Soil arching effect of Lattice-Shaped Diaphragm Wall as bridge foundation

Abstract

As a new type of bridge foundation, Lattice-Shaped Diaphragm Wall (hereinafter for LSDW) is highly concerned in relevant construction area but its research is far from achievement. Based on PFC^2D, the soil arching effect of LSDWs is studied thoroughly in this paper and the special attention is given to its influencing factors. It turns out to be that a differential wall-soil settlement can be found at the lower location of soil core of an LSDW which is one of the trigger factors of soil arching; meanwhile, the differential settlement degree can reflect the exertion degree of soil arching; the shape of soil arching is basically a hemisphere which can be explained by the theory proposed by Hewlett and Randolph; normally, the chamber number is a negative factor for the development of soil arching; the soil arching effect is significantly influenced by the distance of two adjacent wall elements and the foundation depth, and a relatively large or small value of these factors is disadvantageous to the exertion of soil arching; in addition, the soil arching effect increase with the growth of stiffness and friction coefficient of particles and the friction coefficient of particles has insignificant influence on the development of soil arching effect compared with particle stiffness.

Keywords

LSDW / soil arching / PFC ^2D / shape of soil arching / influencing factors

Introduction

Lattice Shaped Diaphragm Wall (hereinafter for LSDW) is a new type of bridge foundation composed of a cap and diaphragm walls [1,2], as shown in Fig. 1. The diaphragm walls under the cap are connected with rigid joints that form a rectangular frame or a frame with multi-chambers in horizontal section [3]. With the properties of high construction efficiency, low cost, small noise and great rigidity, LSDW is especially suitable for being used as the large-span bridge foundations [4].

As a new type of bridge foundation, LSDW is highly concerned in relevant construction area but its research is far from achievement. Wen et al. [1] have studied the diaphragm wall-soil-cap interaction in rectangular closed diaphragm wall through a model test. It was observed that the effects of the cap and the soil resistance under the cap should not be ignored in bearing capacity calculations due to the load shearing percentage of soil resistance under the cap can be 10%~20%. Based on lateral static tests on three single-chamber model walls with different sizes, the bearing characteristic of closed diaphragm wall foundation as well as single traditional diaphragm wall were investigated [5]. Song et al [6] have performed an in-situ static vertical loading test of rectangular diaphragm wall in loess subgrade by self-balanced method. According to the testing results and based on the physico-mechanical properties of loess, load transfer characteristics of the rectangular diaphragm wall in loess subgrade were analyzed in detail. In total, the relevant researchers [1,5–7] are mainly concentrated on the bearing behavior of rectangular closed diaphragm wall (namely, LSDW with single chamber see Fig. 1(b)). The studies on the bearing behavior of LSDW with multi-chamber are rare by now.

The wall elements of an LSDW are constructed in turn and can be divided into many segments, and the wall element constructed at the beginning can be termed as the preceding wall element while the subsequently constructed wall element is termed as the following wall element as shown in Fig. 2. It is worthwhile to note that both of the construction process of the preceding wall element and the following wall element consists of four steps. Among these steps, steps 1 and 2 are mainly completed by an excavator.

For an LSDW, soil behavior in the chamber is similar with the soil plug in the pipe pile [8]. For the soil plug in the pipe pile, soil arching can dominate the load transfer mechanism [9]. The soil may not fully fill the chamber due to the soil arching effect [10]. Therefore, the investigation of soil arching effect for LSDW can be useful to figure out its vertical bearing behavior. In this paper, the soil arching effect of LSDW is studied based on PFC^2D thoroughly, and the special attention is given to the influencing factors to soil arching including chamber number and size as well as soil particle parameters. The relevant conclusion can be beneficial for understanding the soil arching of LSDW at micro scale.

Basic example

Establishment of numerical models

In this paper, three models including LSDW with single chamber (hereinafter for LSDW-1), LSDW with two chambers (hereinafter for LSDW-2) and LSDW with three chambers (hereinafter for LSDW-3) are established as the basic example by adopting the particle-flow-code software of PFC^2D. Considering that the actual size of the model will produce enormous numbers of particles for PFC^2D, the calculating process normally will have strict requirement on computer performance and can take huge amount of time. Therefore, the analysis of a practical engineering by PFC^2D usually refers to the geotechnical centrifuge test principle to meet the requirement of saving computing time. By reducing the scale of models to produce less number of particles based on the geotechnical centrifuge test principle, Zhou et al [11,12] simulated the failure mode of slope and analyzed a soil nails support excavation successfully. In this paper, the modeling of LSDWs refers these literatures. Namely, the scales of the numerical models are 1/100 of the prototypes, and the gravity is enlarged by 100 times. Meanwhile, the density, inner frictional angle and cohesion of soil remain unchanged.

In order to ensure the aggregation of soil particle with circle shape behave basically the same to the actually soil. The micro parameters of soil particles and the bond parameters between particles should be tested for many times by numerical biaxial compression tests to meet the requirement. Finally, the parameters of soil particles are determined, as listed in Table 1, and the numerical result of biaxial compression test can be found in Fig. 3. Based on the parameters of soil particle, the numerical models for the basic example can be established as shown in Fig. 4.

Results of numerical calculation

(1) Settlement analysis

Based on the built-in fish language, the displacement contour of soil particles for three models under the settlement of 10 mm can be drawn in Fig. 5. In it, the settlement values of particles in different colors can be found in the legend of Fig. 5.

As can be seen from Fig. 5, the settlement of upper soil particles under the cap of three models (LSDW-1, LSDW-2 and LSDW-3) are basically even. However, the settlement of soil particles at lower locations under the cap becomes uneven especially at the bottom of the foundations. Namely, substantial differential wall-soil settlements are generated at the bottom of three models which can offer a favorable condition to the soil arching.

In order to further investigate the differential wall-soil settlement, the differences between wall and soil settlements changing with time step are illustrated in Figure 6. It can be found that the wall-soil differential settlement increases with time steps. Meanwhile, the difference among three curves in Figure 4 during 0~50000 steps is barely small. However, the difference grows with the development of time step. Basically, the wall-soil differential settlement of LSDW-1 is subsequently larger than which of LSDW-2 and LSDW-3. For an LSDW, the stress overlap area will be expanded as the increment of its chamber number. Namely, the growth of chamber number will deepen the group-wall effect of LSDW [3]. This may explain the difference between three curves in Figure 4. In addition, the difference of wall-soil differential settlement for three models may also reflect the different exertion degree of soil arching for three models which will be discussed in the following part in detail.

(2) Analysis of soil arching shape

Studies have shown that the direction line of maximum principal stress traces of soil can be the axial line of soil arching [13,14]. In order to investigate the soil arching shape of LSDW, the maximum principal stress contour of soil particle of LSDW-1 is studied as an example. The installation of measurement circle [15] can measure the normal stresss_x, s_y and shear stress t_xy. Then, the principal stress of soil particles (including the maximum principal stress s₁, the minimum principal stress s₃ and the main direction a₀) can be obtained by the following equations.

(1){\sigma }_{\mathrm{1},\mathrm{3}}={\displaystyle \frac{{\sigma }_x+{\sigma }_y}{\mathrm{2}}}\pm \sqrt{{\left({\displaystyle \frac{{\sigma }_x-{\sigma }_y}{\mathrm{2}}}\right)}^{\mathrm{2}}+{\tau }_{xy}^{\mathrm{2}}}\mathrm{.}

(2){\alpha }_{\mathrm{0}}={\displaystyle \frac{\mathrm{1}}{\mathrm{2}}}\arctan \left({\displaystyle \frac{\mathrm{2}{\tau }_{xy}}{{\sigma }_x-{\sigma }_y}}\right),\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}({\alpha }_{\mathrm{0}}\in \left(-{\displaystyle \frac{\pi }{\mathrm{2}}},{\displaystyle \frac{\pi }{\mathrm{2}}}\right])\mathrm{.}

According to the data of principle stress and direction of soil particles acquired by equations (1) and (2), the distribution of the maximum principal soil stress near the wall end for LSDW-1 is illustrated in Figure 6. In Figure 7, the size of the red cross reflects the value of principal stress and the deflection angle of the red cross represents the direction of principal stress. It can be seen that the soil arching is generated from the depth of 0.365 to 0.375 m along the dotted blue line. The soil arching of LSDW-1 basically appears to be a semicircular shape which agrees well with the theory of semi-spherical model proposed by Hewlett and Randolph [16].

In Fig. 8, the contour of soil principal stress for LSDW-2 is given. It can be seen that there are almost three soil arches are generated around the wall bottom, and all the arches are basically semicircular which is marked with white line in Fig. 8. Therefore, the shape of soil arching is basically a hemisphere which can be explained by the theory proposed by Hewlett and Randolph.

(3) Validation

It should be noted that the soil arching of LSDWs is buried in the deep soil which is quite different from that of pile groups. This makes the monitoring works of soil arching for LSDWs becomes significantly difficult. In order to verify the results obtained from PFC^2D, two 3D models of LSDWs with real size are numerically studied in this paper. The examined examples are two LSDWs (LSDW-1 and LSDW-2), as shown in Fig. 9. It should be noted that the chamber size, wall depth and thickness are basically the same for the two models. The parameters of numerical models and wall-soil interface element are listed in Tables 2 and 3, respectively.

According to the numerical models established in FLAC^3D, the vertical displacement contours of two LSDWs under the maximum 0.1 m settlement can be illustrates in Fig. 10. It can be seen that the settlement of upper soil under the cap of two models (LSDW-1 and LSDW-2) are basically even. However, the settlement of soil at lower locations under the cap becomes uneven especially at the bottom of the foundations. Namely, substantial differential wall-soil settlements are aroused at the bottom of three models which can offer a favorable condition to the soil arching. This phenomenon can also be found in Fig. 5 based on the acquired data of PFC^2D.

In order to compare the results of soil arching shape by FLAC^3D and PFC^2D, the contours of maximum principle stress for two models are superimposed in Figure 11. It can be inferred that the shape of soil arching appears basically to be a hemisphere for LSDW-1 and LSDW-2 which agree well with what reflects in Figs. 7 and 8 based on the results of PFC^2D. Therefore, the result of soil arching effect analyzed by PFC^2D in this paper is basically reliable and can be used as a reference for further study.

Definition of soil arching coefficient

In order to simplify the comparison of soil arching effect for foundations under different conditions, a coefficient,l_tg, is proposed in this paper refers to the concept of soil arching ratio widely used in pile foundation to study soil arching. The soil arching coefficient,l_tg, can be given by the equation (3) as follows.

(3){\lambda }_{tg}={\displaystyle \frac{q_{tx}}{q_{pj}}}={\displaystyle \frac{(q_a\cdot l_a-f_w\cdot l_w-q_b\cdot l_b)/\mathrm{2}{l}_n+\gamma \cdot H}{(q_a\cdot l_a-f_w\cdot l_w)/l_a+\gamma \cdot H}}

In it, q_tx is the average stress of the load undertaken by soil around wall bottom and q_pj is the average stress of the load borne by both soil and wall bottom; q_a is the distributed load acting on the wall top and l_a is the wall width which is illustrated in Figure 12; q_b is the average stress of the load shared by wall bottom and l_b is the total length of wall bottom; f_w is outer skin friction and l_w is the length of side wall; g is the unit weight of soil and H is the wall depth.

According to equation (3), the smaller of l_tg is, the stronger of soil arching will be. In order to simplify the comparison, the soil arching of LSDW is treated as being not happened or corrupted whenl_tg is larger than 0.8.

Influencing factors analysis

Chamber number

In order to investigate the influence of chamber number on the soil arching effect of LSDW, the soil arching coefficients of three basic examples in Section 2 are calculated as shown in Figure 13. It can be seen that the soil arching coefficientl_tg of LSDW-1 is smaller than which of LSDW-2 and LSDW-3 in sequence. According to the definition ofl_tg, the soil arching effect of LSDW-1 is orderly stronger than which of LSDW-2 and LSDW-3 under the same settlement. Therefore, the chamber number is a negative factor to the development of soil arching for an LSDW. The more chamber number is, the harder for the exertion of soil arching for an LSDW will be.

In Section 2.1, the wall-soil differential settlement of LSDW-1 is subsequently larger than which of LSDW-2 and LSDW-3. This result conforms to what expressed in Figure 13. Therefore, the wall-soil differential settlement of LSDW can reflect the exertion degree of soil arching.

Chamber size and wall depth

In Figure 14, the soil arching coefficients of several LSDW-1s with 5 different chamber sizes are demonstrated to figure out the influence of chamber size on the soil arching effect of LSDW.

It can be seen from Figure 14 that the soil arching coefficient of LSDW-1 with 4 m chamber size is orderly larger than which of LSDW-1s with 6 and 8 m chamber size under different settlement. However, the soil arching coefficient of LSDW-1 with 10 m chamber size is smaller than which of LSDW-1 with 12 m. According to equation (3), the exertion degree of soil arching effect for LSDW-1 with 4 m chamber size is the smallest, and is subsequently smaller than which for LSDW-1s with 6 and 8 m chamber size. The exertion degree of soil arching effect for LSDW-1 develops with the increment of chamber size when the distance of two adjacent wall elements is smaller than 10 m. The exertion degree of soil arching effect for LSDW-1 with 10 m chamber size is the largest and is stronger than which for LSDW-1 with 12 m chamber size. Therefore, the soil arching of LSDW is significantly influenced by the distance of two adjacent wall elements, and a relatively large or small value of chamber size is disadvantageous to the exertion of soil arching.

The influence of wall depth on the exertion degree of soil arching is illustrated in Fig. 15. It can be seen that the soil arching coefficient of LSDW-1 with 15 m wall depth is smaller than which of LSDW-1 with 25 m wall depth during the whole loading process. Meanwhile, the soil arching coefficient of LSDW-1 with 25 m wall depth is smaller than which of LSDW-1 with 20 m wall depth. Namely, the exertion degree of soil arching effect for LSDW-1 with 20 m wall depth is orderly larger than which for LSDW-1 with 25 and 15 m wall depth. Therefore, the soil arching of LSDW is significantly influenced by the wall depth, and a relatively large or small value of wall depth is disadvantageous to the exertion of soil arching. In addition, the varying extent of soil arching coefficient for LSDW with small wall depth range (from 15 to 20 m) is larger than which with large wall depth range (from 20 to 25 m). It can be concluded that the exertion degree of soil arching for LSDW is more sensitive in the range of shallow wall depth.

Soil particle parameters

The influence of soil particle parameters (including particle stiffness and friction coefficient) on the exertion degree of soil arching is demonstrated in Fig. 16. It can be seen from Fig. 16(a) that the soil arching coefficient decreases with the increment of particle stiffness especially whenk_n and k_s drop from 5.0×10⁷ N/m to 7.5×10⁷ N/m. The soil arching effect develops with the growth of particle stiffness, but the increasing rate drops significantly.

It can be seen from Fig. 16(b) that the soil arching coefficient decreases with the increment of particle friction coefficient. Namely, the soil arching effect develops with the increment of particle stiffness, but the increasing rate drops is less than which of particle stiffness acting on the soil arching effect of LSDW. Therefore, it can be concluded that the soil arching effect increase with the growth of stiffness and friction coefficient of particles and the friction coefficient of particles has insignificant influence on the development of soil arching effect compared with particle stiffness.

Conclusion

From above investigation, the main conclusions can be summarized as follows:

(1) A differential wall-soil settlement can be found at the lower location of soil core of an LSDW which is one of the trigger factors of soil arching; meanwhile, the differential settlement degree can reflect the exertion degree of soil arching. The shape of soil arching is basically a hemisphere which can be explained by the theory of semi-spherical model proposed by Hewlett and Randolph.

(2) The chamber number is a negative factor for the development of soil arching; the soil arching effect is significantly influenced by the distance of two adjacent wall elements and the foundation depth, and a relatively large or small value of these factors is disadvantageous to the exertion of soil arching. In addition, the exertion degree of soil arching for LSDW is more sensitive in the range of shallow wall depth.

(3) The soil arching effect increase with the growth of stiffness and friction coefficient of particles and the friction coefficient of particles has insignificant influence on the development of soil arching effect compared with particle stiffness.

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