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Numerical study on the group wall effect of nodular diaphragm wall foundation in high-rise buildings

  • Lijuan Wang , Qihua Zhao EMAIL logo and Jiujiang Wu EMAIL logo
Published/Copyright: November 15, 2023
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Open Geosciences
From the journal Open Geosciences Volume 15 Issue 1

Abstract

As a new type of foundation, the nodular diaphragm wall (N-D wall) has large transverse stiffness and high bearing capacity, with low noise and low vibration, which is suitable for high-rise buildings in cities with limited land area. The reduction coefficient of each load composition under the same displacement conditions and the ABAQUS finite element numerical analysis software are introduced to analyze the group effect of N-D wall foundations. The results show that the compressive group wall effect coefficient is greater than 1, while the uplift group wall effect coefficient is less than 1. Under the same displacement condition, the group effect of the compressive wall is more obvious than that of the uplift wall, and the group effect of the middle wall is more obvious than that of the sidewall. The wall group effect gradually develops downward with the increase in displacement. The ultimate compressive capacity is mainly controlled by the friction resistance, which is especially obvious in the sidewall. The cap resistance load-sharing ratio decreases first and then increases with the settlement. The cap resistance is not evenly distributed, the stress at the corner is the lowest, and the stress is mainly concentrated in the middle. The influence of wall spacing, length, and width on the uplift bearing capacity is highly significant, while the influence of nodular part angle is slightly significant. The influence of wall width, length, and spacing on compressive bearing capacity is highly significant, while the influence of nodular part angle is weak. The influence of nodular part angle on the uplift bearing capacity of group wall foundation is stronger than that of the compressive bearing capacity.

Keywords: N-D wall; wall group effect; numerical simulation; friction resistance; nodular part resistance; cap resistance load-sharing ratio

1 Introduction

The rapid expansion of urban space and population scale promoted the upward development of buildings, which gave birth to a large number of high-rise buildings with a height of more than 100 m. With the action of earthquake and wind load, these high-rise building foundations are facing huge vertical load and overturning moment at the same time, the bearing capacity and stability of the foundation are facing more and more stringent requirements, and the related problems in the project are getting more and more attention. If the design of these building foundations is not reasonable, the bearing capacity and stability of the foundation are insufficient, which will cause the deformation and cracking of the superstructure, and eventually lead to destruction. In addition, the traditional pile foundation construction needs to occupy a large space, which often has a great impact on neighboring projects, and it is difficult to construct for some projects with narrow space. Therefore, in the urban space environment with tight site, other more appropriate forms of infrastructure are needed.

As we all know, the underground diaphragm wall foundation has large transverse stiffness and high bearing capacity [1–5], with low noise and low vibration, which is suitable for high-rise construction projects in cities with limited land area [2,3]. However, the uplift capacity of traditional diaphragm wall foundation is not good enough. In order to remedy this defect, Japanese scholars proposed a new foundation form of the N-D wall foundation, which was successfully applied in Tokyo Sky Tree Project, as shown in Figure 1, and is gradually being popularized in other anti-uplift and anti-floating engineering fields [4,5]. Compared with the traditional pile (underground diaphragm wall) foundation, the nodular part can greatly improve the bearing capacity of the N-D wall foundation, so as to reduce the cross-section and volume of the foundation, and finally shorten the construction period of the foundation by 20% and the maximum reduction of earthwork excavation by 30% [6].

Figure 1 Application example of the N-D wall foundation [2]: (a) Tokyo Sky Tree, (b) foundation structure, and (c) tower foundation plan.
Figure 1

Application example of the N-D wall foundation [2]: (a) Tokyo Sky Tree, (b) foundation structure, and (c) tower foundation plan.

The N-D wall refers to the underground continuous wall foundation composed of the middle nodular part (mobilizing the bearing capacity of the middle soil layer with good soil quality) and the bottom nodular part (mobilizing the bearing capacity of the end layer), as shown in Figure 2 [6]. Due to the existence of the nodular parts, the load transfer mechanism of the N-D wall is similar to that of the nodular pile (nonuniform section pile foundation with nodular part); thus, the research on the N-D wall can refer to the relevant research results of the nodular pile.

Figure 2 Single N-D wall.
Figure 2

Single N-D wall.

Many studies have shown that nodular piles have a higher vertical bearing capacity than circular piles with uniform sections [7–12]. This occurs because the nodular part compresses the soil, which compacts the soil around the pile. In addition, the vertical bearing force of the nodular part increases the additional stress of the soil and finally increases the shear strength of the soil around the pile [13]. At the same time, the bottom nodular part can share part of the bottom resistance, which improves the bearing capacity of the foundation. Different from the load transfer mechanism of the circular pile with a uniform section, the nodular part has a greater influence on the friction resistance [14]. When the diameter of the circular pile with a uniform section is the same as that of the nodular part, the friction resistance of the nodular pile is 2.5–5.0 times greater than that of the circular pile. At the same time, because gravel can be filled around the nodular pile, its drainage performance is better, which improves the anti-liquefaction performance of the foundation. In order to compare the bearing difference between ordinary pipe piles and nodular piles, Zhang [15] carried out a vertical force comparison test, and the test results showed that nodular piles had the characteristics of friction piles, and their side friction resistance was significantly greater than that of ordinary pipe piles. The ultimate compressive bearing capacity of nodular piles increased by 20% and the ultimate pulling capacity of nodular piles increased by 60% compared with ordinary pipe piles. Phutthananon et al. [16] studied the bearing capacity and load transfer mechanism of pre-bored grouting planted nodular pile using field tests and numerical analysis and compared them with bored pile. The results show that the bearing capacity of pre-bored grouting planted nodular pile is higher than that of bored pile, and the deformation of the pile body mainly takes into account the deformation of prefabricated pile. The existence of nodular part is conducive to improving the bearing performance of the pile type. At the same time, it is found that pre-bored grouting planted nodular pile also plays a positive role in the effectiveness of side friction resistance. Using ABAQUS finite element software, Chen et al. [17] concluded that the compression performance of statically drilled rooted bamboo piles was better than the uplift performance, which was due to the fact that the bamboo nodulars could not directly contact the soil and could not share the load. In addition, the friction resistance between the non-nodular soil and the soil only transferred the shear stress but did not share the upper load.

Both underground diaphragm walls and pile foundations are often not single walls (piles) but a variety of combination forms [18]. Cap – soil – wall (pile) influence each other, and each shares a certain proportion load, cobearing the load; the bearing mechanism will be different from a single structure; the foundation bearing capacity is not equal to the simple sum of individual capacities. At the same time, the wall friction resistance and bottom resistance downward diffusion increase the settlement of the foundation; therefore, the wall group effect cannot be ignored in foundation design calculations. Yang et al. [19] found that the pile group effect has a great influence when the spacing of the pile group is less than three times the diameter of the section of the pile group. Zhou [20] studied the wall group effect of uplift resistance of soil at the bottom of expansion using the particle flow numerical simulation, and the conclusion was that when the uplift value is small (s/D < 0.1, “s” is the displacement value, and “D” is the pile diameter), the wall group effect is not clear. With the increase in uplift displacement, the bottom nodular part resistance of the pile group is less than that of a single pile, indicating that the pile group effect begins to appear. When the displacement value s/D is less than 0.5, the uplift resistance of the central pile is slightly larger than that of the side pile. When the displacement value s/D is greater than 0.5, the uplift resistance of the side pile is greater than that of the center pile. Using the static load test of a variable diameter nodular pile, Gong et al. [21] found that the upper friction resistance of a single pile in a composite foundation was smaller than that of a free single pile, while the lower friction resistance was larger than that of a free single pile. According to the vertical stress model test of a wedge pile group with an enlarged bottom, Wu et al. [22] found that the pile group effect coefficients were 0.95 and 0.88 when the cap was low. In theoretical calculations, the effect coefficient of a wedge pile group with an expanded bottom can be determined by referring to the uniform section pile code. Sun and Zhu [23] adopted a model test to test the stress and settlement of the wall and the surrounding soil of an underground continuous wall with four different shapes of “—,” “L,” and “+” types under vertical load, analyzed the wall group effect, and explored the mechanism of the wall group effect. Wang [24] conducted a model test on a rectangular closed wall foundation with a homemade lever loading device and studied the development of the interaction vertical bearing characteristics of the wall–soil–cap and negative friction resistance as well as the wall group effect. The experimental results show that the efficiency and load-bearing performance of the wall group can be effectively improved by appropriately increasing the inner side length of the closed connected wall foundation under the condition of keeping the wall height and thickness unchanged. Huo et al. [25] found using a model test of a grated underground diaphragm wall that compared with the size of cells, the number of cells has a more significant impact on the wall group effect, and reducing the number of cells is more conducive to improving the bearing capacity than increasing the size of cells.

The emergence of the N-D wall provides a new technical solution for the selection of deep foundation, which has a high promotion and application value. At present, relevant engineering applications have appeared in the foundation of tall buildings (such as power towers, TV towers, and high-rise buildings) and the development of underground space in Japan [5]. However, the related research of this new type of foundation has just started, the theory lags behind the practice, and the lack of relevant research on the mechanical characteristics of the group wall restricts the popularization and application of the N-D wall foundation to a certain extent. ABAQUS is a nonlinear finite element analysis software developed by Dassault SIMULIA, which has a variety of soil constitutive models that can reflect the geotechnical properties in a more realistic and effective way and has a powerful contact surface processing module to simulate the contact between the geotechnical body and the structure [26]. The precise initial stress balance also makes ABAQUS one of the most important finite element analysis software packages in geotechnical engineering, so ABAQUS is widely used in numerical simulation of geotechnical engineering. The reduction coefficient of each load composition under the same displacement condition and the ABAQUS finite element numerical analysis software are introduced to analyze the group wall effect of the N-D wall foundation and reveal the influence of the nodular part on the wall group foundation. The relevant research results will be conducive to promoting the development of the new basic technology and eventually promoting its application in the construction of urbanization engineering, so as to obtain important theoretical value and engineering practicability.

In this study, referring to the definition of pile group effect, the group wall effect of the N-D wall foundation can be calculated according to formula (1), and the reduction coefficient is calculated according to formula (2). In the formula, η is the wall group effect coefficient, Q ug is the ultimate bearing capacity of wall group foundation, Q us is the ultimate bearing capacity of single wall, n is the number of walls, α is the reduction coefficient, σ s is the stress value in a single wall, and σ is the stress value in the group walls.

(1) η = Q ug n Q us ,

(2) α = σ s − σ σ s .

2 Materials and methods

2.1 Field test

The soil layer profile and N value of the test site and the structure of the test wall are shown in Figure 3 [4]. The test wall is 12.5 m high, the section is 700 mm × 1,200 mm, and the tilt angle of the middle section is 45°. The test site is filled with silt and silty fine sand from 0 to 3.5 m depth, the depth range of 3.5–12.5 m is silt with N value greater than 50, the range below 12.5 m depth is silt and silty sand with N value greater than 50, the middle section is located in the silt layer about 9.75 m deep, and the N value is greater than 50.

Figure 3 Soil profile and test wall.
Figure 3

Soil profile and test wall.

The field test adopts tension–pressure cyclic graded loading, as shown in Figure 4 [4]. The load of each stage is 1,200 kN, the duration is 30 min, the maximum pressure load is 10,800 kN, and the maximum tensile load is 22,800 kN.

Figure 4 Loading scheme.
Figure 4

Loading scheme.

2.2 Numerical simulation

In the process of model establishment, the secondary factors are ignored, and the problem is simplified to a certain extent. Considering the symmetry of the foundation and loading conditions, the axisymmetric model is established with only half. The elastic model is used for wall materials, the Mohr–Coulomb constitutive model is used for soil, and it is assumed that the soil is isotropic. The contact surface is set for the wall–soil contact pair, and the parameters of the contact surface are constant in the calculation process. For the friction parameters of the contact surface, ψ (pile–soil interface friction angle) is suggested to be ( 0.75 − 1 ) ϕ or tan − 1 ( sin ϕ ⋅ cos ϕ 1 + sin 2 ϕ ) [27–30] ( ϕ is the friction angle of the soil, and tan ψ is the pile–soil friction coefficient).

Parameter values of numerical simulation model materials for field test are summarized in Table 1. The site soil layer is simplified into three layers, and the value of soil layer parameters is mainly determined according to the corresponding N value (standard penetration number) and combined with the Engineering Geology Manual (2018).

Table 1

Field test calculation parameters

Type Depth (m) Elasticity modulus (MPa) Poisson’s ratio Cohesion (kPa) Friction angle (°) Density (kg/m3)
Soil ① 0–3.5 15 0.4 3 35 1,500
Soil ② 3.5–12.5 30 0.35 5 42 1,800
Soil ③ 12.5–32 50 0.35 5 42 1,600
Wall 0–12.5 25,000 0.2 — — 2,500

The group wall foundation calculation parameters of the model are shown in Table 2. The thickness of each single wall in the model group is 0.6 m, the width is 1.8 m, the dip angle of each nodular part is 45°, the spacing is 0.4 L (L is the wall length), and the spacing of each wall is 2D (D is the nodular part diameter expansion size). In the calculation of finite element software, the accuracy and rationality of the calculation results are closely related to the selection of the calculation area. If the calculation area is too large, the computation time will be very long; if the calculation area is too small, it will produce an evident boundary effect, which considerably influences the accuracy of the calculation results.

Table 2

Group wall foundation calculation parameters

Type Depth (m) Elasticity modulus (MPa) Density (kg/m3) Poisson’s ratio Cohesion (kPa) Friction angle (°)
Soil 32 15 1,800 0.4 3 35
Wall 12.5 25,000 2,500 0.2 — —
Cap 1 20,000 2,500 0.2 — —

For the calculation of pile foundation engineering, some scholars give the size of the reference calculation range. For example, the pile foundation model established by Randolph and Wroth [31] extends 12.5 times the pile diameter downward along the depth direction and 25 times the pile diameter along the radial direction. Dehong et al. [32] and Zhou et al. [33] suggested that the horizontal direction of the analysis area should be 50 times the pile diameter and that the distance under the pile bottom should be 1.5 times the pile length. Zhou et al. [34] used the Drucker–Prager model to simulate the elastoplastic deformation characteristics of soil and believed that 0.7 times the pile length in the radial direction and 0.6–0.7 times the pile length in the vertical direction could meet the engineering requirements.

In view of the aforementioned research results, the horizontal calculation range of the N-D wall foundation is 50 m (approximately 28 times the wall thickness) and the vertical calculation range is 32 m (approximately 2.5 times the wall length). After the trial calculation, the finally established numerical calculation model (1/2 model) is not affected by the boundary effect, as shown in Figure 5 (C3D8R is used as soil and wall element type).

Figure 5 Numerical calculation model: (a) 1/2 model, (b) Group N-D walls, and (c) wall size (m).
Figure 5

Numerical calculation model: (a) 1/2 model, (b) Group N-D walls, and (c) wall size (m).

3 Results and discussion

3.1 Numerical simulation verification

Figure 6 shows the comparison curve between the test value and the numerical calculation results of load–displacement at the top of the wall under vertical cyclic loads at all levels. As can be seen from the figure, the curves of the numerical calculated values and the experimental values are in good agreement, the change trend is the same, and both show a slow change type, indicating that the establishment of the numerical model and the setting of parameters are reasonable, and the numerical calculation can better analyze the vertical bearing characteristics of the nodular wall foundation.

Figure 6 Comparison of simulation and test load–displacement curves.
Figure 6

Comparison of simulation and test load–displacement curves.

3.2 Wall group effect coefficient analysis

In Figure 7, the load–displacement curves of each wall in the group walls are not consistent with those of a single wall, which indicates that the wall group effect exists in the foundation. As seen from Figure 7(a), an inflection point appears in the wall group foundation load–displacement curve when the uplift displacement is 22 mm, and the load corresponding to the uplift displacement of 22 mm is taken as the ultimate uplift bearing capacity of the foundation. Before the uplift load reaches the ultimate bearing capacity, the load–displacement curves of the sidewall and middle wall basically coincide, indicating that the group effect of the two walls is relatively close to the uplift stress. In Figure 7(b), the inflection points in the wall group foundation load–displacement curves are not obvious, but it can be seen that after the displacement exceeds 30 mm, the curves are basically in a straight-line state, so the load corresponding to the compressive displacement of 30 mm can be used as the ultimate compressive bearing capacity of the foundation.

Figure 7 Load–displacement curve of the N-D wall foundation: (a) uplift and (b) compression.
Figure 7

Load–displacement curve of the N-D wall foundation: (a) uplift and (b) compression.

In Table 3, when the ultimate bearing capacity is reached, the compressive group wall effect coefficient is greater than 1, while the uplift group wall effect coefficient is less than 1. The main reason for this difference is that the cap resistance enhances the bearing performance of the foundation under compressive stress, while the wall group effect weakens the bearing performance of the foundation under tensile stress.

Table 3

Ultimate bearing capacity and wall group effect coefficient

Single (kN) Wall group (kN) Effect coefficient
Uplift 4,032 10,344 0.855
Compression 5,410 16,376 1.009

3.3 Wall top stress group effect

In the initial stage of loading, the influence range of the sidewall–soil–middle wall interaction is the largest and then decreases with increasing displacement. Therefore, as shown in Figure 8, the wall top stress group effect weakens with increasing displacement and tends to be stable until the load reaches the ultimate bearing capacity. In Figure 8(a), when the uplift displacement is less than 22 mm, the middle wall top stress reduction coefficient is greater than that of the sidewall because both sides of the middle wall are affected by the sidewall, which makes the middle wall group effect stronger. When the uplift displacement reaches 22 mm, the sidewall reaches the ultimate bearing capacity state, and the soil outside the sidewall is damaged by shear stress, while the soil inside the sidewall is compressed by the wall limit, friction resistance, and nodular part resistance, so the shear strength is improved. When the uplift displacement reaches 30 mm, the soil on both sides of the middle wall is damaged, and the wall top stress reduction coefficient is stable. Similarly, in Figure 8(b), when the settlement displacement reaches 30 mm, the sidewall reaches the ultimate bearing capacity, and the wall top stress reduction coefficient reaches stability. At this time, the shear strength of the soil on both sides of the middle wall is strengthened by the compaction of the cap and sidewall, the bearing capacity is improved, the wall group effect is not stable, the wall top stress reduction coefficient continues to decrease, and the trend of decrease is increasingly gentle and finally reaches stability. At the initial loading stage of the two curves, the wall top stress reduction coefficient changes slowly, mainly considering that in the initial stage, the cap plays a role in resisting the weakening of the group wall effect caused by settlement.

Figure 8 Curve of the wall top stress reduction coefficient with displacement: (a) uplift and (b) compression.
Figure 8

Curve of the wall top stress reduction coefficient with displacement: (a) uplift and (b) compression.

The results show that the group effect of the compressive wall is more obvious than that of the uplift wall, and the group effect of the middle wall is more obvious than that of the sidewall. The main reason for this difference is that the group effect is strengthened by the interaction between the cap, soil, and wall applied with compressive stress. For the middle wall, the soil on both sides is affected by the cap effect and wall limit, which makes this group effect more obvious.

3.4 Friction resistance group effect

The curves in Figures 8(a) and 9(a) have similar trends, i.e., the friction resistance reduction coefficient decreases with increasing uplift displacement and tends to be stable when the ultimate bearing capacity is reached. As the friction resistance has not fully played its role in the initial stage of uplift, the curve is relatively gentle. With the increase in uplift displacement, the friction resistance is in full play, and the curve becomes steeper and steeper until the ultimate bearing capacity is reached and becomes stable. Figure 9(b) shows that at the initial loading stage, the friction resistance reduction coefficient tends to increase because at the initial stage, the soil in a certain depth range sinks and compacts with the cap sink, the relative displacement between the wall and soil is small, and the friction resistance cannot play its role fully. When the displacement reaches 30 mm, it gradually stabilizes. As the settlement continues to increase, the relative displacement between the wall and soil increases and the friction resistance begins to play a full role. The group effect becomes increasingly weaker until it reaches the ultimate bearing capacity and tends to be stable.

Figure 9 Curve of the friction resistance reduction coefficient with displacement: (a) uplift and (b) compression.
Figure 9

Curve of the friction resistance reduction coefficient with displacement: (a) uplift and (b) compression.

Figures 10 and 11 show that the friction resistance distribution is different between the sidewall and the middle wall, as well as the inner and outer surface of the sidewall, and they are all obviously smaller than the single wall. As shown in Figure 11(a), the outer surface of the sidewall has greater friction resistance than any wall in a group wall foundation, which also verifies the weakening effect of the cap effect on friction resistance on the wall under compressive stress.

Figure 10 1/2 wall–soil interface shear stress of the N-D wall (uplift) (Pa): (a) group walls and (b) single wall.
Figure 10

1/2 wall–soil interface shear stress of the N-D wall (uplift) (Pa): (a) group walls and (b) single wall.

Figure 11 1/2 wall–soil interface shear stress of the N-D wall (compression) (Pa): (a) group walls and (b) single wall.
Figure 11

1/2 wall–soil interface shear stress of the N-D wall (compression) (Pa): (a) group walls and (b) single wall.

3.5 Bottom resistance group effect

In Figure 12, the reduction coefficient of wall bottom resistance first increases with increasing displacement and then decreases due to loading. The load is mainly composed of cap resistance and friction resistance. The bottom resistance group effect is not obvious. With increasing settlement, the load gradually decreases and the cap effect gradually decreases, which makes the bottom resistance group effect more obvious. When the settlement reaches 22 mm, the cap effect does not increase. With the increase in settlement, the bottom resistance plays a stronger role and the group effect becomes weaker. When the ultimate bearing capacity is reached (displacement 30 mm), the bottom resistance reduction coefficient has not reached stability, meaning that the bottom resistance has not reached the limit value. By comparing Figure 9(b) and Figure 12, the group effect coefficient of bottom resistance in the group walls is smaller than that of the side friction resistance, which means that the bottom resistance wall group effect is stronger than the side friction resistance.

Figure 12 Curve of the bottom resistance reduction coefficient with displacement.
Figure 12

Curve of the bottom resistance reduction coefficient with displacement.

3.6 Nodular part resistance group effect

In Figure 13(a), the nodular part resistance reduction coefficient curves increase first and then decrease with the displacement, indicating that the nodular part resistance group effect is not obvious at the initial stage of loading. When the uplift displacement reaches 10 mm, it reaches the maximum, while in Figure 9(a), the friction resistance group effect of the sidewall reaches its maximum at the beginning of loading. Meanwhile, the resistance reduction coefficient of the middle nodular part is greater than that of the bottom nodular part, indicating that the wall group effect of the middle nodular part is stronger than that of the bottom nodular part. The aforementioned phenomenon shows that the wall group effect develops downward gradually with increasing displacement. When the uplift displacement reaches 18 mm, the nodular part resistance group effect reaches unification, and when the displacement reaches 30 mm, it reaches stability.

Figure 13 Curve of the resistance reduction coefficient of the nodular part with displacement: (a) uplift and (b) compression.
Figure 13

Curve of the resistance reduction coefficient of the nodular part with displacement: (a) uplift and (b) compression.

Comparing Figure 13(b) with Figure 12, it can be seen that under compressive stress, the nodular part resistance group effect is similar to the bottom resistance group effect; both increase first and then decrease with settlement. The nodular part resistance group effect reaches its maximum when the settlement value is 18 mm, and the bottom resistance group effect reaches its maximum when the settlement value is 22 mm. This indicates that the wall group effect also develops downward with increasing displacement under compressive stress. When the settlement reaches 30 mm (ultimate bearing capacity), the curve is not stable, indicating that the ultimate compressive bearing capacity is mainly controlled by friction resistance, which is especially obvious in the sidewall. By comparing Figure 13(a) and (b), it is not difficult to find that the nodular part resistance reduction coefficient of side wall is larger than that of middle wall, and the nodular part resistance reduction coefficient of compression wall is larger than that of uplift wall.

Figures 14 and 15 show that the nodular part resistance distribution is different between the sidewall and the middle wall, as well as the inner and outer surfaces of the sidewall. The nodular part resistance of the sidewall is less than that of the middle wall, and both are less than that of the single wall. Under uplift stress, the soil between the walls is subjected to the confining effect of the walls and cannot freely diffuse outward. Therefore, the distribution of nodular part resistance on the inner surface of the sidewall and on both sides of the middle wall is uniform due to the confining effect of the walls, while it is not uniform on the outer surface of the sidewall and both sides of the single wall. As shown in Figure 15, the nodular part resistance is not evenly distributed, meaning that the nodular part resistance plays a small role during compressive stress, and the outward diffusion effect of soil between walls is small, which is not affected by the confining effect of walls.

Figure 14 1/2 nodular part resistance at ultimate uplift capacity: (a) group walls and (b) single wall.
Figure 14

1/2 nodular part resistance at ultimate uplift capacity: (a) group walls and (b) single wall.

Figure 15 1/2 nodular part resistance at ultimate compression capacity: (a) group walls and (b) single wall.
Figure 15

1/2 nodular part resistance at ultimate compression capacity: (a) group walls and (b) single wall.

3.7 Cap resistance

Figure 16(a) shows that the cap resistance increases with increasing settlement displacement. When the displacement value reaches 30 mm (ultimate bearing capacity), the curve does not slow down, and the potential of cap resistance is still great. At the beginning of the load, the load is first transmitted from the cap to the top of the soil, and with the increase in the displacement, the load is gradually transferred downward so that the load shared by the soil at the bottom of the cap decreases. When it reaches the ultimate bearing capacity, the soil exhibits plastic deformation failure, the bearing capacity weakens, and the load shared by the soil at the bottom of the cap increases again, which shows that the curve in Figure 16(b) decreases first and rises again. Figure 17(b) shows that the cap resistance is not evenly distributed, the soil at the corner is extruded outwardly by the confining effect of the wall, and the stress at the corner is the lowest, which is mainly concentrated in the middle.

Figure 16 Curve of cap resistance and load-sharing ratio changing with displacement: (a) cap resistance–displacement curve and (b) load-sharing ratio of cap resistance.
Figure 16

Curve of cap resistance and load-sharing ratio changing with displacement: (a) cap resistance–displacement curve and (b) load-sharing ratio of cap resistance.

Figure 17 Cap resistance distribution under ultimate compressive capacity: (a) view of cap bottom and (b) 1/4 cap resistance distribution.
Figure 17

Cap resistance distribution under ultimate compressive capacity: (a) view of cap bottom and (b) 1/4 cap resistance distribution.

3.8 Sensitivity analysis

The bearing capacity of group wall foundation is closely related to its structural design. Wall spacing, width, length, and nodular part angle are all important parameters in the design of foundation structure. In this test, the aforementioned factors are independent of each other, and the interaction effect is not considered. The design scheme L16 (45) is selected for the test, as shown in Table 4, where D is the diameter of the nodular part.

Table 4

Group wall foundation factor level

Spacing (A) Width (B) Length (C) Angle (D)
1 1D 1.5D 10D 15°
2 1.67D 2.5D 12.5D 25°
3 3D 3.5D 14.5D 35°
4 7D 4.5D 16.5D 45°

The orthogonal test results of uplift force are shown in Table 5; with the range R A > R C > R B > R D, it can be seen that the degree of influence of uplift bearing capacity on design parameters of group wall foundation structure from strong to weak is as follows: spacing, length, width, and angle. Variance S j shows that the influence of wall spacing, length, and width on uplift bearing capacity is highly significant, while the influence of angle is slightly significant. In the actual project, the aforementioned design parameter values are not blindly increased to obtain a higher bearing capacity, but should be adjusted according to comprehensive factors such as soil layer properties, concrete volume, construction machinery, and working environment.

Table 5

Uplift orthogonal test scheme and result

Spacing (A) Width (B) Length (C) Angle (D) Vacant Bearing capacity（MN）
1 1 1 1 1 1 13.63
2 1 2 2 2 2 37.76
3 1 3 3 3 3 53.40
4 1 4 4 4 4 69.96
5 2 1 2 3 4 18.90
6 2 2 1 4 3 21.22
7 2 3 4 1 2 52.46
8 2 4 3 2 1 51.92
9 3 1 3 4 2 19.36
10 3 2 4 3 1 36.96
11 3 3 1 2 4 17.88
12 3 4 2 1 3 26.42
13 4 1 4 2 3 16.42
14 4 2 3 1 4 12.00
15 4 3 2 4 1 19.81
16 4 4 1 3 2 18.35
K 1j 174.75 68.31 71.08 109.73 122.32
K 2j 144.50 107.94 102.89 121.98 127.93
K 3j 100.63 143.55 136.68 127.61 117.46
K 4j 66.58 166.65 175.80 130.35 118.75
K 1j 43.69 17.08 17.77 27.43 30.58
K 2j 36.13 26.98 25.72 30.50 31.98
K 3j 25.16 35.89 34.17 31.90 29.36
K 4j 16.65 41.66 43.95 32.59 29.69
R j 27.04 24.59 26.18 5.15 2.62
S j 1704.06 1384.65 1516.85 259.74 16.55
S j Degree of freedom Mean sum of square F- value Significance level
A 1704.06 3 568.02 FA = 102.98 ＞ 29.46 = F0.01 (3, 3) Highly
B 1384.65 3 461.55 FB = 83.67 ＞ 29.46 = F0.01 (3, 3) Highly
C 1516.85 3 505.62 FC = 91.66 ＞ 29.46 = F0.01 (3, 3) Highly
D 259.74 3 86.58 F D = 15.70＞9.28 = F 0.05 (3, 3) Slightly
Vacant 16.55 3 5.52

The results of the compression orthogonal test are shown in Table 6, with the range R B > R C > R A > R D; it can be seen that the influence degree of the compressive bearing capacity of the design parameters of the group wall foundation structure from strong to weak is as follows: width, length, spacing, and angle. The variance S j shows that the influence of width, length, and spacing on uplift bearing capacity is highly significant, while the influence of pitch angle is weak. The wall width has the most significant influence on the bearing capacity. Considering the load sharing of the bearing table under compressive stress, the change of the wall width leads to the corresponding change of the cap bottom area, which causes the change of the friction resistance and the cap resistance, thus affecting the bearing capacity. By comparing Tables 5 and 6, it can be found that the influence of angle on the uplift bearing capacity of group wall foundation is stronger than that of the compressive bearing capacity.

Table 6

Compression orthogonal test scheme and result

Spacing (A) Width (B) Length (C) Angle (D) Vacant Bearing capacity (MN)
1 1 1 1 1 1 25.64
2 1 2 2 2 2 35.48
3 1 3 3 3 3 43.60
4 1 4 4 4 4 51.86
5 2 1 2 3 4 27.96
6 2 2 1 4 3 30.50
7 2 3 4 1 2 40.12
8 2 4 3 2 1 41.34
9 3 1 3 4 2 27.70
10 3 2 4 3 1 37.04
11 3 3 1 2 4 29.42
12 3 4 2 1 3 35.78
13 4 1 4 2 3 26.76
14 4 2 3 1 4 30.34
15 4 3 2 4 1 31.46
16 4 4 1 3 2 32.34
K 1j 156.58 108.06 117.9 131.88 135.48
K 2j 139.92 133.36 130.68 133.00 135.64
K 3j 129.94 144.60 142.98 140.94 136.64
K 4j 120.90 161.32 155.78 141.52 139.58
K 1j 39.15 27.02 29.48 32.97 33.87
K 2j 34.98 33.34 32.67 33.25 33.91
K 3j 32.49 36.15 35.75 35.24 34.16
K 4j 30.23 40.33 38.95 35.38 34.89
R j 8.92 13.32 9.47 2.41 1.03
S j 175.22 374.97 198.27 19.52 2.71
S j Degree of freedom Mean sum of square F- value Significance level
A 175.21 3 58.40 FA = 64.6＞29.46 = F0.01 (3, 3) Highly
B 374.97 3 124.99 FB = 138.42＞29.46 = F0.01 (3, 3) Highly
C 198.27 3 66.09 FC = 73.19＞29.46 = F0.01 (3, 3) Highly
D 19.51 3 6.50 FD = 7.20＜9.28 = F0.05 (3, 3) Weak
Vacant 2.71 3 0.90

4 Conclusion

In this article, the reduction coefficient of each load composition under the same displacement condition is introduced, and the group effect of N-D wall foundations is analyzed by combining ABAQUS finite element numerical analysis software. The conclusions are as follows:

  1. The compressive group wall effect coefficient is greater than 1, while the uplift group wall effect coefficient is less than 1.

  2. During the whole loading process, the top stress group effect decreases with increasing displacement. The reduction coefficients of the side wall and the middle wall are 0.08 and 0.01, respectively, when the ultimate uplift bearing capacity is reached and 0.17 and 0.24, respectively, when the ultimate compressive bearing capacity is reached. Under the same displacement condition, the group effect of the compressive wall is more obvious than that of the uplift wall, and the group effect of the middle wall is more obvious than that of the sidewall.

  3. The friction resistance group effect decreases with the increase in displacement applied with uplift stress and increases first and then decreases with the increase in settlement applied with compressive stress due to the cap effect. The reduction coefficients of the side wall and the middle wall are 0.06 and 0.08, respectively, when the ultimate uplift bearing capacity is reached and 0.02 and 0.13, respectively, when the ultimate compressive bearing capacity is reached. The distribution of friction resistance is different between the sidewall and the middle wall as well as the inner and outer surface of the sidewall, and they are all obviously smaller than that of the single wall. Under the same displacement, the friction resistance group effect of the sidewall applied with compression stress is stronger than that applied with uplift stress, and neither is obvious. The middle wall has a stronger friction resistance group effect when applied with compression stress.

  4. The bottom resistance group effect increases first and then decreases with increasing settlement. Under the ultimate bearing capacity, the reduction coefficients of side wall and middle wall are 0.2 and 0.3, respectively, the group effect of the middle wall is stronger than that of the sidewall, and the group effect of the bottom resistance is stronger than that of the friction resistance.

  5. The nodular part resistance group effect increases first and then decreases with increasing displacement. The reduction coefficients of the side wall and the middle wall are 0.24 and 0.18, respectively, when the ultimate bearing capacity is reached and 0.74 and 0.61, respectively, when the ultimate bearing capacity is reached. The middle nodular part resistance group effect is stronger than that of the bottom one, and the group effect gradually develops downward with increasing displacement. The ultimate compressive capacity is mainly controlled by the friction resistance, which is especially obvious in the sidewall.

  6. The nodular part resistance distribution is different between the sidewall and the middle wall, as well as the inner and outer surfaces of the sidewall. The nodular part resistance of the sidewall is less than that of the middle wall, and both are less than that of the single wall. The group effect of the sidewalls is stronger than that of the middle wall.

  7. With the increase in the settlement, the load-sharing ratio of the cap resistance decreases first and then increases and finally becomes stable. When the ultimate compressive capacity is reached, the load sharing-ratio of cap resistance is 0.17. The cap resistance is not evenly distributed, the stress at the corner is the lowest, and the stress is mainly concentrated in the middle.

  8. The influence of wall spacing, length, and width on the uplift bearing capacity is highly significant, while the influence of nodular part angle is slightly significant. The influence of wall width, length, and spacing on compressive bearing capacity is highly significant, while the influence of nodular part angle is weak. The influence of nodular part angle on the uplift bearing capacity of group wall foundation is stronger than that of the compressive bearing capacity.

  1. Funding information: This study was funded by Sichuan Science and Technology Program (no. 2019YJ0323), National Nature Science Foundation of China (no. 41272333, 42007247), National Program on Key Basic Research Project of China (Grant 2011CB013501), and National Foreign Expert Project of China (no. DL2023036001L).

  2. Conflict of interest: Authors state no conflict of interest.

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Received: 2022-06-22
Revised: 2023-07-07
Accepted: 2023-10-06
Published Online: 2023-11-15

© 2023 the author(s), published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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https://doi.org/10.1515/geo-2022-0562
Keywords for this article
N-D wall; wall group effect; numerical simulation; friction resistance; nodular part resistance; cap resistance load-sharing ratio
Creative Commons
BY 4.0

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  10. Uncertainty assessment of 3D geological models based on spatial diffusion and merging model
  11. Evaluation of dynamic behavior of varved clays from the Warsaw ice-dammed lake, Poland
  12. Impact of AMSU-A and MHS radiances assimilation on Typhoon Megi (2016) forecasting
  13. Contribution to the building of a weather information service for solar panel cleaning operations at Diass plant (Senegal, Western Sahel)
  14. Measuring spatiotemporal accessibility to healthcare with multimodal transport modes in the dynamic traffic environment
  15. Mathematical model for conversion of groundwater flow from confined to unconfined aquifers with power law processes
  16. NSP variation on SWAT with high-resolution data: A case study
  17. Reconstruction of paleoglacial equilibrium-line altitudes during the Last Glacial Maximum in the Diancang Massif, Northwest Yunnan Province, China
  18. A prediction model for Xiangyang Neolithic sites based on a random forest algorithm
  19. Determining the long-term impact area of coastal thermal discharge based on a harmonic model of sea surface temperature
  20. Origin of block accumulations based on the near-surface geophysics
  21. Investigating the limestone quarries as geoheritage sites: Case of Mardin ancient quarry
  22. Population genetics and pedigree geography of Trionychia japonica in the four mountains of Henan Province and the Taihang Mountains
  23. Performance audit evaluation of marine development projects based on SPA and BP neural network model
  24. Study on the Early Cretaceous fluvial-desert sedimentary paleogeography in the Northwest of Ordos Basin
  25. Detecting window line using an improved stacked hourglass network based on new real-world building façade dataset
  26. Automated identification and mapping of geological folds in cross sections
  27. Silicate and carbonate mixed shelf formation and its controlling factors, a case study from the Cambrian Canglangpu formation in Sichuan basin, China
  28. Ground penetrating radar and magnetic gradient distribution approach for subsurface investigation of solution pipes in post-glacial settings
  29. Research on pore structures of fine-grained carbonate reservoirs and their influence on waterflood development
  30. Risk assessment of rain-induced debris flow in the lower reaches of Yajiang River based on GIS and CF coupling models
  31. Multifractal analysis of temporal and spatial characteristics of earthquakes in Eurasian seismic belt
  32. Surface deformation and damage of 2022 (M 6.8) Luding earthquake in China and its tectonic implications
  33. Differential analysis of landscape patterns of land cover products in tropical marine climate zones – A case study in Malaysia
  34. DEM-based analysis of tectonic geomorphologic characteristics and tectonic activity intensity of the Dabanghe River Basin in South China Karst
  35. Distribution, pollution levels, and health risk assessment of heavy metals in groundwater in the main pepper production area of China
  36. Study on soil quality effect of reconstructing by Pisha sandstone and sand soil
  37. Understanding the characteristics of loess strata and quaternary climate changes in Luochuan, Shaanxi Province, China, through core analysis
  38. Dynamic variation of groundwater level and its influencing factors in typical oasis irrigated areas in Northwest China
  39. Creating digital maps for geotechnical characteristics of soil based on GIS technology and remote sensing
  40. Changes in the course of constant loading consolidation in soil with modeled granulometric composition contaminated with petroleum substances
  41. Correlation between the deformation of mineral crystal structures and fault activity: A case study of the Yingxiu-Beichuan fault and the Milin fault
  42. Cognitive characteristics of the Qiang religious culture and its influencing factors in Southwest China
  43. Spatiotemporal variation characteristics analysis of infrastructure iron stock in China based on nighttime light data
  44. Interpretation of aeromagnetic and remote sensing data of Auchi and Idah sheets of the Benin-arm Anambra basin: Implication of mineral resources
  45. Building element recognition with MTL-AINet considering view perspectives
  46. Characteristics of the present crustal deformation in the Tibetan Plateau and its relationship with strong earthquakes
  47. Influence of fractures in tight sandstone oil reservoir on hydrocarbon accumulation: A case study of Yanchang Formation in southeastern Ordos Basin
  48. Nutrient assessment and land reclamation in the Loess hills and Gulch region in the context of gully control
  49. Handling imbalanced data in supervised machine learning for lithological mapping using remote sensing and airborne geophysical data
  50. Spatial variation of soil nutrients and evaluation of cultivated land quality based on field scale
  51. Lignin analysis of sediments from around 2,000 to 1,000 years ago (Jiulong River estuary, southeast China)
  52. Assessing OpenStreetMap roads fitness-for-use for disaster risk assessment in developing countries: The case of Burundi
  53. Transforming text into knowledge graph: Extracting and structuring information from spatial development plans
  54. A symmetrical exponential model of soil temperature in temperate steppe regions of China
  55. A landslide susceptibility assessment method based on auto-encoder improved deep belief network
  56. Numerical simulation analysis of ecological monitoring of small reservoir dam based on maximum entropy algorithm
  57. Morphometry of the cold-climate Bory Stobrawskie Dune Field (SW Poland): Evidence for multi-phase Lateglacial aeolian activity within the European Sand Belt
  58. Adopting a new approach for finding missing people using GIS techniques: A case study in Saudi Arabia’s desert area
  59. Geological earthquake simulations generated by kinematic heterogeneous energy-based method: Self-arrested ruptures and asperity criterion
  60. Semi-automated classification of layered rock slopes using digital elevation model and geological map
  61. Geochemical characteristics of arc fractionated I-type granitoids of eastern Tak Batholith, Thailand
  62. Lithology classification of igneous rocks using C-band and L-band dual-polarization SAR data
  63. Analysis of artificial intelligence approaches to predict the wall deflection induced by deep excavation
  64. Evaluation of the current in situ stress in the middle Permian Maokou Formation in the Longnüsi area of the central Sichuan Basin, China
  65. Utilizing microresistivity image logs to recognize conglomeratic channel architectural elements of Baikouquan Formation in slope of Mahu Sag
  66. Resistivity cutoff of low-resistivity and low-contrast pays in sandstone reservoirs from conventional well logs: A case of Paleogene Enping Formation in A-Oilfield, Pearl River Mouth Basin, South China Sea
  67. Examining the evacuation routes of the sister village program by using the ant colony optimization algorithm
  68. Spatial objects classification using machine learning and spatial walk algorithm
  69. Study on the stabilization mechanism of aeolian sandy soil formation by adding a natural soft rock
  70. Bump feature detection of the road surface based on the Bi-LSTM
  71. The origin and evolution of the ore-forming fluids at the Manondo-Choma gold prospect, Kirk range, southern Malawi
  72. A retrieval model of surface geochemistry composition based on remotely sensed data
  73. Exploring the spatial dynamics of cultural facilities based on multi-source data: A case study of Nanjing’s art institutions
  74. Study of pore-throat structure characteristics and fluid mobility of Chang 7 tight sandstone reservoir in Jiyuan area, Ordos Basin
  75. Study of fracturing fluid re-discharge based on percolation experiments and sampling tests – An example of Fuling shale gas Jiangdong block, China
  76. Impacts of marine cloud brightening scheme on climatic extremes in the Tibetan Plateau
  77. Ecological protection on the West Coast of Taiwan Strait under economic zone construction: A case study of land use in Yueqing
  78. The time-dependent deformation and damage constitutive model of rock based on dynamic disturbance tests
  79. Evaluation of spatial form of rural ecological landscape and vulnerability of water ecological environment based on analytic hierarchy process
  80. Fingerprint of magma mixture in the leucogranites: Spectroscopic and petrochemical approach, Kalebalta-Central Anatolia, Türkiye
  81. Principles of self-calibration and visual effects for digital camera distortion
  82. UAV-based doline mapping in Brazilian karst: A cave heritage protection reconnaissance
  83. Evaluation and low carbon ecological urban–rural planning and construction based on energy planning mechanism
  84. Modified non-local means: A novel denoising approach to process gravity field data
  85. A novel travel route planning method based on an ant colony optimization algorithm
  86. Effect of time-variant NDVI on landside susceptibility: A case study in Quang Ngai province, Vietnam
  87. Regional tectonic uplift indicated by geomorphological parameters in the Bahe River Basin, central China
  88. Computer information technology-based green excavation of tunnels in complex strata and technical decision of deformation control
  89. Spatial evolution of coastal environmental enterprises: An exploration of driving factors in Jiangsu Province
  90. A comparative assessment and geospatial simulation of three hydrological models in urban basins
  91. Aquaculture industry under the blue transformation in Jiangsu, China: Structure evolution and spatial agglomeration
  92. Quantitative and qualitative interpretation of community partitions by map overlaying and calculating the distribution of related geographical features
  93. Numerical investigation of gravity-grouted soil-nail pullout capacity in sand
  94. Analysis of heavy pollution weather in Shenyang City and numerical simulation of main pollutants
  95. Road cut slope stability analysis for static and dynamic (pseudo-static analysis) loading conditions
  96. Forest biomass assessment combining field inventorying and remote sensing data
  97. Late Jurassic Haobugao granites from the southern Great Xing’an Range, NE China: Implications for postcollision extension of the Mongol–Okhotsk Ocean
  98. Petrogenesis of the Sukadana Basalt based on petrology and whole rock geochemistry, Lampung, Indonesia: Geodynamic significances
  99. Numerical study on the group wall effect of nodular diaphragm wall foundation in high-rise buildings
  100. Water resources utilization and tourism environment assessment based on water footprint
  101. Geochemical evaluation of the carbonaceous shale associated with the Permian Mikambeni Formation of the Tuli Basin for potential gas generation, South Africa
  102. Detection and characterization of lineaments using gravity data in the south-west Cameroon zone: Hydrogeological implications
  103. Study on spatial pattern of tourism landscape resources in county cities of Yangtze River Economic Belt
  104. The effect of weathering on drillability of dolomites
  105. Noise masking of near-surface scattering (heterogeneities) on subsurface seismic reflectivity
  106. Query optimization-oriented lateral expansion method of distributed geological borehole database
  107. Petrogenesis of the Morobe Granodiorite and their shoshonitic mafic microgranular enclaves in Maramuni arc, Papua New Guinea
  108. Environmental health risk assessment of urban water sources based on fuzzy set theory
  109. Spatial distribution of urban basic education resources in Shanghai: Accessibility and supply-demand matching evaluation
  110. Spatiotemporal changes in land use and residential satisfaction in the Huai River-Gaoyou Lake Rim area
  111. Walkaway vertical seismic profiling first-arrival traveltime tomography with velocity structure constraints
  112. Study on the evaluation system and risk factor traceability of receiving water body
  113. Predicting copper-polymetallic deposits in Kalatag using the weight of evidence model and novel data sources
  114. Temporal dynamics of green urban areas in Romania. A comparison between spatial and statistical data
  115. Passenger flow forecast of tourist attraction based on MACBL in LBS big data environment
  116. Varying particle size selectivity of soil erosion along a cultivated catena
  117. Relationship between annual soil erosion and surface runoff in Wadi Hanifa sub-basins
  118. Influence of nappe structure on the Carboniferous volcanic reservoir in the middle of the Hongche Fault Zone, Junggar Basin, China
  119. Dynamic analysis of MSE wall subjected to surface vibration loading
  120. Pre-collisional architecture of the European distal margin: Inferences from the high-pressure continental units of central Corsica (France)
  121. The interrelation of natural diversity with tourism in Kosovo
  122. Assessment of geosites as a basis for geotourism development: A case study of the Toplica District, Serbia
  123. IG-YOLOv5-based underwater biological recognition and detection for marine protection
  124. Monitoring drought dynamics using remote sensing-based combined drought index in Ergene Basin, Türkiye
  125. Review Articles
  126. The actual state of the geodetic and cartographic resources and legislation in Poland
  127. Evaluation studies of the new mining projects
  128. Comparison and significance of grain size parameters of the Menyuan loess calculated using different methods
  129. Scientometric analysis of flood forecasting for Asia region and discussion on machine learning methods
  130. Rainfall-induced transportation embankment failure: A review
  131. Rapid Communication
  132. Branch fault discovered in Tangshan fault zone on the Kaiping-Guye boundary, North China
  133. Technical Note
  134. Introducing an intelligent multi-level retrieval method for mineral resource potential evaluation result data
  135. Erratum
  136. Erratum to “Forest cover assessment using remote-sensing techniques in Crete Island, Greece”
  137. Addendum
  138. The relationship between heat flow and seismicity in global tectonically active zones
  139. Commentary
  140. Improved entropy weight methods and their comparisons in evaluating the high-quality development of Qinghai, China
  141. Special Issue: Geoethics 2022 - Part II
  142. Loess and geotourism potential of the Braničevo District (NE Serbia): From overexploitation to paleoclimate interpretation
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