Experimental and numerical investigation on horizontal bearing behaviors of caisson-type diaphragm wall with variable cross-sections

Abstract

This study investigates the horizontal load-bearing behavior of the Caisson-type Diaphragm Wall with Variable Cross-sections (CDWVC), a novel foundation system that integrates closed and open wall segments to improve performance and material efficiency. A series of 1g model tests was conducted using instrumented plexiglass models under controlled soil conditions to evaluate the bearing behavior under lateral loading. Finite difference simulations were also performed to complement the experimental findings and provide additional insights. The performance of CDWVCs with varying closed segment heights and open segment widths was analyzed. Results indicate that taller closed segments reduce horizontal displacements under equivalent loads and shift the rotation point closer to the surface, thereby improving overall stability. While increasing the height of the closed wall segment leads to modest improvements in horizontal ultimate bearing capacity, these gains are often outweighed by significant increases in material consumption. Conversely, expanding the width of the open wall segment results in a more substantial increase in horizontal ultimate bearing capacity relative to material usage, improving load transfer and overall stability. This design strategy achieves a favorable balance between load capacity and material efficiency compared to increasing closed wall height. The findings underscore the importance of design choices in the performance of CDWVCs under horizontal loading conditions.

Graphical abstract

Keywords

CDWVC / horizontal bearing behavior / model test / load-bearing capacity / material efficiency

1 Introduction

Diaphragm walls, functioning as a versatile “three-in-one” structural system that integrates soil retention, load-bearing, and waterproofing capabilities [1] are widely used in civil engineering for deep foundations, excavation support, and waterfront structures [2]. With the widespread adoption of mechanized rapid construction techniques, diaphragm wall foundations are characterized by efficiency, cost-effectiveness, and adaptability, along with low noise and high structural integrity, making them particularly suited for large-span bridge foundations. Among the most commonly used diaphragm wall foundations for large-span bridges are “caisson-type diaphragm walls”, also referred to as “rectangular closed diaphragm walls” (RCDW) or “lattice-shaped diaphragm walls” (LSDW), along with “multi-wall foundations”, as shown in Fig.1. These foundations are extensively applied in the construction of urban viaducts, railways, and cross-sea bridges.

Research on caisson-type diaphragm walls, multi-wall foundations, and related foundation types has gained considerable attention, with various studies focusing on their performance under different load conditions. For instance, Wu et al. [3,4] developed an iterative load transfer procedure for settlement evaluation and investigated the soil arching effect of LSDW as bridge foundations through field tests and relevant numerical studies. They found that the horizontal bearing capacity of LSDWs is significantly greater than that of group piles based on a comparative numerical study of static and seismic responses of LSDWs and group piles under similar material quantities in soft soil [5]. Furthermore, Wu et al. [6] indicated that using LSDWs instead of group piles in soft soil would enhance bearing capacity and reduce settlement for practical bridge foundations, supported by small-scale model tests and numerical analysis using FLAC^3D. Their work also comprehensively evaluated the bearing behavior of LSDWs under horizontal cyclic loads in soft soils [7].

In terms of dynamic performance of RCDW, Cao et al. [8] proposed an approximate analytical solution for the vertical dynamic impedance and shaft resistance of RCDW embedded in a homogeneous soil medium and resting on a rock base. This solution provided a theoretical framework for understanding the dynamic behavior of RCDWs in layered soil profiles. Regarding liquefaction mitigation, Li et al. [9] conducted dynamic centrifuge tests and demonstrated that RCDWs can effectively reduce liquefaction in soil cores during seismic events, emphasizing the significance of wall geometry in preventing liquefaction in vulnerable soils. Complementing this, Zhang et al. [10] used numerical simulations to show that RCDWs can delay liquefaction onset during moderate and major earthquakes, reinforcing their application in earthquake-prone areas. For multi-wall foundations, Wu et al. [11] explored the scouring effects caused by unidirectional flow around multi-wall foundations using FLOW-3D, incorporating large-eddy simulation techniques. Their findings expanded understanding of fluid-structure interaction and its impact on foundation stability.

It should be noted that although caisson-type diaphragm walls (as shown in Fig.1(a)) offer high vertical and horizontal bearing capacity and have proven cost-effective in terms of material-to-capacity ratio, they present notable limitations in practical implementation. The construction process is often complex due to the need for rigid joints between segments and the presence of a soil core, which affects both the internal construction sequence and load transfer mechanisms. Specifically, the inner skin friction around the soil core is significantly lower than the outer friction along the wall segments, resulting in underutilization of the foundation’s full bearing potential. Moreover, the differential earth pressure inside and outside the core can induce stress imbalance and structural inefficiency. In contrast, multi-wall foundations (Fig.1(b)) eliminate the soil core and simplify construction by using open, joint-free segments, which improves external frictional resistance and reduces construction complexity and cost. However, this design comes at the expense of global stiffness and lateral load resistance, as the lack of structural continuity between individual wall segments leads to reduced integrity and seismic vulnerability.

To address the limitations of existing diaphragm wall foundations, such as the high material consumption and construction complexity of caisson-type walls, and the reduced rigidity of multi-wall foundations, a new foundation type termed the Caisson-type Diaphragm Wall with Variable Cross-sections (CDWVC) is proposed in this study, as illustrated in Fig.2. The upper section of the CDWVC adopts a closed-wall configuration similar to the caisson-type diaphragm wall shown in Fig.1(a), with adjacent wall segments connected by rigid joints to form a closed rectangular frame topped with a cap plate, thereby ensuring high structural stiffness and integrity. In contrast, the lower section incorporates a multi-wall sheet pile structure, analogous to conventional multi-wall foundations, to improve soil interaction and reduce material usage. The two sections are rigidly connected to form an integrated system, resulting in a continuous transition from a rigid upper structure to a more economical open-wall lower segment. This hybrid configuration effectively combines the advantages of both foundation types and provides a new design strategy for large-span bridge foundations. The construction procedure for the CDWVC is shown in Fig.2(b).

The CDWVC, as illustrated in Fig.2, is a novel foundation system proposed in this study by integrating the structural advantages of caisson-type and multi-wall diaphragm walls. While both foundation types have been widely applied in bridge engineering and studied extensively, the CDWVC represents a new structural form that has not yet been addressed in existing literature. At present, no studies have examined its mechanical behavior, construction performance, or design strategies, and it remains at an early stage of development. In particular, its response to horizontal loading requires urgent investigation, as resistance to wind, wave, traffic, and seismic forces is a fundamental concern in foundation engineering [12–16]. To fill this gap, this study conducts 1g indoor model tests and finite difference simulations to evaluate the horizontal bearing behavior of CDWVCs with varying closed segment heights and open segment widths. Comparative analysis is also performed against traditional pile foundations with equivalent material usage. The findings reveal the influence of key design parameters on displacement, internal force distribution, and soil resistance, providing a basis for optimizing both structural performance and material efficiency, and promoting the engineering application of this new foundation system.

2 Experiment setup and testing methodology

2.1 Design and manufacture of CDWVC models

This experiment is based on a real engineering project, a long-span high-speed railway bridge in China, originally designed with a group pile foundation. For comparison, CDWVC models were constructed to match the dimensions of the group pile foundation. Given the site’s geological conditions, it is classified as a typical marine deposition area, with clayey soil in the upper layer and sandy soil in the lower layer. The specific soil parameters are presented in Tab.1.

In this study, two sets of model tests were conducted to evaluate the performance of different foundation types. The first set compared the CDWVC with a group pile foundation, while the second set compared the CDWVC with a traditional caisson diaphragm wall (CDW). In both test sets, the foundation types were designed with the same embedment depth and simulated site conditions. Additionally, the CDWVCs and group pile models were constructed using an equivalent volume of concrete. The detailed dimensions of the models used in these tests are illustrated in Fig.3. Specifically, CDWVC-1 and CDWVC-2 have closed section heights that are 1/2 and 1/3 of the CDW foundation, respectively. Additionally, CDWVC-1, CDWVC-2, and CDW foundations share the same sectional dimensions for the closed sections and maintain the same overall foundation depth.

In this experiment, the similarity ratios listed in Tab.2 were established based on geometric similarity and dimensional analysis, following the Buckingham π theorem. This approach ensures that the scaled model effectively reflects the mechanical behavior of the prototype under horizontal static loading. Based on prior successful experiments, the model piles (walls) were constructed using plexiglass. To ensure accuracy, the plexiglass was custom-manufactured, with cutting, wiring, and surface treatments carried out by professionals, achieving an assembly tolerance within a 2 mm margin of error. To better replicate real-world conditions, after the testing elements were installed on the plexiglass plates and columns, AB glue was applied to affix sand to the plexiglass surface. This treatment simulated the friction between the foundation and the soil, roughening both the inner and outer surfaces to mimic actual wall-soil contact conditions at the site. Following the method outlined by Wu et al. [6] and other relevant studies, optimal results were achieved by using standard sand with a grain size of 0.5–1.5 mm and a density of 50–70 grains per square centimeter [17].

2.2 Testing element layout

To ensure precise measurements of stress variations within the model, strain gauges were strategically placed following the principle of model symmetry, enabling a systematic investigation of the stress distribution. Similarly, soil pressure cells were evenly arranged at intervals, as shown in Fig.4, to collect soil pressure data at designated points. This arrangement allowed for the accurate measurement of pressure data, which, through appropriate conversions and calculations, enabled the determination of variations in key parameters such as wall bending moments, displacements, and soil pressures under different horizontal load conditions.

Based on the displacements of the force application points measured by the dial indicators under each level of load, and the strain gauge data from various cross-sections of the pile shaft and wall body, the rotation angles θ and horizontal displacement values y at each measured cross-section along the pile shaft and wall body were calculated using the following formula [7]. These equations are derived based on the assumption of a linear strain distribution across the cross-section, consistent with classical elastic beam theory and commonly adopted in testing of pile foundations.

(1){\theta }_{i+1}={\theta }_i-(\mathrm{\Delta }{\epsilon }_{i+1}+\mathrm{\Delta }{\epsilon }_i)\frac{l_i}{2b_0},

(2)y_{i+1}=y_i+\theta l_i-(\mathrm{\Delta }{\epsilon }_{i+1}+2\mathrm{\Delta }{\epsilon }_i)\frac{l_i^2}{6b_0},

where Δε_i and Δε_i+1 represent the cross-sectional strains of i and i + 1, respectively; θ_i and θ_i+1 represent the cross-sectional rotation angles of i and i + 1, respectively; y_i and y_i+1 represent the cross-sectional horizontal displacements of i and i + 1, respectively; b₀ represents the distance between the cross-sections of i and i + 1; l_i represents the length of element i.

Based on the shell bending theory and the definition of the moment of inertia, the bending strain data measured at each test cross-section can be used to calculate the bending moment M_i between various cross-sections of the wall according to the following formula:

(3)M_i=EI\frac{{\epsilon }_{\mathrm{s}}-{\epsilon }_{\mathrm{c}}}{b_0},

where b₀ represents the spacing between tensile and compressive strain measurement points; E represents the elastic modulus of the tested wall; I represents the moment of inertia of the full cross-section of the wall relative to its neutral axis; ε_s and ε_c represent the measured tensile and compressive strain values at each measurement point on the various cross-sections of the wall, respectively.

Subsequently, using the horizontal displacements at the top of the wall as boundary conditions, the shear force F(D) of the wall body under various levels of load is calculated according to the following formula.

(4)F(D)=\frac{\mathrm{d}M}{\mathrm{d}D}.

2.3 Loading device and scheme

Due to the small-scale ratio of the model wall, the load values converted according to similarity theory are relatively small. Consequently, a simple and user-friendly pulley system was employed as the loading equipment. This system theoretically increased the load of the weights to three times their original value through pulley transmission. However, factors such as friction during the loading process resulted in the actual tensile force transmitted to the top of the foundation being less than three times. To accurately measure the horizontal load at the top of the pile cap, a tension meter was utilized for calibration. After repeated measurements and calibrations, the actual tensile force of the pulley system was determined. By weighing the weights in the weight box, the horizontal load at the top of the pile cap could then be calculated. The weights used were laboratory-calibrated steel weights, and loading was conducted in stages. A schematic diagram of the model loading setup is presented in Fig.5, which includes the weight box, pulley system, weights, steel wire rope, and other components.

3 Experimental results and analysis

3.1 Displacement characteristics under horizontal load

3.1.1 Analysis of horizontal displacement at the top of the pile/wall cap

Based on the measured horizontal displacement values obtained from the dial indicators installed at the top of the pile cap under various levels of load, the S_h–H₀ curves, which depict the relationship between the horizontal displacement S_h at the top of the four types of tested foundation caps and the horizontal load H₀, can be plotted, as shown in Fig.6.

As can be seen from Fig.6, the horizontal displacement S_h of the four types of foundations increases with the increase of the horizontal load H₀. Among them, the S_h–H₀ curves of CDWVC-1 and CDWVC-2 display a gradual progression without distinct inflection points, making it challenging to determine their respective ultimate bearing capacities. To facilitate a more comprehensive analysis of the displacement behavior of different foundations under varying loads and to more accurately assess their ultimate loads, the horizontal load (H₀) versus horizontal displacement gradient (ΔS_h/ΔH₀) curves are derived from the S_h–H₀ curves, as illustrated in Fig.7.

It can be inferred from Fig.7 that the horizontal displacement (S_h) of the group piles increases progressively with the horizontal load (H₀). Under lower loads, the S_h–H₀ curve exhibits a linear trend, transitioning to nonlinear behavior as the load increases. The S_h–H₀ curves for CDWVC-1, CDWVC-2, and CDW similarly display linear growth under smaller loads, but the displacement gradient (ΔS_h/ΔH₀) increases sharply as the load approaches the ultimate capacity, indicating a transition to nonlinearity. Among these, CDWVC-2 reaches its ultimate capacity first, followed by CDWVC-1, and finally CDW, suggesting that the height of the closed section has a significant impact on the horizontal displacement response, with greater closed section heights resulting in smaller displacements under equivalent loads.

According to the criteria for determining the horizontal ultimate bearing capacity of the foundation types, as depicted in Fig.7, the horizontal displacement of the group piles shows a pronounced increase at the 13th load level (6.8 kN), which can be regarded as the ultimate load. Similarly, the ultimate loads for CDWVC-1, CDWVC-2, and CDW are determined to be 7.3, 6.5, and 7.5 kN, respectively.

Overall, the ultimate bearing capacities of the CDW and CDWVC foundations are either greater than or comparable to the group pile foundation. For the CDWVC foundations, the closed section length plays a crucial role in enhancing the bearing capacity. Specifically, CDWVC-1, with a closed section length of 1/2 that of the CDW foundation, shows only a slight reduction in ultimate bearing capacity, approximately 2.67% lower. In contrast, CDWVC-2, with a closed section length of 1/3 of CDW, experiences a more substantial reduction, showing a 13.3% decrease in ultimate capacity compared to CDW. This analysis demonstrates that the closed section length proportionally influences the foundation’s horizontal bearing capacity, with longer sections providing higher capacities. The increase, however, is nonlinear.

Additionally, selecting an appropriate closed section length (such as 1/2) can achieve a bearing capacity close to that of the fully closed CDW foundation. However, if the closed section is too short, the bearing capacity drops sharply. For instance, when the closed section is only 1/3 of the height, the bearing capacity is reduced to a level comparable to or even lower than that of the group pile.

To further compare the performance of these foundations, Tab.3 presents the results from indoor model tests. It is clear that CDWVC-1 reduces material consumption by 20.65% compared to CDW, while its ultimate bearing capacity decreases by only 2.67%. This underscores the outstanding load-bearing performance of CDWVC foundations, which retain significant capacity even within acceptable horizontal displacement limits. Furthermore, when comparing CDWVC-1 to the group pile foundation, despite their similar material usage, CDWVC-1 outperforms with a 7.35% higher bearing capacity. This makes CDWVC-1 particularly suitable for applications requiring strict horizontal displacement control, such as bridge or soft soil foundations.

The comparison between CDWVC-1 and CDWVC-2 reveals that while CDWVC-2 uses 8.67% less material, its bearing capacity decreases by 10.96%. This highlights the critical role of selecting the appropriate height for the closed section to maximize horizontal load-bearing capacity. Considering the complexities involved in constructing diaphragm walls, including guide wall installation, steel cage placement, and mud management, CDWVC offers distinct advantages. Unlike CDW, which requires rigid joint connections, CDWVC’s design simplifies construction, reducing both workload and technical challenges. As a result, CDWVC not only demonstrates superior horizontal bearing properties but also delivers notable economic benefits, making it an effective and efficient foundation choice.

3.1.2 Analysis of horizontal displacement of pile/wall body

The horizontal displacement of the wall body can be calculated using the bending moment-strain relationships derived from the tests, as expressed in Eqs. (1) and (2). Fig.8 presents the S_h−D curves, which illustrate the variation of horizontal displacement with depth for both group pile and diaphragm wall foundations. Positive horizontal displacement values indicate movement in the direction of the applied load, while negative values signify displacement in the opposite direction.

As shown in Fig.8, regardless of whether the foundation consists of group piles, a CDWVC, or a CDW, the largest horizontal displacement occurs near the ground surface. Along the length of the wall, the displacement gradually decreases until it reaches zero, at which point it begins to increase in the opposite direction. Additionally, as the applied load increases, the horizontal displacement of both the piles and the wall increases accordingly. This behavior suggests that the CDWVC rotates around a specific point along its body under horizontal load, and the foundation exhibits a characteristic of overall tilting failure.

The horizontal displacement of the wall increases with the load applied at the top and decreases linearly with increasing depth into the soil. The depths corresponding to the zero-displacement points for CDWVC-1, CDWVC-2, and CDW are 0.825, 0.800, and 0.850D, respectively. By comparing the three diaphragm walls with varying closed section heights, it can be observed that the height of the closed section influences the stiffness of the diaphragm wall, which in turn affects the location of the zero-displacement point along the wall body.

3.2 Analysis of bending moment and shear force

During the test, the wall structure remained intact without any visible cracks. Fig.9 presents the M–D curves, showing the bending moment distribution along the wall/pile bodies for the four types of foundations. It can be inferred that diaphragm walls with varying closed section heights, as well as pile group foundations, exhibit similar bending moment distribution patterns along their respective wall/pile bodies. Under horizontal loads, the bending moments of both pile and diaphragm wall foundations increase as the wall-top load rises. With increasing depth, the bending moments initially increase and then decrease, exhibiting a nonlinear pattern. The maximum bending moment for CDWVC-1 occurs at approximately 0.45D below the surface, for CDWVC-2 at around 0.425D, and for CDW at about 0.5D. As the wall-top load continues to increase, the point of maximum bending moment shifts downward. Throughout the entire wall structure, no zero-bending moment point is observed, indicating that the overall stiffness of CDWVC is relatively high.

The F−D relationship curves for group piles and diaphragm walls, based on Eq. (4), are shown in Fig.10. It can be observed that the shear force distribution patterns of group piles, CDWVC, and CDW are generally consistent. The shear force reaches its maximum at the top of the wall/pile where the load is applied and increases with the rise in horizontal load at the top. As the depth into the soil increases, the shear force decreases approximately linearly. At the point where the bending moment in the wall/pile section reaches its maximum, the shear force becomes zero. Below this zero-shear point, the shear force along the depth of the CDWVC and CDW walls displays a parabolic distribution. Near the base of the wall, the shear force decreases slightly, likely due to the soil near the wall base entering a plastic state, causing partial stress release and reducing its interaction with the wall, thereby weakening the shear force effect. As seen in Fig.10, variations in the height of the closed section of the diaphragm wall also affect the position of the zero-shear point. The greater the height of the closed section, the lower the position of the zero-shear point. The depths of these zero-shear points for CDWVC-1, CDWVC-2, and CDW foundations are approximately 0.450D, 0.425D, and 0.500D, respectively.

3.3 Analysis of soil resistance

Under horizontal loads, the distribution of lateral soil resistance along the side of a CDWVC foundation wall represents a highly complex interaction between the wall and the surrounding soil. During the loading process at the top of the wall, the lateral soil resistance primarily manifests in two forms: active earth pressure and passive earth pressure. Negative values indicate active earth pressure, while positive values represent passive earth pressure (the same applies in the following discussion). Fig.11 illustrates the P_qw–D, showing how the soil resistance on the outer side of the front wall varies with the depth of the wall.

As shown in Fig.11, under horizontal loading, the load applied at the top of the wall is transferred through the wall body to the surrounding soil on the front side of the wall. Above the wall’s inflection point, the soil adjacent to the wall is compressed and exhibits passive earth pressure. This passive pressure increases with the rise in wall-top load and decreases with increasing soil depth. Below the inflection point, the wall and soil begin to separate, causing the lateral soil resistance to shift into a state of active earth pressure. By comparing CDWVC and CDW, it is observed that while the distribution patterns of lateral soil resistance along variable-section diaphragm walls with different closed section heights are generally similar, the soil resistance below the inflection point in CDW is significantly greater than that in CDWVC. This is attributed to the greater overall stiffness of CDW, which enables the wall-top load to be more efficiently transmitted to the lower sections of the wall.

4 Numerical investigation

4.1 Input parameters and establishment of numerical CDWVC models with different cross-section sizes

To further investigate the influence of closed segment wall height and open segment width on the bearing characteristics of CDWVC foundations, numerical models were developed using FLAC^3D. The wall was modeled as a linear elastic material, and the soil was represented using the Mohr-Coulomb constitutive model. Input parameters for both the wall and soil are provided in Tab.4. Considering that CDWVC integrates features of both LSDW and multi-wall foundations, the boundary conditions and modeling assumptions established for LSDW systems were adopted as a reference. The computational domain was defined with a horizontal extent of ten times the longer side of the foundation and a vertical depth of twice the foundation depth, following the recommendations by Wu et al. [7] for the lateral response analysis of similar deep wall systems. The base boundary was fixed in all directions, while the lateral boundaries were constrained horizontally to prevent rigid body motion, allowing for realistic soil deformation.

A mesh sensitivity analysis was conducted to ensure numerical stability and result reliability. Multiple mesh densities were tested, and the selected mesh achieved a balance between computational efficiency and result accuracy, with less than 3% variation in ultimate bearing capacity across refinement levels. The grid was refined in the vicinity of the wall–soil interface to better capture stress and displacement gradients. The convergence criterion followed FLAC^3D’s static solution standard, with the average force ratio set to 1 × 10⁻⁶, ensuring global equilibrium was achieved in all simulations. All simulations satisfied this criterion within a reasonable number of iterations.

In this study, the soil-wall interface parameters were determined following the method proposed by Wu et al. [18]. Specifically, the interface cohesion (c_c) and friction angle (φ_c) were set as fractions of the corresponding soil layer properties, reflecting realistic interaction conditions. The normal stiffness (k_n) and shear stiffness (k_s) were assigned values proportional to the soil’s modulus, ensuring appropriate stiffness representation at the interface. These parameters are summarized in Tab.5.

To facilitate the comparison, the same geological model used in the indoor tests is selected to establish six CDWVC models: four with varying closed section wall heights but identical open section wall widths, and two with different open section wall widths but the same closed section wall height. All six models share the same embedment depth (25 m), wall thickness (0.8 m), and cap side dimensions (8 m × 8 m). The schematic diagrams of the models are illustrated in Fig.12.

4.2 Determination criteria of the ultimate load for CDWVC

The horizontal ultimate load of a CDWVC, determined by numerical simulation and analysis, can be evaluated using the following criteria.

1) Yield or failure detection through load-displacement curve: The ultimate load is identified by characteristic changes in the load-horizontal displacement curve. If the curve shows a sharp drop and the horizontal displacement at the next load level is five times that of the previous level, the ultimate bearing capacity is considered to be the load from the previous level.

2) Based on allowable horizontal displacement: When the load-displacement curve shows a gradual change, the ultimate bearing capacity is taken as the load corresponding to a horizontal displacement of more than 40 mm at the top of the wall.

3) Material Strength Limit: If neither of the above criteria is met, and the wall top load reaches the material’s strength limit in the simulation, the corresponding load is considered the ultimate bearing capacity.

4.3 Influence of closed wall segment height on the bearing behavior of CDWVCs

Fig.13 shows the horizontal displacement versus horizontal load (S_h–H₀) curves for CDWVCs with different closed section wall heights. The curves exhibit similar trends, especially at the initial stage of loading where they almost coincide. As the load increases, the differences become more pronounced. According to the criteria for determining the horizontal ultimate bearing capacity of CDWVC, the ultimate capacities for wall heights of 8, 12, 16, and 20 m are 62560, 64840, 65450, and 66800 kN, respectively.

Fig.14 presents illustrates the horizontal displacement distribution along the wall depth (S_h–D) for four CDWVC walls with varying closed wall heights under horizontal loading. The displacement patterns show a general tilting failure, with a pivot point occurring at a specific depth along the wall. As the height of the closed wall segment increases, the pivot point moves closer to the wall’s top. For closed section heights of 8, 12, 16, and 20 m, the depths of the zero-displacement points are 0.85, 0.825, 0.8, and 0.775D, respectively. This demonstrates that the height of the closed wall segment significantly influences the depth of the pivot point, with shorter closed wall segments causing the rotational point to move deeper into the foundation, while taller segments improve stability by positioning the pivot point closer to the surface.

To further compare the bearing capacities and material consumption of the four foundations, Tab.6 provides a detailed comparison of the ultimate loads and material usage for CDWVCs with different closed wall heights. From the data, it is evident that the ultimate load of CDWVC-6 (66800 kN) increased by only 6.8% compared to CDWVC-3 (62560 kN), while the concrete volume required increased by 42.9% (from 358.4 to 512 m³). Similarly, CDWVC-4 and CDWVC-5 show marginal increases in ultimate load (3.6% and 4.6%, respectively) but significant increases in material consumption (14.3% and 28.6%, respectively). This indicates that the height of the closed wall segment has a relatively minor impact on the horizontal ultimate bearing capacity of CDWVCs, while shorter closed wall heights provide higher load-carrying efficiency in terms of material usage.

4.4 Influence of open wall segment width on the bearing behavior of CDWVCs

Fig.15 displays the S_h–H₀ curves for two CDWVC with different open wall segment widths. The trends of the two curves are basically the same, and they even almost coincide during the initial loading stage. Initially, the curves show similar trends, with the horizontal displacement values closely following each other. However, as the load increases, the difference becomes more pronounced, with CDWVC-7 displaying larger horizontal displacements than CDWVC-8 under the same load. A wider open segment (CDWVC-8) results in smaller displacements for a given load, and it can bear a greater load for the same horizontal displacement. This occurs because the wider open segment increases contact between the wall and soil, enhancing load transfer through wall-side friction and soil resistance.

Fig.16 illustrates the distribution of horizontal displacement along the wall depth (S_h–D) for two CDWVC with different open wall segment widths under horizontal loading. The displacement patterns in both cases show a general tilting failure, with a pivot point forming along the wall depth. Notably, CDWVC-7 exhibits a slightly deeper pivot point compared to CDWVC-8. As the applied load increases, the horizontal displacement becomes more pronounced. Specifically, for larger depths, CDWVC-7 exhibits significantly greater horizontal displacements compared to CDWVC-8. This suggests that the wider open wall segment in CDWVC results in a shallower pivot point, offering better resistance to horizontal displacement and enhancing overall stability under the same load.

Based on the criteria for determining the horizontal ultimate bearing capacity of CDWVC, the horizontal ultimate bearing capacities of CDWVC-7 and CDWVC-8 are 66.56 and 69.87 kN, respectively. To provide a more detailed comparison, Tab.7 presents the ultimate load and material consumption for both CDWVCs.

From Tab.7, the ultimate load of CDWVC-8 (69870 kN) increased by 4.98% compared to CDWVC-7 (66560 kN), while the material consumption increased by 11.42% (from 448 to 499.2 m³). In contrast, Tab.6 reveals that increasing the closed wall height also shows limited improvement in bearing capacity. For instance, the ultimate load of CDWVC-6 increased by only 6.8% compared to CDWVC-3, but this was accompanied by a significant material consumption increase of 42.9%.

When comparing these two design strategies, the increase in bearing capacity relative to material usage is more efficient for increasing the open segment width than for increasing the closed wall height. CDWVC-8 (with a wider open wall segment) provides a better balance between load-carrying improvement and material efficiency than increasing the height of the closed wall, where the increase in material consumption is significantly higher without a proportional improvement in capacity. Therefore, expanding the open wall segment appears to be a more effective approach when seeking a balance between material use and load capacity enhancement.

5 Conclusions and discussion

This study utilized a combination of indoor model tests and numerical simulations to evaluate the performance of CDWVC under horizontal loading conditions. The main conclusions are as follows.

1) The horizontal displacement at the wall top increases progressively with load. Taller closed segments reduce displacement and enhance stability. The optimal performance is observed when the closed section height is half of the total wall height, balancing capacity and material use.

2) The horizontal displacement of the wall decreases with depth, with the largest values near the surface. Taller closed segments raise the rotation point, reduce deep displacement, and improve overall wall stiffness.

3) Bending moment and shear force distributions exhibit nonlinear patterns, with peak values shifting downward under increasing load. Greater closed segment height deepens the location of the peak and zero-shear points, enhancing lateral resistance.

4) Soil resistance along the wall shows distinct active and passive pressure zones. CDWVC foundations display slightly lower soil resistance than fully closed diaphragm walls at greater depths due to reduced stiffness but maintain sufficient load transfer capability.

5) Increasing the closed segment height moderately improves horizontal bearing capacity, but the benefit declines as material consumption rises. A closed segment height of 0.5H appears to offer a practical balance.

6) Expanding the open segment width results in a more significant improvement in ultimate capacity relative to material use. It also reduces displacement and improves load transfer, making it a more efficient strategy than increasing closed wall height.

The findings of this study offer practical guidance for the design and construction of CDWVC foundations. The identified optimal configuration, such as a closed segment height of 0.5H and wider open segments, can help improve structural performance while reducing material use. These results support the application of CDWVC in large-span bridge foundations, particularly where horizontal load resistance, construction efficiency, and cost-effectiveness are key considerations.

Compared with traditional foundation systems, the CDWVC exhibits a favorable balance between structural performance and construction practicality. Relative to caisson foundations, the CDWVC eliminates the need for internal soil excavation, which reduces earthwork volume and enhances construction safety and efficiency. Furthermore, the in situ casting process ensures better soil-structure contact, promoting more effective load transfer. When compared with group pile foundations, the CDWVC may require slightly more material, but it offers significantly greater structural stiffness and horizontal load-bearing capacity. In contrast to fully closed diaphragm walls, the CDWVC maintains comparable lateral performance while achieving substantial savings in material usage through cross-sectional optimization. These features indicate that the CDWVC is a structurally robust and cost-efficient alternative for large-span bridge foundations, particularly in scenarios requiring high horizontal resistance, simplified construction, and improved material utilization.

Given the current developmental stage of the CDWVC foundation system, the use of scaled physical model tests provides an effective and feasible approach to investigate its mechanical behavior. Nonetheless, several limitations should be acknowledged. The model tests are subject to scale effects, boundary constraints, and measurement uncertainties, which may influence the interpretation of absolute values. The numerical simulations are based on idealized material properties and simplified boundary conditions, which may differ from actual field scenarios. These factors should be considered when applying the results to practical design. Future research involving full-scale or field tests is expected to further enhance the reliability of the findings and support the engineering application of this novel foundation system. Additionally, more extensive parametric studies, particularly involving a wider range of open segment widths and other key geometric variables, could help to optimize the balance between structural performance and material efficiency.

References

[1] Wen H, Cheng Q G, Meng F C, Chen X D. Diaphragm wall soil cap interaction in rectangular closed diaphragm wall bridge foundations. Frontiers of Architecture and Civil Engineering in China, 2009, 3(1): 93–100

[2] Cheng Q G, Wu J J, Song Z, Wen H. The behavior of a rectangular closed diaphragm wall when used as a bridge foundation. Frontiers of Structural and Civil Engineering, 2012, 6(4): 398–420

[3] Wu J J, Wang L J, Cheng Q G. Soil arching effect of Lattice-Shaped Diaphragm Wall as bridge foundation. Frontiers of Structural and Civil Engineering, 2017, 11(4): 446–454

[4] Wu J, Naggar E H M, Cheng Q, Wen H, Li Y, Zhang J. Iterative load transfer procedure for settlement evaluation of lattice-shaped diaphragm walls in multilayered soil. Computers and Geotechnics, 2020, 120: 103409

[5] Wu J J, Cheng Q G, Wen H, Li Y, Zhang J L, Wang L. Comparison on the horizontal behaviors of lattice-shaped diaphragm wall and pile group under static and seismic loads. Shock and Vibration, 2016, 2016: 1289375

[6] Wu J J, Cheng Q G, Wen H, Cao J. Comparison on the vertical behavior of lattice shaped diaphragm wall and pile group under similar material quantity in soft soil. KSCE Journal of Civil Engineering, 2015, 19(7): 2051–2060

[7] Wu J J, Hu H D, Zhang Y, Pu L J, Yin J. Experimental investigation on the behavior of cyclic-laterally loaded lattice-shaped diaphragm wall in soft soil. Ocean Engineering, 2024, 303: 117805

[8] Cao G, Zhu M, Gong W, Jiang K, Wang B. Dynamic response of axially loaded end-bearing rectangular closed diaphragm walls. Zeitschrift für Naturforschung. Section A. Physical Sciences, 2020, 75(7): 621–636

[9] Li Y, Cheng Q G, Zhang J L, Lyu B, Wang Y F, Wu J J. Seismic behavior of rectangular closed diaphragm walls in gently sloping liquefiable deposit: Dynamic centrifuge testing. Journal of Geotechnical and Geoenvironmental Engineering, 2019, 145(12): 04019105

[10] Zhang J L, Cheng Q G, Li Y, Zhang E M, Wang Y F, Wu J J, Xie S. Mechanism of liquefaction mitigation by rectangular closed diaphragm walls in sloping liquefiable deposits. Soil Dynamics and Earthquake Engineering, 2021, 142: 106582

[11] Wu J J, Wang L J, Cheng Q G. Numerical modeling of current-induced scour around multi-wall foundation using large-eddy simulation. Frontiers of Structural and Civil Engineering, 2023, 17(4): 546–565

[12] Zheng C, Kouretzis G, Ding X. Analysis of laterally loaded floating piles using a refined Tajimi model. International Journal for Numerical and Analytical Methods in Geomechanics, 2024, 48(11): 2727–2744

[13] Zou X J, Chen S, Hu J F, Yang Z J. Capacity of monopile-bucket composite foundations in sand-overlaying-clay deposits under lateral loading. Ocean Engineering, 2024, 304: 117849

[14] Potini F, Conti R. Horizontal bearing capacity of RC piles in cohesive soil: Numerical and theoretical modelling. Computers and Geotechnics, 2024, 175: 106638

[15] Wang C, Ding X, Liu H, Zhang Y T, Cao G W, Wang Z L. Centrifuge model tests on bearing behavior of lateral-loaded single pile in coral sand. Acta Geotechnica, 2024, 19(7): 4581–4603

[16] Zou X J, Chen S, Tu X Y, Yang Z J. Effects of Local Scouring on load-bearing behaviors of monopile-friction wheel hybrid foundations on sandy deposit soil under lateral loading. International Journal of Geomechanics, 2024, 24(6): 1–21

[17] Wu J J, Zhang Y, Li Y, Wen H, Wang L J. Uplift behavior of nodular diaphragm wall: Experiment and theory. International Journal for Numerical and Analytical Methods in Geomechanics, 2024, 48(5): 1197–1226

[18] Wu J, Li Y, Cheng Q G, Wen H, Liang X. A simplified method for the determination of vertically loaded pile–soil interface parameters in layered soil based on FLAC^3D. Frontiers of Structural and Civil Engineering, 2016, 10(1): 103–111

RIGHTS & PERMISSIONS

Higher Education Press