Abstract
In the present study, a dimensional total-stress elasto-plastic FEM analysis was conducted, which was based on the Mohr-Coulomb constitutive model. The model was combined with a practical engineering case in order to investigate ground displacements and stress conditions during the installations of a medium-sized and a small-sized circular diaphragm wall, as well as the subsequent soil excavations within the walls. The distribution characteristics of the lateral radial displacements and stress conditions in the ground following the wall installations and excavations within the walls were investigated. Also, two different excavation methods, as well as three different soil depths for the walls, were considered. The distributions of the internal forces along the depth directions of the radial sections of the walls were also analyzed in this study. The analysis results showed that the slotting order had made the model nonaxisymmetric, which had further influenced the distribution characteristics of radial stress and displacements. It was found that the distributions of the horizontal radial displacements, along with the stress levels of the soil behind the walls, were only minimally affected by the excavations of the soil in the shaft. The internal force distribution of the wall radial section caused by the direct excavation method and the reverse excavation method is very small, that is, the wall bending moment generated by the reverse excavation process is larger, and the most obvious near the rock-socketed depth. The distribution pattern of the bending moment depth corresponding to different excavation construction methods is similar. Furthermore, the soil penetration depths of the walls were determined to have had little influence on the internal force distributions of the radial sections of the walls above the foundation pit. However, there was a greater influence observed on the internal force distributions of the radial sections of the walls below the foundation pit.
1. Instruction
Any type of shaft excavation requires soil retaining structures to be installed prior to the commencement of the soil excavation process. In China, these retaining structures are known as diaphragm walls. It has been observed that the influences of shaft excavations on the surrounding rock and soil, as well as on existing structures, are remarkable (Ng et al. [1]; Schafer and Triantafyllidis [2]). It has been agreed that the impacts of the construction of grooves and walls in mining shafts on the stress distributions of the surrounding soil cannot be ignored (Arai et al. [3]; Chu et al. [4]). Small- and medium-sized circular shafts are often encountered in many municipal construction projects in China, such as during the construction of natural gas pipelines. Prior to the excavation of such shafts, it is often necessary to construct small- and medium-sized circular underground diaphragm walls. Due to the significant force arch effects, the stress formations of these small- and medium-sized circular diaphragm walls will be different from those of the generally used large-sized diaphragm walls.
The processes involved in the construction of diaphragm walls are complex, and generally include section excavations under bentonite slurry, followed by the application of concrete and hardening of the concrete. There are two ways in which shaft excavations are carried out: direct methods and inverse methods. The two construction methods have different effects on the stress distributions and displacements of the soil behind the walls (Lan and Manh [5]). From the perspective of improving the construction efficiency, the direct methods are the optimal choice. However, from the perspective of construction safety, the inverse methods are more appropriate (Kang et al. [6]).
The reactions of the surrounding soil of mining shafts are influenced by a number of issues relating to localized parameters, structural formations of the retaining structures, construction sequences, and so on. It has been found that finite element analysis methods can be effective design tools for shaft excavation and support projects (Lee et al. [7]; Liu et al. [8]; Khoiri and Ou [9]). The mechanical behaviors of small- and medium-sized circular shaft diaphragm walls are known to be different from those of large-sized underground diaphragm walls. The stability of structures themselves plays an important role in the structural designs. A phenomenon referred to as the “self-stabilizing effect” of circular diaphragm walls is known to exist. At the present time, there have only been a few research studies conducted on the mechanical characteristics of small- and medium-sized circular diaphragm wall structures. However, there have been many studies conducted regarding the construction processes of other large-sized underground diaphragm wall structures which have used finite element methods. A two-dimensional FEM model for the entire construction process of an underground diaphragm wall was established by Gunn et al. [10]. The model’s construction sequence had included grooving, concrete applications, and subsequent hardening of the concrete. De Moor [11] established 2D finite element analysis models for a series of plane (horizontal) sections through a series of wall panels with given depths. Also, three-dimensional FEM analyses of the effects of diaphragm wall installations were conducted by Ng et al. [12]. The stress characteristics of a single-diaphragm wall panel construction were analyzed by Ng and Yan [13] using a three-dimensional finite difference method. The results of the three-dimensional FEM analysis of a straight diaphragm wall were published by Gourvenec and Powrie [14]. Li [15] established the circular diaphragm wall foundation pit excavation model by using the method of numerical simulation, and studied and analyzed the influence law of the thick excavation depth, inner diameter, and other factors on the internal force and displacement of the circular diaphragm wall. Dong et al. [16] established a finite element numerical model to simulate the shaft construction process and studied the mechanical influence of soil excavation on the circular underground diaphragm wall under different construction methods. The analysis of all models examined the mechanical behavior of the wall structure in the installation stage but did not analyze the mechanical behavior of the soil around the wall installation stage. This paper not only analyzes the mechanical behavior of the wall under different construction methods, but also analyzes the soil around the wall, but provides theoretical support for the installation of small and medium-sized circular underground continuous wall.
A three-dimensional total stress elasto-plastic FEM analysis was conducted for the purpose of examining the ground movements and stress conditions following the installations of circular diaphragm walls and after excavations of the soil within the walls by Arai et al. [3]. It has been found that in order to capture the main features of the excavation behaviors, various modelling assumptions needed to be considered when developing detailed 3D finite element models for the design of deep excavations, as put forward in the studies conducted by Dong et al. [17]. In addition, the influences of different design parameters on the mechanical behaviors of the structures were examined. In the abovementioned study, the mechanical behaviors of large-sized structures were investigated during both the wall installation stage and the soil excavation stage. However, small- and medium-sized circular diaphragm walls have their own characteristics with regard to mechanical details during the construction processes, whether during the stage of slotting into the walls or during the soil excavation stage. The purpose of this research was to provide experience what may potentially be used to support the development of efficient design concepts for small- and medium-sized circular diaphragm walls.
In order to obtain the accurate mechanical behaviors of the examined diaphragm walls, it was necessary to establish a fine finite element analysis model for the entire construction process of the small- and medium-sized circular diaphragm walls. For this study’s model, constitutive data were required for the soil, structural components, and the soil-structure interfaces. Also, some of the details between the structures, such as the joist steel between the tank sections, also need to be considered in the model. All of the calculations described in this study were conducted using ABAQUS V6.17 software. The finite element research literature on displacement is shown in Table 1.
2. Numerical Modeling of the Construction of the Diaphragm Walls and the Soil Excavations within the Walls
2.1. Engineering Prototype
The Nantanhai River Shield Project is located in Jiangmen City, and is part of the second phase of the natural gas pipeline network of Guangdong Province. The project steps are mainly composed of constructing a shield TBM launching shaft, receiving well, and tunnel crossing, and the installation of a gas pipeline. The total length of the tunnel is 1,057 m. The geological features of the tunnel are mainly wind-blown conglomerate and highly weathered conglomerate. When the tunnel construction is completed, a gas pipeline with a diameter of 914 mm will be laid. Figure 1 shows a schematic diagram of the crossing zone and the nearby traffic location. The underground diaphragm wall of the shield TBM launching shaft is composed of ten “八” shaped gutters, as shown in Figure 2. The joints between the gutters are connected with steel H-bars. The excavation method of the soil is a direct excavation process. The reinforced concrete lining wall was poured in layers inside the underground continuous wall, and the lining wall was cylindrical in structure. The bottom adopted a concrete cover plate, with an average thickness of 2 m. The design geometry parameters of the shield TBM launching shaft is shown in Table 2.
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In accordance with the perimeter of the circular shaft, the underground diaphragm wall was divided into several gutters, and the gutters were numbered counter-clockwise. The construction of underground diaphragm wall was carried out using a jumping construction method. The method was essentially divided into the following steps:(1)Under the action of the mud retaining wall, a mechanical excavator had excavated into the first section of the groove by splitting the width;(2)The joist steel was welded to both sides of the prefabricated steel cage and then placed into the slot;(3)Concrete applications were applied;(4)The construction of the next gutter was separated by two gutters from the first one. The next gutter was constructed as described above, and then Steps 1 to 4 of the operation were repeated;(5)After the panel concrete had hardened, construction of the adjacent gutter was carried out as described in Steps 1 to 3;(6)The above steps were repeated until the diaphragm wall had been formed into a closed whole structure.
2.2. Engineering Geological Conditions
In the study area, the groundwater level was approximately 2.5 m, and the regional stratum distribution was observed to be regular. The basic mechanical parameters of each soil layer from top to bottom are shown in Table 3.
2.3. Results of the FEM Analysis
2.3.1. Outline of the FEM Model
In the present study, three-dimensional numerical simulations were carried out using the commercially available FEM analysis software ABAQUS V6.17. Figures 3(a) and 3(b) show the FEM mesh with a volume of 60 m in depth and in area. A circular shaft with an internal diameter of 14 m was located in the center of the analysis zone, as shown in Figure 3(d). The model size was selected in order to avoid any measurable effects from the boundary areas in the final results. In this research study, eight-node hexahedron elements were used for three-dimensional FEM. The analyzed zone had contained a total of 21,760 nodes and 23,137 elements. Since the area of the TBM launching shaft was the key research object for this study, the area meshing was properly encrypted. The displacements of the nodes along the side boundaries were fixed in the radial direction, while the displacements of those along the bottom boundary were fixed in the Z-direction. The soil was assumed to behave as an elasto-perfect plastic body using the Mohr-Coulomb failure criterion, and would thereby obey the associated flow rule. The ground was divided into five horizontal layers, and the soil properties are listed in Table 3. These properties were selected to represent realistic values on the basis of the engineering geological survey reports of the site and the adjacent areas.
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The multiple wall panels among slots were connected by steel H-bars which had been welded on both sides of steel cages, as illustrated in Figure 3(c). It was assumed that the steel H-bars would behave as line elastomer with elastic modulus of 206 GPa and a Poisson’s ratio of 0.3. The steel H-bars were 22 m in length, the H-section steel structures are illustrated in Figure 4(a), and H-bar steel annular distribution is illustrated in Figure 4(b).
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2.3.2. Contact Properties
The contact pairs of the FEM model were located as follows: (1) Between the surface of the gutters of the diaphragm wall and the inner surfaces of the H-section steel; (2) Between the surface of diaphragm wall and the soil; and (3) Between the outer surfaces of the H-section steel and the soil. The distribution details of the three types contact pairs are shown in Figure 5. Due to the excavation of the TBM launching shaft, the contacts between the surface of the inner wall of the shaft and the soil was determined to be invalid. In this study, the sliding friction contact type was selected for the model. The coefficient of friction between the structure and the soil was 0.3, and the differences in the different soil layers were not considered on the basis of the results of previous related studies (Yang et al. [18]). Since the coefficient of the friction between the walls and H-bars is known to be generally greater than the coefficient of the friction between the structure and the soil, this study adopted a coefficient of 0.32.
In the current study, a tie constraint was adopted between the bottom of the diaphragm wall and the soil, and it was adopted between the outer surface of the lining wall and the inner surface of the diaphragm wall. Since the soil had already been removed when the lining wall was installed, there was no need to establish contact between the other side of the lining wall and the soil in this study.
2.3.3. Numerical Simulations
Prior to the simulation of the shield TBM launching shaft construction process, the initial ground stress balance of the entire model was required in order to deduct the settlement displacements of the soil mass caused by the self-determined heavy stress of soil. The simulation of the shield TBM launching shaft construction process was divided into two stages as follows: Stage 1 included the diaphragm wall construction; and Stage 2 included the shaft soil excavation and lining wall generation. The two stages were described in detail in the following section.
Stage 1. Diaphragm wall construction stage
The order of the conditions was: “1B-1 C-4B-4 C-7B-7 C-2B-2 C-6B-6 C-10B-10 C-3B-3 C-5B-5 C-8B-8 C-9B-9 C,” in which B indicated the removal of the slot segment of the serial number, and the application of a bentonite slurry with pressure increasing linearly with depth along the excavation area; and C indicated the removal of the bentonite slurry pressure at the slot section of each serial number, and the activation of a solid concrete wall. In order to simplify the steps of the analysis, the process was divided into nine separate analysis steps, and the construction sequence is shown in Figure 6. Step 1: An initial stress balance was applied to the soil model, and the vertical stress and Earth pressure coefficient of each layer were input according to the soil parameters detailed in Table 3; Step 2 (B1, B4, B7): The soil element Gutters 1, 4, and 7 were removed, and bentonite slurry in which the pressure increased linearly with depth was applied along the excavation area, as shown in Figure 7. The unit weight of the slurry was 11.0 kN/m3; Step 3 (C1, C4, C7): The pressure of the bentonite slurry in Gutters 1, 4, and 7 was removed and the concrete wall solid element was activated; Step 4 (B2, B6, B10): The same operation as Step 2 was performed for Gutters 2, 6, and 10; Step 5 (C2, C6, C10): The same operation as Step 3 was performed for Gutters 2, 6, and 10; Step 6 (B3, B5, B8): The same operation as Step 2 was performed for Gutters 3, 5, and 8; Step 7 (C3, C5, C8): The same operation as Step 3 was performed for Gutters 3, 5, and 8; Step 8 (B9): The same operation as Step 2 was performed for Gutter 8; Step 9 (C9): The same operation as Step 3 was performed for Gutter 8.
Stage 2. Shaft excavation stage Excavation 1: In the range of the shaft, the first layer of soil was removed using an element life-death technique, and the thickness of the soil is 4 m; Concrete lining wall 1: The inner wall model of the first layer was activated using a unit death-or-death technique, and the wall model height was 4 m; Excavation 2: In the range of the shaft, a second layer of soil was removed using the same technique as in Excavation 1, and the thickness of the soil was also 4 m; Concrete lining wall 2: The inner wall model of the second layer was activated using a unit death-or-death technique, and the wall model height is 4 m; Excavation 3: In the range of the shaft, a third layer of soil was removed using the same technique as in the previous excavations, and the thickness of the soil was also 4 m; Concrete lining wall 3: The inner wall model of the third layer was activated using a unit death-or-death technique, and the wall model height was 4 m; Excavation 4: In the range of the shaft, a fourth layer of soil was removed using the same technique as in the previous excavations, and the thickness of the soil was also 4 m; Concrete lining wall 4: The inner wall model of the fourth layer was activated using the a death-or-death technique, and the wall model height was 4 m; Excavation 5: In the range of the shaft, a fifth layer of soil was removed using the same technique as in the previous excavations, and the thickness of the soil was 4.48 m; Concrete lining wall 5: The inner wall model of the fifth layer was activated using a unit death-or-death technique, and the wall model height was 2.48 m.In the present study, different construction methods (a direct method and reverse method) were adopted for the analysis process. When the soil mass was excavated using the direct method and the excavation had reached a horizontal elevation at the bottom of the foundation pit, a shaft floor had been generated and a secondary lining of the surrounding structure was constructed. The reverse construction method was the opposite of the normal construction method. It was implemented in order to construct the lining wall while digging continued, and then the shaft floor was constructed.
In accordance with the actual conditions of the simulated foundation pit project, the boundary conditions of the foundation pit engineering model were set as follows: (1) The displacement boundary was set in the boundary condition; (2) The displacements in the x, y, and z directions were restrained at the bottom of the foundation pit; (3) No constraints were imposed at the top of the soil; (4) The displacements in the x and y directions were restrained at the sides of the model’s borders.
3. Numerical Results
3.1. Radial Stress Variations during the Installation Process
As shown in Figure 8, the soil element indicated by the red dot was selected to analyze the relationship between the radial horizontal stress and the soil depth. The relationships between the radial stress and the depth of the soil under different working conditions after the installations of Gutters 5, 6, and 7 are shown in Figures 9(a)–9(c), respectively. Figure 9(a) shows the radial stress of the soil following the installation of Gutter 5 at the end of the construction of the circular diaphragm wall, which was observed to be lower than the initial radial stress in Layers 1, 2, 3, and 4. Meanwhile, the radial stress of Layer 5 was found to be greater than the initial radial stress. It is worth noting that when the bentonite slurry pressure was applied to Gutter 5 (B3, B5, B8), the radial stress of Layers 3 and 4 (located behind Gutter 5) had displayed major increases. However, as the concrete was poured (C3, C5, C8), the radial stress had decreased and then returned to the initial stress state. It was also found that Gutters 6 and 7 had shown the same evolutionary characteristics as Gutter 5.
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The distributions of the radial stress behind all of the walls at the soil depth of 20.48 m during the various steps of the construction are shown in Figure 10. As can be seen in Figure 10(a), when bentonite slurry pressure was applied in Gutters 1, 4, and 7, the radial soil pressure at the central point in the annular direction behind the gutters had increased to the maximum, while the soil pressure on both sides of the gutters had displayed obvious decreases. It was found that after pouring the concrete into the gutters, the radial soil pressure of the soil masses located after the gutters had decreased; the soil pressure stress on both sides of the gutters had increased; and the radial soil pressure at the middle point in the annular direction behind the gutters had also increased to the maximum. Therefore, it can be seen that the construction of the gutters had a major influence on the soil pressure of the adjacent gutters. Figure 10(a) also shows that with the completion of the concrete pouring and hardening processes (C1, C4, C7), the soil pressures of the corresponding 36°, 72°, 180°, and 288° points and the initial state of the soil pressure were basically identical. Therefore, it was deduced that the gutter constructions had impacts on the distances of the radial soil pressure distributions at the D1 (D1: degree of the gutter ring). In this study, the D1 was 36°.
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In Figure 10(b), when bentonite mud pressure is applied to Gutters 2, 6 and 10, radial Earth pressure behind the slot also increased to the maximum value, and soil pressure on both sides behind the gutters decreased significantly. After pouring concrete, the radial stress of the soil after Gutters 2, 6, and 10 decreases obviously, and the soil pressure on both sides of the soil behind the gutters increases obviously. And the Figures 10(c) and 10(d) also detail the same evolutionary characteristics. Therefore, it was concluded from the characteristics of soil pressure evolution that when the bentonite slurry pressure was applied in each gutter, the soil mass had moved outward in a radial direction. Meanwhile, the annular soil body on both sides of the gutters had moved inward.
It can also be seen in Figure 10 that the initial distribution of the stress had been uniform, and the soil pressure had become uneven with the progress of the asymmetric construction. It was found that at the completion of the construction, due to the influences of the construction between the grooves, the soil pressure levels of some of the grooves on the wall sides (3, 5, 9, 10) at the middle point of the annular direction were no longer at the maximum. As a whole, the soil pressure had presented a petal shape, which had indicated that the soil pressure had been redistributed during the construction of the circular diaphragm wall. It had also indicated that the wall model was no longer axisymmetric prior to the commencement of the soil excavation process.
3.2. Lateral Soil Pressure Coefficient
In order to analyze the evolution of the soil pressure coefficient behind the wall during the construction process, the evolution of the soil pressure coefficient during the construction process at each layer after Gutter 7 was plotted, as shown in Figure 11. It was found that when the bentonite slurry pressure had been applied (B1, B4, B7), the soil pressure coefficient had significantly increased in Layers 1, 2, 3, and 4, with the most obvious increasing trend observed in Layer 4. After the wall had been formed (C1, C4, C7), the soil pressure coefficient had become greatly reduced. However, the soil pressure coefficient was still greater than the initial state. The soil pressure coefficient at depths below 1.35 D2 (30 m) were found to have remained basically unchanged during the entire construction process. These findings had indicated that the disturbance range of the open wallboard construction to the soil depth was between 0 and 1.35 D2 (30 m). On the completion of the wall construction, the soil pressure coefficients of Layers 1, 2, 3, and 4 were found to have increased greatly, while the soil pressure coefficients of Layer 5 had decreased to a certain extent.
The relationships between the radial stress ratio of each soil layer behind Gutter 7 and the distance behind the wall are shown in Figure 12. It was found that when the bentonite slurry pressure was applied (B1, B4, B7), the radial stress ratios of Layers 1, 2, 3, and 4 had increased. However, that of wall (C1, C4, C7) had decreased. The radial stress ratios of the Layer 3 and Layer 4 were found to have majorly changed; the radial stress ratio of the fourth layer changes at a faster rate. While those of Layers 1 and 2 had only changed to lesser degrees, and the change rate is similar. The variation trends and influence ranges of the different soil layers were found to vary, which may have been related to soil properties and gutter depths. The Layers 1, 2, 4, and 5, the radial stress ratios had significantly changed with distance in the range of approximately 0.5 D2 (D2: depth of the gutter), and the range of the Layer 3 was approximately D2. The distances between the construction influence boundaries and the wall back were as follows: Layer 1 : 43 m (1.9 D2); Layer 2 : 36 m (1.6 D2); Layer 3 : 45 m (2 D2); Layers 4 and 5 : 26 m (1.1 D2). However, these findings were not consistent with the research results presented by Arai et al. [3]. This may have been due to the different soil depths, gutters sizes, and soil properties.
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3.3. Displacement Profiles during the Installation Process
3.3.1. Radial Displacements of the Soil
Figure 13 shows the relationship between the horizontal displacements and the depth of the lateral soil mass at Gutters 5, 6, and 7 under different working conditions. Figure 13 shows that the displacements had presented folds with depth. At the end of construction, Layers 1, 2, 3, and 4 had moved toward the outside of the shaft, while Layer 5 had moved toward the inside of the shaft. These observations were found to be consistent with the radial stress distributions. It was also noted that Gutters 6 and 7 had exhibited similar variations.
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Figure 14 shows the relation curves of the surface radial displacements with radial distances after the gutters. It can be seen that due to the pressure of the bentonite slurry, the soil masses in the (B1, B4, B7) stage had all moved toward the outside of the wall. Meanwhile, during the (C1, C4, C7) stage, the soil pressure had dropped and the soil masses had moved toward the inside of the wall. It was found that at the end of the construction process, the maximum horizontal displacement had occurred at 0 m behind the wall, and the horizontal displacements in the range of 0 to 1.3 m had shown outward movement. However, the horizontal displacements in the range of 2.1 to 21 m had shown inward movement. It was determined that the influence range was approximately 43 m (1.9 D2).
3.3.2. Vertical Displacements of the Soil
As shown in Figure 15, the settlement of the surface had changed with the normalized distance behind the wall. Due to the pressure of bentonite slurry, there was a slight uplift observed at the (B1, B4, B7) stage, and the stress rates had dropped during the concrete pouring and hardening stages (C1, C4, C7). It was found that at the end of the construction process, the maximum settlement had occurred at 0 m behind the gutters, which was found to be consistent with Arai’s research findings. There were found to be slight fluctuations in the range from 0 to 1 m behind the wall, and there was a decreasing trend observed in the other ranges behind the wall. Also, the displacements at 28 m behind the wall were basically small, which indicates that the influence range for the settlement was approximately 28 m (1.27 D2).
Figure 16 shows the butterfly diagram of the radial displacement annular distributions of the soil mass at the depth of 20.48 m. As shown in Figure 16(a), when bentonite slurry pressure had been applied in Gutters 1, 4, and 7, the soil mass behind the wall had deviated outward, and the maximum displacement was at the annular midpoint of the soil mass behind the gutters. The displacement distributions of Gutters 1, 4, and 7 were determined to be the same. When the concrete pouring and hardening processes were complete, the soil had moved inward. It was observed that as the concrete was poured and had hardened, the pressure of the bentonite slurry acting on the periphery of the gutters had disappeared and the displacement distributions of the soil had changed. When all of the gutter construction had been completed, each gutter had displayed a slight deviation from the wall. However, the maximum displacement of each gutter still remained at the mid-point of the gutter loop.
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Figure 17 shows how the radial stress ratios behind Gutters 1, 2, 3, 4, and 5 had fluctuated in the middle position of the tally weathered conglomerate (Layer 4). During the entire diaphragm wall construction process, local formations were considered to be the causes of the fluctuations of hog and stress transfers. Therefore, based on Step 2, Gutter 1 was considered to be the first excavation, followed by Gutters 4 and 7. The radial stress ratios behind Gutters 4 and 7 had both increased from 1.0 to 1.37, while the radial stress ratios behind the adjacent gutters (Gutters 2, 3, and 5) had decreased from 1.0 to 0.9. In this study’s analysis process (Step 4), Gutters 2, 6, and 10 were excavated, and the corresponding radial stress ratios behind Gutters 1, 3, and 5 were found to have significantly decreased. In Step 6, when Gutters 3, 5, and 8 were excavated, the corresponding radial stress ratios behind Gutters 2 and 4 had also displayed obvious decreases. Meanwhile, it was observed that the radial stress ratios behind Gutter 1 had only minimally changed. When the construction of the diaphragm wall was completed (Step 9), it was determined that Gutters 1, 2, 3, 4, and 5 were 1.14, 1.08, 1.13, 1.13, and 1.08, respectively. It was found that the variation trend shown in Figure 17 was basically consistent with the findings of Arai et al. [3].
3.4. Lateral Stress and Displacement Variations during the Soil Excavation Stage
According to the measured engineering data of Taipei, Wu et al. [19] had divided the horizontal displacements of the wall into four types as follows: Standard type, rotary type, multi-folded type, and cantilever type. It can be seen from Figure 18 that the excavation displacement curve of the circular diaphragm wall was similar to the multi-folded type, which may have been caused by the large differences in soil properties. With the excavation of the engineering shaft, the horizontal displacements of the retaining structure had become increasingly larger, and the maximum horizontal displacement position had continued to move downward. The main reasons for this phenomenon were determined to be the increasing soil pressure with the increases in the shaft depth, and the theological changes of the soil mass deformations over time. In this shaft project, the maximum displacement of the circular diaphragm wall along the depth direction was 18.24 m and was located at 0.82 H, which was similar to the study results of Zeng et al. [20]. Due to the increases in the soil pressure, at the end of shaft excavation process, the soil mass near the wall had moved slightly toward the wall, and the horizontal displacements of the soil mass along the depth direction were mainly at between 10 and 20 m below the connecting wall. This is determined to be due to the fact that the soil penetration depth of the circular diaphragm wall was relatively small, and could not limit the displacements below the bottom of the shaft.
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In the present study, by comparing the distribution curves of the soil pressure and soil displacements in both the smooth and inverse conditions, the displacements and soil pressure distribution models for the round shaft were similar in form in the two methods (direct and inverse), as detailed in Figure 19. This was due to the fact that the circular shaft had a good spatial arch effect, which had positive effects on the deformations of the shaft. However, these findings were different from those reported by Zeng et al. [20]. In the aforementioned study, the displacement pattern laws of the normal and reverse methods were not found to be similar. It should be noted that the direct method included the entire process, and the reverse method was used for the wall lining while excavations were completed.
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3.5. Vertical Shear Force and Bending Moment Variations during the Soil Excavation Stage
Figures 20(a) and 20(b) show the changes of the bending moment and vertical shear force in the different groove sections and the depth distributions, respectively. In the figures, the hollow point represents the smooth construction conditions, while the solid point represents the reverse construction conditions. Figure 20 shows that the bending moment of the wall which had been caused by the reverse construction was large, and was the most obvious near the rock-socketed depth. However, the distribution mode of the bending moment-depth which had corresponded to the different construction methods was found to be similar. The results had indicated that the stress concentrations of the model in the rock-socketed part of the soil wall were large.
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Figure 21 shows the change curve of the circumferential stress of the H-bars between Gutters 7 and 8 with depth after the soil excavation process. It can be seen in the figure that the circumferential stress between Gutters 7 and 8 was dominated by extrusion stress. The circumferential extrusion stress had increased with the depth of the shaft. Incidentally, there were certain stress concentrations at the insertion points of the H-bars. The ratios between the maximum circumferential stress (depth of 21.5 m) and the minimum circumferential stress (ground surface) under each construction condition were 59.65, 76.74, 91.86, 99.29, 102.93, and 108.66, respectively. The stress concentration multiples had gradually increased with the excavation depths.
3.6. Influences of the Soil Penetration Depths on the Internal Force Distributions of the Wall
The depth of the wall penetration is an important design parameter for underground continuous walls. In the present study, based on a finite element model, the distribution curves of the radial section’s internal force along the wall depth with the corresponding depth of wall penetration were 1.52 m, 6.52 m, and 11.52 m at the completion of the foundation pit excavation, as shown in Figure 22. As can be seen in Figure 22(a), the distribution curve of the radial section’s shear force above the foundation pit with the corresponding soil penetration depth of 6.52 m was almost consistent with that of the wall at the soil penetration depth of 1.52 m. When the soil penetration depth of the wall reached 11.52 m, the distribution curve of the radial section’s shear force above the foundation pit was observed to have changed along the depth direction. However, the changes were insignificant. The same rule had also been shown in the distributions of the bending moments along the depths of the radial section of the wall. However, when the soil penetration depth had reached 11.52 m, the bending moment near the bottom of the foundation pit had significantly decreased (Figure 22(b)). It was found that the depth of the wall into the soil had major influences on the distributions for both the shear force and the bending moments in the range below the foundation pit.
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4. Field Monitoring Data Analysis Results
4.1. Monitoring Program
The soil pressure and horizontal displacements of the shield TBM launching shaft during the entire construction process were monitored in this study, and the monitoring points were arranged near the outer side of Gutter 7. The monitoring hole of the soil pressure along the depth was set 0.6 m away from the outer side of Gutter 7. Also, soil pressure boxes were set every 3 m along the direction of the drilling depth. The drilling depth was 24 m, and a total of 24 soil pressure boxes were set. In order to analyze the influence ranges of the trenching and excavation processes on the horizontal displacements of the soil masses, three inclined pipes were set at 0.6 m, 1.4 m, and 2.4 m, respectively, outside Gutter 7. The horizontal distance between the inclined pipes was 2.76 m, and the depth of the inclined pipes was also 24 m. The layouts of the monitoring hole plane and section are detailed in Figure 23.
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4.1.1. Installations of the Soil Pressure Boxes
An engineering geological drilling rig was used to drill to the specified depth at a pre-set position, and drilling diameter was 108 mm. Several steel bars were connected using electric welding in order to form a 24 m long steel bar. Spot welding was to fix the soil pressure boxes on the steel bar. The distance between the soil pressure boxes was 3 m (Figure 22). After all of the soil pressure boxes had been fixed, data lines were arranged and bundled along the steel bar. Then, the steel bar was lifted and inserted into the monitoring hole (Figure 24). It should be noted that the centers of the bottom surfaces of the soil pressure boxes were opposite to the center of the circular shaft. This was done to ensure that the measured soil pressure was the radial horizontal soil pressure. When the entire steel bar was inserted into the hole, prepared clay powder was poured into the hole until it was compacted and filled. Finally, all the data lines of the soil pressure boxes were connected to an automatic data acquisition module (Figure 25). A debugging automatic data acquisition program was implemented in order to achieve the automatic acquisition of the soil pressure data.
4.1.2. Installation of the Inclined Pipe
First of all, a geological drill was used to drill to the specified depth at a pre-set position, and the drilling diameter was 98 mm. Then, pre-made PVC pipes were connected to each other and placed into the drilling hole. It is worth noting that in order to ensure that the measured horizontal displacement is radial, the inclined tube pulley groove is required to coincide with the central axis of the circular diaphragm wall (Figure 26). Also, in order to reduce the monitoring costs and improve the monitoring accuracy, a manual pulley monitor was adopted in this project, and special personnel were arranged to use the manual pulley inclinometer to monitor the horizontal displacements of soil masses along the direction of depth every day in the ring section.
4.1.3. Collection of the Monitoring Data
In the present study, for the purpose of realizing a comparison between the monitoring data and the numerical simulations, the monitoring data were sorted according to the working conditions provided by the numerical simulations. Also, due to the fact that sufficient construction time was required for the grooving and wall formation processes during the actual construction, the soil pressure and horizontal displacements had also changed during the grooving and wall formation processes. In this study’s analysis, those changes were ignored since only the accumulated soil pressure and horizontal displacements during the grooving and wall formation processes were relevant. In this way, the actual monitoring and analyses of the horizontal displacements and soil pressure under the corresponding working conditions of the numerical model could be effectively realized.
4.2. Variations in the Soil Pressure
During the wall-forming stage, the radial horizontal soil pressure had changed with depth under the various working conditions, as shown in Figure 27(a). The variations in the horizontal radial soil pressure with depth were observed to be basically linear. When Gutter 7 was completed, the horizontal radial soil pressure along the depth direction was at the maximum, which had indicated that the lateral wall soil mass had generated large horizontal radial soil pressure under the action of the slurry horizontal pressure. The horizontal radial soil pressure had decreased along the depth direction following the completion of concrete pouring and hardening processes in Gutter 7. It was found that with the completion of the entire wall pouring and hardening process, the horizontal radial soil pressure in Gutter 7 had increased along the depth direction. However, it could not be restored to that state when Gutter 7 was completed. It was found that the other gutter construction processes had little influence on the changes in the lateral soil pressure along the depth of Gutter 7. Figure 27(b) shows the changes in the lateral soil pressure with depth under the different working conditions at the excavation stage. It was interesting to note that, when compared with large-sized foundation pit diaphragm walls, the excavations of the soil masses inside the small- and medium-sized circular diaphragm walls had almost no influence on the soil pressure behind the wall. In the vicinity of the toe of the wall, the excavations were observed to have a certain influence on the soil pressure. However, the influence was minimal. The results of this study’s numerical model had also revealed the same rule.
(a)
(b)
4.3. Variations in the Horizontal Radial Displacements
During the wall forming stage, the relationships between the horizontal radial displacements and the depths in each working condition of the #1, #2, and #3 inclined pipes were as shown in Figures 28–30, respectively. At the gutter formation stage (B1, B4, B7), under the action of the horizontal pressure of the bentonite slurry, the horizontal radial displacement direction of the soil masses on the side wall of the Gutter 7 monitoring points was outside the wall, and had reached the maximum. This had indicated that the horizontal pressure of the bentonite slurry was greater than that of the radial horizontal soil pressure of the gutter. It was found that when the concrete in the gutters had hardened (C1, C4, C7), the horizontal slurry pressure on the soil had disappeared. Also, the horizontal radial displacement direction of the soil masses on the side walls of Gutter 7 had then still pointed outside the wall, but had rebounded to a certain extent. It was observed that with the construction of the other gutters taking place, the horizontal displacements of Gutter 7 were further restored to approximately 0 mm (C2, C6, C10). Moreover, with the subsequent construction of the gutters, the horizontal radial displacements had increased (C9). The radial distances between the #1, #2, and #3 inclined pipes and wall sides were 0.6 m, 1.4 m, and 2.4 m, respectively. As can be seen in Figures 28 to 30, the influence of the grooving on horizontal radial displacements of the soil masses after the gutters were completed was within a 1.4 m range, and when the radial distances had reached 2.4 m, the influence of the grooving on the horizontal radial displacements of the soil masses was already very small. The field monitoring data and the model calculation data were found to have a good consistency with regard to the changed trend.
It was observed that during the excavation stage, the relationships between the horizontal displacements and the depths under different working conditions of the #1, #2, and #3 inclined pipes were are detailed in Figures 31–33, respectively. It can be seen from Figures 31 to 33 that the influences of the soil excavations in the shaft on the horizontal radial displacements of the soil masses were very small, which was consistent with the rule revealed by this study’s numerical model calculations. The results had also fully confirmed that the overall self-stability effect of small- and medium-sized circular underground diaphragm walls was very strong, and the cylinder-type structure was beneficial to the overall stability of the continuous wall.
5. Conclusions and Suggestions
5.1. Conclusions
The processes involved in the installations of small- and medium-sized circular diaphragm walls, along with the effects of soil excavations within the walls, were analyzed in this study as three-dimensional problems. The main findings regarding the lateral stress in the soil, soil displacements, and bending moments of vertical sections of the wall were examined using three-dimensional FEM analysis and field monitoring methods as follows:(1)Numerical calculations using FEM analysis were carried out for the purpose of examining the effects of the installations of small- and medium-sized circular diaphragm walls. This investigation had included the wall formation stage and the subsequent soil excavation stage. Also, the connections and contacts of steel H-bars between the gutters were considered using a numerical model. Then, by comparing the numerical simulations with the actual monitoring data, the distribution laws of the horizontal radial displacements and horizontal radial stress along the depth of the soil masses behind the wall were revealed. It was determined that the results obtained using this study’s numerical model were basically consistent with the actual monitoring results, regardless of which stage was being examined (for example, the wall forming stage or the subsequent excavation stage).(2)The results of this study’s analyses showed that the situation was no longer asymmetric during the wall formation stage, as indicated by the slotting sequences.(3)The bending moments of the wall caused by the reverse construction process were observed to be large, and were the most obvious near the rock-socketed depth. However, the distribution modes of the bending moment-depths which corresponded to the different excavation construction methods were found to be similar. Furthermore, the stress concentrations of the model in the rock-socketed part of the soil wall were found to be high.(4)The results of this study’s numerical model settlement and field monitoring showed that the excavation depths of the vertical shaft had displayed little influence on the horizontal radial soil pressure and displacements at the sides of the wall. Moreover, the excavation depths were found to have little influence on the circumferential stress of the wall. The numerical results also showed that the bending moment distributions of the vertical section of the wall were only minimally affected by both the smooth and inverse construction methods of the excavations.(5)It was found that the circumferential stress of the steel H-bars between Gutters 7 and 8 with depth following the soil excavation was dominated by the extrusion stress. The circumferential extrusion stress had increased with the depth of the shaft. There was found to be certain stress concentrations of the steel H-bars at some of the soil depths, and the stress concentration multiples had gradually increased with the excavation depths.
5.2. Suggestions
In this study, Mohr-Coulomb soil constitutive model is used to describe the stress-strain relationship of circular diaphragm wall. The influence of spatial structure characteristics of small and medium-sized circular diaphragm wall on soil pressure distribution mode behind the wall is not considered. In engineering, this effect is manifested as the self-stabilized “force arch” effect of circular soil. The next step is to study the theoretical problem of soil pressure distribution pattern behind small- and medium-sized circular diaphragm wall.
Notion
| γ: | Unit weight of the soil (kN/m3) |
| φ: | Friction angle (°) |
| E: | Young’s Modulus (MPa) |
| C: | Cohesion force (kPa) |
| h: | The height of web |
| : | The thickness of web |
| bf: | The flange width |
| tf: | The flange thickness |
| B: | The process of removing serial numbers of slots and applying bentonite slurry |
| C: | The process of removing pressure from the bentonite slurry in the trough and activating solid concrete walls |
| D1: | Degree of the gutter ring |
| D2: | The height of web depth of the gutter. |
Data Availability
The data used to support the findings of this study are available from the corresponding author upon request.
Conflicts of Interest
The authors declare that they have no conflicts of interest.