and about 1.6 for gravelly layer. Therefore, H was selected to be 40
For the Group B, He = 30 m and H = 60 m were used. This group is used for figuring out the three dimensional effect more comprehensively, though He and H are seldom reaching that value in practice.
4.1.2 Average Horizontal (H
h) and Vertical Spacing of Struts (H
v)
The average vertical spacing of struts (Hv) is related to the number of excavation stages as the level of each strut is normally set 1 m above the previous stage of excavation. Therefore, the number of construction stages depends on Hv. The value of Hv were set as 2.73 m, 3.33 m, 4.29 m for Group A and 2.86 m, 3.33 m, 4 m for Group B.
The average horizontal spacing of struts (Hh) were set to be 4 m, 5 m and 6m for both groups, which are the most common spacing used in Taiwan. Because the length and width of excavation are not always dividable by Hh, the following formula was used to calculate the number of struts needed:
) (Lw Hh floor
N
where N is the number of struts and Lw is the length or width of the excavation, depends on which side is calculated. The operator “floor” is used to round down (L w Hh) to an integer.
The horizontal positions of struts were calculated following the equation.
1
L S N
R
could make S accurate to one decimal point.
As can be seen in the formulae above, the Hh would become Lw/N, but not equal to the Hh set previously. The Hh, after the processes above, is in the range between 2.67 m and 5.92 m for Group A and between 3 m and 5.94 m for Group B.
4.1.3 Maximum Water Head Difference (H
w)
In practice, the ground water table inside the excavation should be maintained about 1 m below the surface of the following excavation. The ground water table is about 2 m to 6 m below the ground surface in Taipei basin; therefore, the lowering of the ground water table inside the excavation is necessary. However, the dewatering would lead to a higher water head difference between the inside and the outside of the excavation, where the large water pressure would have the diaphragm wall deformed.
The final excavation surfaces are 20 m for Group A and 30 m for Group B, while the final ground water tables inside the excavation are 21 m and 31 m, respectively. The ratio of the maximum water head difference to the excavation depth
e w
H
H were selected
to be 0.95, 0.7 and 0.45. To simplify the model, the level of outer ground water table did not drop accordingly during the construction. Instead, it remained constant throughout the entire time.
4.1.4 Thickness of Wall (D)
The thickness of wall, in a typical design, is about 5 percent of the excavation depth. To examine the influence of the wall stiffness to the three dimensional effect, the wall of 0.5 m, 1.8 m and 1.2 m thick were used in the simulations.
4.1.5 Dimensions of Excavation (L and B)
All of the excavation sites in the geometry study were rectangular ones. L is the
dimensional model, the primary and complimentary walls could be switched to obtained more simulation results. In other words, the primary wall is not always the longest one.
It depends on which wall deformation is to be observed, and the complimentary wall is the one next to it.
Lwere set to be 0.5, 0.7, 1.1, 1.3 and 1.7. Therefore, 30 sets of excavation dimensions were determined. Considering the exchange of the primary and complimentary wall,
He
L and BL can vary from 0.29 to 6 and 0.5 to 2, respectively. More details on the dimensions of excavation can be seen in Table 4.2 and Table 4.3.
The factors mentioned above except L and B are shown more briefly in Fig.4.1, and the mesh density of finite element model could be seen in the Fig.4.2.