Deformation Law of Tunnels Using Double-Sidewall Guide Pit Method under Different Excavation Sequences

Abstract

The double-sidewall guide pit method finds extensive application in the construction of large cross-section tunnels in soft rock strata due to its minimal disruption to the surrounding rock, thereby enhancing tunnel stability. To investigate the loading and deformation patterns of the surrounding rock and tunnel support using the double-sidewall guide pit method, this study compares the impacts of various construction sequences on surface settlement, surrounding rock stress, and lining stress using indoor model tests. The experimental results show that after excavating the upper guide hole on one side, the excavation of the lower guide hole on the same side is carried out. The upper and lower support structures form a closed loop, and the structure can better constrain the surrounding rock and control the deformation of the surrounding rock, whereas the lower structure can share the stresses suffered by the upper structure. Therefore, compared with the upper and lower excavation methods, the surface settlement caused by the left and right excavation methods is smaller, the disturbance to the surrounding rock is smaller, and the supporting structure is more evenly and stably stressed in the excavation process.

1. Introduction

In recent years, the double-sidewall guide pit method has emerged as a crucial construction approach for mitigating disturbances to adjacent structures and tunnel deformations. This method addresses challenges posed by the dense urban population, extensive surface buildings, and the substantial infrastructure of subway pipe foundations and lines. Compared with other tunnel excavation methods, the double-sidewall guide pit method has great advantages in controlling surface settlement and horizontal displacement and is suitable for the construction of large cross-section tunnels [1,2,3]. Different excavation sequences of guide pits will have different effects on surface settlement, surrounding rock stresses, and lining stresses.

There are many factors affecting the construction of the double-sidewall-guide pit method. In terms of theory, Zhao et al. [4,5,6] studied the effect of the double-sidewall-guide pit method on surface settlement, vault settlement, and horizontal deformation and concluded that the tensile stress is dominant in the connection part of the initial support and diaphragm wall and the compressive stress is dominant in the middle and lower parts of the support structure. Liu et al. [7] studied the mechanical response of the support structure in the construction of a double-sidewall-guide pit in Class V enclosing rock. Liu et al. [8,9,10] conducted on-site monitoring and analysis of the large cross-section double-sidewall tunnels using the double-sidewall guide pit method and concluded that the deformation and force of the surrounding rock and lining are mainly directly related to the construction process and geological conditions used. Cui et al. [11,12] explored how the mechanical behavior of the surrounding rock palm surface changed with the construction sequence and determined and elucidated the influence of the construction sequence on the surface displacement caused by a tunnel excavation. Ling et al. [13,14,15,16] optimized the excavation sequence of the cross-section of tunnels using the double-sidewall guide pit method according to an actual situation on site, and the study showed that the support structure induced by the excavation sequence after the optimization was very good. Wang et al. [17,18] optimized the core column width of tunnels using the double-sidewall guide pit method, and the analysis showed that there was an optimal value for the core column width that could improve the stability of the surrounding rock. Jiao and Yang et al. [19,20,21,22,23,24,25] optimized construction parameters, compared the effects of different curvature radii and excavation schemes on the stability of surrounding rock, and selected the best construction scheme. Li et al. [26,27,28] optimized the construction sequence of the double-sidewall guide pit method, adapted the excavation form of the upper and lower sections, and preserved the core rock columns in the middle soil layer, which accelerated their construction progress and improved the overall stability of the tunnel.

This paper, building upon prior research findings, undertakes a comparative analysis of surface settlement, surrounding rock stress, and lining stress resulting from diverse construction sequences. The investigation employs indoor model tests to elucidate the mechanical response characteristics of both the surrounding rock and supporting structure during tunnel excavation under various construction sequences.

2. Introduction to the Experiment

2.1. Test Material and Apparatus Arrangement

This paper derives from a practical construction project and its test prototype parameters, as detailed in

Table 1. Physico-mechanical parameters of a moderately weathered rock stratum.

Stratigraphy	Physical Indicators			Mechanical Indicators
Moderately weathered muddy siltstone	Natural Density (kN/m3)	Modulus of elasticity/(MPa)	Poisson’s ratio	Cohesion (kPa)	Angle of internal friction (°)
	23.5	1758	0.34	654	33.21

. To enhance the simulation of an authentic tunnel construction process and capture the effects of variations in the mechanical behavior of peripheral rock support, the indoor physical model test is conducted at a scale of 1:45. The similarity ratios for stress, elastic modulus, and cohesive force can be deduced by integrating the three fundamental theorems of similarity theory with the basic equations of elasticity: $C_{\sigma }=C_E=C_C=45$. The displacement similarity ratio is $C_{\delta }=45$. The strain similarity ratio is $C_{\epsilon }=1$. The internal friction angle similarity ratio is $C_{\phi }=1$.

Following an examination of analogous materials in the surrounding rock, quartz sand was selected as the filling material, whereas lower-strength materials like clay or barite powder were chosen as the cementing material. Multiple sets of straight shear tests were conducted, and using iterative comparisons and analyses of model materials, the proportions of quartz sand, clay or barite powder, lubricant, and water were adjusted within a defined range to establish mechanical indices. The basic physical parameters of the tested soil are presented in

Table 2. Experimental soil ratio and physical parameters.

Quartz Sand	Clays	Lubricants	Water	Cohesion (kPa)	Angle of Internal Friction (°)
47%	8%	1%	14%	12.70	32.33

.

Following multiple tests, it was observed that the lining composed of barite powder exhibited a low modulus of elasticity and failed to meet the required similarity ratio. Consequently, the lining model material was altered to a mixture of gypsum, water, and a small amount of cement. The modulus of elasticity of the lining’s analogous materials varies with the mass ratio of gypsum, water, and cement. To achieve the stipulated similarity ratio, unconfined uniaxial compressive strength tests were conducted on the lining’s similar materials with different mix ratios, utilizing an electronic universal testing machine. The stress–strain curves and modulus of elasticity were measured, and after several tests, it was determined that the gypsum: water: cement ratio of 1:0.75:0.25 met the similarity requirements. The finalized mix yielded a similar material modulus of elasticity of 558.66 MPa.

The primary objective of this test is to analyze the loading and deformation patterns of perimeter rock support induced by various construction sequences. The measured parameters encompass surface deformation, perimeter rock stress, and lining stress. Surface deformation is quantified using a percentage meter with a range of 0–10 mm and an accuracy of 0.01 mm, as depicted in Figure 1. The DMTY-type resistive strain earth pressure box, illustrated in Figure 2, is employed to gauge static or dynamic earth pressure values in the surrounding rock. Data on the stresses of both the surrounding rock and the lining are collected using the DH3818Y static strain tester, as shown in Figure 3.

2.2. Model Experimental Setup

Indoor model tests are used to study field engineering problems with a certain scaling based on the similarity theory. Geotechnical engineering, especially underground structural engineering, has complex geological conditions and many uncertainties in engineering, so it is still difficult to accurately solve the structural forces in mathematical calculation and mechanical analysis. Indoor model tests can remove mathematical and mechanical difficulties using real physical entities, and reflect the physical and dynamic response of the surrounding rock support structure in the process of tunnel excavation in a detailed, real, and direct way [29,30,31].

The geometric scale for this indoor physical modeling test is 1:45, and the vertical loading is achieved using a custom-made steel frame and model box. The overall dimensions of the model box are 180 × 150 × 50 cm (length × height × thickness), as illustrated in Figure 4. The frame of the model box consists of impermeable square steel panels with a thickness of 30 mm, which are spliced together. Positioned in front of the frame is a 10 mm thick acrylic glass plate, while the remaining sides are constructed with 10 mm thick wooden boards, covered with a layer of rubber for effective sealing. In accordance with the specifications of the actual project, the upper part of the tunnel features 65 cm thick surrounding rock, and the lower part has 50 cm thick surrounding rock.

2.3. Experimental Program and Experimental Macrophenomena

This test replicates the excavation process of a tunnel using the double sidewall guide pit method, dividing the tunnel into six guide pits, as illustrated in Figure 5. The experiment is categorized into two groups: the first group, an excavation sequence optimization group, employs the up-and-down excavation method. It is initiated by excavating the upper left and right guide holes, followed by the upper intermediate guide holes. Subsequently, the lower left and right guide holes are excavated, concluding with the excavation of the lower intermediate guide holes, sequenced as ①–②–③–④–⑤–⑥. The second group follows the left-and-right excavation method, where the left and right cross sections are initially constructed to promptly form the support system, and the intermediate section is subsequently developed, sequenced as ①–④–②–⑤–③–⑥.

Following the determination of the matching ratio from the proportioning test, the perimeter rock similar material is meticulously prepared. The soil body is then filled to the specified height, with the preburial of the tunnel lining model. Subsequently, the surrounding soil is compacted, ensuring full contact between the outer surface of the lining and the soil body. Simultaneously, the earth pressure box is preburied at the designated position, and the perimeter rock similar materials are left undisturbed for 12 h after filling to ensure that the perimeter rock deformation, soil solidification, and settlement essentially stabilize. After achieving stabilization, the experimental setup proceeds with the installation of a percentage meter to measure surface settlement. The initial reading is recorded after meter setup, and subsequent readings are noted before and after each step of the guide hole excavation. A strain signal acquisition and analysis system is established in the computer, capturing the initial values of the earth pressure box and the strain gauge. Simultaneously, the software is configured to automatically save data, facilitating continuous data collection from the earth pressure box and the strain gauge. Guide holes are then excavated in different sequences, and the temporary support of each section is sequentially dismantled after all guide holes have been excavated. An interval of 12 h is maintained between each support dismantling, followed by an additional 12-h period of standing time after the removal of all temporary supports. After the stabilization of the soil body deformation, relevant test data are recorded. The entire experimental process is depicted in Figure 6, Figure 7 and Figure 8.

3. Analysis of Test Data

3.1. Analysis of Surface Deformation Results

Figure 9 shows that the surface settlement above the center line of the tunnel is more pronounced compared to the left line. For lateral monitoring points, the final settlement value at monitoring point 1 is 0.238 mm, which is 10.70% larger than the final settlement value of 0.215 mm at monitoring point 4. The settlement at monitoring point 2 is 12.03% larger than that at monitoring point 5, and the settlement at monitoring point 3 is 26.09% larger than that at monitoring point 6. This discrepancy arises from the multiple construction disturbances of the left and right guide holes and the middle guide hole affecting the surface above the center line, resulting in greater settlement. In contrast, the left line experiences a relatively smaller impact from the excavation of the left and middle guide holes, with the excavation of the right guide hole having less influence. Examining longitudinal monitoring points, the settlement at monitoring point 1 surpasses that at monitoring point 2 by 34.46%, monitoring point 2 exceeds monitoring point 3 by 205.17%, monitoring point 4 surpasses monitoring point 5 by 36.06%, and monitoring point 5 exceeds monitoring point 6 by 243.48%. This pattern indicates that the closer the location to the opening, the larger the surface settlement, while locations further from the opening exhibit smaller settlement values. The disturbance caused by the excavation of the first guide hole affects the surface of the cave entrance, and subsequent guide hole excavations continue to impact the surface, resulting in larger settlement values closer to the entrance. In this test, monitoring points 5 and 6, located at the surface of the unexcavated soil behind the tunnel, experienced minimal settlement.

While the excavation of the upper guideway exerts a more pronounced impact on surface settlement, the timely application of the upper guideway to the support structure following the completion of excavation serves to support and restrict the vertical displacement of the soil body. Consequently, the excavation of the lower guideway has a comparatively smaller impact on surface settlement. Focusing on monitoring point 1 for analysis, the surface settlement pattern of the tunnel reveals that the excavation of the upper guide hole directly beneath monitoring point 1 exerts the most significant influence on its settlement. Monitoring point 1 settles by 0.034 mm, 0.034 mm, and 0.052 mm after the excavation of the upper-left 1, upper-right 1, and upper-right 1 guide holes, respectively, accounting for 14.29%, 14.29%, and 21.85% of the total settlement value. The excavation of the upper guideway represents a crucial construction phase necessitating prompt application of support structures and vigilant monitoring. Subsequent excavation of the lower guideway has a diminished impact due to the support and restraint provided by the upper superstructure. The settlement from the excavation of the second and third ring sections amounts to 0.060 mm and 0.008 mm, respectively, constituting 25.21% and 3.36% of the total settlement value.

The general trend of surface settlement at monitoring point 1 indicates that in the early stage when the excavation surface is directly below the monitoring point, settlement drops rapidly with the largest settlement rate. As the excavation surface advances and gradually moves away from the monitoring point, the settlement rate diminishes, and the settlement curve gradually flattens out, ultimately stabilizing. Specific surface deformation data for the second group of tests are depicted in Figure 10. The surface settlement trend caused by different construction sequences exhibits slight variations, yet the overall pattern remains consistent. Settlement is primarily influenced by the excavation of the upper guide hole and the distance between the excavation surface. The second group of the test excavation program involves constructing the left and right side sections first and subsequently excavating the middle section after the upper and lower support structures form a closed loop. Settlement values at monitoring points 1–6 are, respectively, 4.62%, 18.64%, −1.70%, 13.49%, 6.96%, and 58.70% smaller than those of the first group of tests, indicating that the timely formation of the closed loop of the support structure has a certain control effect on surface settlement.

3.2. Analysis of Surrounding Rock Stress Results

The stress-time curve of the surrounding rock in the first test group is depicted in Figure 11. The examination of the figure reveals that the peripheral rock at each point around the tunnel, under the initial stress state, is subjected to compressive stress. The magnitude of the stress is directly correlated with the depth of burial, with greater depths resulting in higher initial stress values. The initial stress value of the peripheral rock at the arch top is 7.449 kPa. The average initial stress value of the peripheral rock at the arch shoulder is 8.497 kPa. The average initial stress value of the peripheral rock at the arch waist is 8.646 kPa. The average initial stress value of the peripheral rock at the foot of the arch is 9.079 kPa. and the average initial stress value of the peripheral rock at the bottom of the arch is 10.113 kPa.

After the excavation of the upper middle 1 guide hole, the peripheral rock at the arch top undergoes a rapid release of the original stress, resulting in a swift decrease in compressive stress from 7.188 kPa to 2.870 kPa. Subsequently, the stress stabilizes under the influence of the supporting structure. The upper guide hole of the second ring, situated adjacent to the peripheral rock of the arch, experiences a gradual increase in peripheral rock stress, as the stress released after excavation is transferred to the arch. The stress value after the completion of the excavation of the middle and upper 2 guide holes reaches 3.680 kPa. The excavation of the lower guide hole of the second ring and the third ring section exerts a lesser influence on peripheral rock stress, leading to a slow and fluctuating increase in stress. The stress value after the completion of the excavation of all guide holes amounts to 4.213 kPa. Upon the removal of the temporary support, the peripheral rock stress increases due to disturbance, resulting in a compressive stress value of 5.241 kPa when all temporary supports are removed.

The stress distribution of the left and right surrounding rock exhibits symmetry, and the stress variation pattern is essentially identical. Consequently, the arch shoulder, arch waist, and arch foot are collectively considered as the left surrounding rock for analysis. Following the excavation of the upper left 1 guide hole, the compressive stress undergoes a rapid decline from 8.342 kPa to 4.860 kPa. Subsequent excavation of the upper left 2 guide holes leads to a slight increase in stress to 5.701 kPa, after which the stress value stabilizes. Minimal fluctuations occur in the subsequent excavation phases, and upon the completion of all guide holes, the stress value reaches 6.035 kPa. The removal of the temporary support induces fluctuations in the surrounding rock stress value due to disturbances. Specifically, when all temporary supports are removed, the compressive stress of the surrounding rock fluctuates, settling at a value of 5.916 kPa.

The arch-waist perimeter rock experiences stress release after the excavation of both upper-left 1 and lower-left 1 guide holes, resulting in a decrease in stress values. Specifically, during the excavation of the upper-left 1 guide hole, the stress decreases from 8.854 kPa to 7.600 kPa, and during the excavation of the lower-left 1 guide hole, it decreases from 8.175 kPa to 7.514 kPa. Subsequent excavation of the adjacent upper-left 2 and lower-left 2 guide holes induces a gradual increase in stress values, reaching from 7.401 kPa to 7.748 kPa during the excavation of upper-left 2 guide hole and from 7.810 kPa to 8.082 kPa during the excavation of lower-left 2 guide hole. Upon the removal of the temporary support, the initial support undergoes inward shrinkage and deformation due to the lack of support. At the arch waist, the surrounding rock briefly forms a critical surface, causing a decrease in stress values. The compressive stress of the surrounding rock settles at a value of 6.431 kPa upon the completion of the removal of temporary support.

The peripheral rock at the foot of the arch, situated below the lower left guide hole, exhibits an overall gradual increase in stress values. The peripheral rock stress value reaches 10.033 kPa upon the completion of all guide hole excavations and further increases to 10.601 kPa after the removal of all temporary supports.

Additionally, the peripheral rock at the bottom of the arch undergoes a stress release after the excavation of the middle-lower 1 guide hole and middle-lower 2 guide holes. The stress value reduces to 7.458 kPa following the excavation of the middle-lower 1 guide hole and further decreases to 7.098 kPa after the excavation of the middle-lower 2 guide hole. Subsequent excavation of the middle and lower 2 guide holes leads to a decrease in stress values from 10.886 kPa to 7.458 kPa and from 7.786 kPa to 7.098 kPa, respectively. The remaining guide hole excavations result in a gradual increase in stress values. Upon the completion of all guide hole excavations, the stress value of the surrounding rock settles at 7.572 kPa. After removing all temporary supports, the stress value of the entire structure reaches 8.381 kPa.

The observed stress change patterns in the surrounding rock reveal that, following guide hole excavation, the area near the excavation zone experiences deformation toward the excavated chamber due to the release of constraints. During this deformation process, a portion of the energy is released, leading to a reduction in compressive stress. The diminished energy is then transferred to the surrounding geotechnical body, resulting in the redistribution of stress within the surrounding rock. Upon the application of the support structure, it generates resistance against the movement of the rock body, establishing corresponding constraints. Consequently, the deformation of the surrounding rock gradually weakens until a new balance is achieved between the surrounding rock and the support structure. Upon the removal of the diaphragm wall providing vertical support and the temporarily elevated arch providing horizontal support, the joint between the initial support and the temporary support undergoes inward shrinkage and deformation due to the lack of support. In this scenario, the nearby surrounding rock temporarily forms a critical surface, leading to a reduction in stress values that are then transferred to the surrounding area.

The specific data on surrounding rock stress in the second group of tests are presented in Figure 12. It is evident from the figure that, due to the different excavation sequences in the second group of tests, the temporal changes in perimeter rock stress at each point differ from those in the first group. Nonetheless, the overall pattern remains consistent. The perimeter rock stress is primarily influenced by the excavation of adjacent guide holes, causing a decrease in stress values near the excavation area and an increase in neighboring perimeter rock stress values. The construction of guide holes at a greater distance has a lesser impact on perimeter rock stress values. To gauge the degree of disturbance of excavation on the surrounding rock, average stress change values were calculated. A larger value indicates a greater disturbance caused by excavation. The average stress change values at the top of the arch, the left and right arch shoulders, the left and right arch waist, the left arch foot, and the bottom of the arch are smaller in the second group by 2.81%, −9.66%, 12.25%, 23.59%, 38.35%, 22.04%, and 16.76%, respectively, compared to the first group. This suggests that the left and right excavation methods result in less disturbance to the surrounding rock. This is attributed to the excavation of upper and lower guide holes on the same side first, forming a closed loop in the upper and lower supporting structures, enabling better restraint of the surrounding rock. Consequently, the deformation of the surrounding rock during excavation is minimized, resulting in smaller changes in stress values.

3.3. Analysis of Lining Stress Results

Figure 13 illustrates the time course curve of lining stress for the first set of tests. Following the excavation of the upper left 1 guide hole, the surrounding rock undergoes deformation towards the excavation chamber. The supporting structure, in turn, bears the force exerted by the surrounding rock. Consequently, the lining stress values of the left arch shoulder, left arch waist, left elevation arch, and the upper left diaphragm wall all experience an increase. Specifically, the stress value of the left arch waist rises from 2.454 kPa to 7.174 kPa, the left elevation arch stress increases from 0.158 kPa to 1.456 kPa, and the stress value of the upper left diaphragm wall rises from −0.973 kPa to 7.730 kPa.

After excavating the upper-right 1 guide hole, the lining stress values for the right arch shoulder, right arch waist, right elevated arch, and upper-right diaphragm wall all experience an increase. Specifically, the stress value of the right arch waist rises from −0.251 kPa to 5.328 kPa, the stress value of the right elevated arch increases from 0.884 kPa to 1.261 kPa, and that of the upper-right diaphragm wall rises from 0.579 kPa to 8.096 kPa. The left side of the supporting structure is relatively unaffected by the excavation of the upper-right 1 guide hole, with stress values showing only slight fluctuations. Following the excavation of the middle-upper 1 guide hole, the overall superstructure experiences an elevation in stress values. The lining stress of the arch top increases from 1.103 kPa to 5.556 kPa, the left arch waist stress rises to 9.583 kPa, the right arch waist stress increases to 7.239 kPa, and the left superelevation arch stress reaches 2.679 kPa. The stress values of the right superelevation arch and left upper diaphragm wall rise to 1.675 kPa and 9.908 kPa, respectively, while the right upper diaphragm wall stress increases to 11.432 kPa. This indicates that the applied vault lining and the middle superelevation arch connect the two sides of the supporting structure into a unified whole, transferring the force exerted by the overlying surrounding rock to the entire superstructure. Consequently, the overall stress value of the structure increases. The arch top and diaphragm wall bear the direct vertical soil pressure, resulting in higher stress values compared to the rest of the structure. The stress values of the right arch waist and right upper diaphragm wall decrease to 2.427 kPa and 10.936 kPa, respectively, while the stress values of the right foot of the arch, the right lower diaphragm wall, and the right superelevation arch rise to 1.126 kPa, 6.924 kPa, and 3.377 kPa, respectively. Construction disturbances lead to damage in the support structure of the remaining guideway, causing stress values to fluctuate. Following the excavation of the middle and lower 1 guide hole, stress values for the upper left diaphragm wall, upper right diaphragm wall, left elevation arch, and right elevation arch decrease to 7.529 kPa, 8.142 kPa, 2.761 kPa, and 2.486 kPa, respectively. Simultaneously, stress values for the left arch waist, right arch waist, left arch foot, right arch foot, lower left diaphragm wall, lower right diaphragm wall, and the bottom of the arch rise to 5.524 kPa, 4.374 kPa, 2.178 kPa, 2.484 kPa, 10.485 kPa, 10.468 kPa, and 3.179 kPa. This indicates that after the excavation of the middle and lower guiding tunnel and the application of the arch bottom supporting structure, the supporting structure of the first ring tunnel connects into a cohesive whole, leading to redistributed and downward concentrated lining stresses.

The construction of the entire upper guide tunnel for the second ring tunnel leads to increased stress values at various points. Specifically, the arch top, left arch waist, right arch waist, left upper diaphragm wall, and right upper diaphragm wall experience increases to 6.690 kPa, 8.894 kPa, 6.973 kPa, 12.405 kPa, and 10.663 kPa, respectively. Concurrently, the stress values of the left lower diaphragm wall and right lower diaphragm wall decrease to 7.287 kPa and 9.834 kPa. This shift suggests that stresses on the second ring support structure are transferred to the first ring, resulting in heightened stress on the upper structure of the first ring. Simultaneously, the lower structure of the second ring, which has not been applied yet, exhibits non-uniform stress distribution and force transmission, leading to upward stress concentration and a reduction in stresses on the lower support structure. Following the excavation of the second ring’s lower guide hole, lining stresses re-center to the lower support structure. Stress values for the arch waist, upper left center diaphragm wall, and upper right center diaphragm wall decrease, while those for the arch foot, arch bottom, lower left center diaphragm wall, lower right center diaphragm wall, and superelevation arch increase.

The stress pattern of the support structure in the third ring section excavation mirrors that of the second ring, albeit with a smaller overall impact due to the increased distance from the first ring. The stress values of the first ring’s support structure fluctuate up and down. Upon the completion of all guide hole excavations, the lower left and lower right diaphragm walls bear the highest stresses at 11.932 kPa and 11.841 kPa, respectively. They are followed by the upper left and right diaphragm walls at 8.536 kPa and 10.626 kPa, and then the arch roof at 7.568 kPa. The stress values for the arch top follow at 7.568 kPa, with the left and right arch waist stresses at 5.897 kPa and 7.415 kPa, respectively. Finally, the stress values for the left and right foot of the arch, the left and right superelevation arches, and the bottom of the arch show minimal differences, maintaining values near 3.503 kPa. This analysis reveals that the primary stress-bearing positions in the double sidewall tunnel are the diaphragm wall, arch top, and lining at the arch waist. The diaphragm wall handles the vertical load imposed by the overlying surrounding rock, while the vault and arch waist bear and transfer the vertical and horizontal loads from the surrounding rock. Monitoring the arch footing, positioned horizontally at the corner of the side wall, is crucial, as per the stress transfer principles mentioned above. Stress concentration is expected in the vertical arch footing of the side wall, making it a significant stress point in the supporting structure. Conversely, stresses in the horizontal arches, foot arch bottom, and temporary elevation arches are relatively small.

Upon the removal of temporary support, the stresses initially borne by the diaphragm wall and temporary elevated arch are transferred to the initial support, resulting in an increase in the stress values of the initial support. Following the removal of the temporary support from the first ring, the stresses on the diaphragm wall and temporary support shift to be supported by the initial support of the first ring and the temporary support of the second ring. The temporary support of the second ring contributes to the support capacity, causing a minor increase in the stress value of the initial support of the first ring. Specifically, the stress values of the arch top, left and right girdle, left and right foot of the arch, and arch bottom increase by 0.474 kPa, 0.524 kPa, 1.690 kPa, 0.803 kPa, 0.484 kPa, and 0.374 kPa, respectively. Upon the removal of the temporary support from the second ring, the initial support of the first ring assumes the majority of the pressure from the overlying peripheral rock, resulting in a significantly higher stress value. The stress values of the arch top, left and right arch waist, left and right footings, and the bottom of the arch increase by 1.210 kPa, 0.755 kPa, −0.590 kPa, 0.910 kPa, 1.210 kPa, and 0.751 kPa, respectively. The third ring’s temporary support, which is distant from the initial support of the first ring, experiences minimal impact upon the removal of the first ring’s initial support. The stress values show slight fluctuations, and the final stress values for the arch, left and right arch waist, left and right arch foot, and the bottom of the arch are 9.498 kPa, 6.221 kPa, 8.152 kPa, 5.120 kPa, 4.658 kPa, and 4.585 kPa, respectively.

Figure 14 illustrates the time course curve of lining stress for the second set of tests. Following the excavation of the upper left 1 guide hole, the stress values for the left arch waist, left elevated arch, and upper left diaphragm wall experience an increase, reaching 9.073 kPa, 0.817 kPa, and 8.703 kPa, respectively. Notably, the stress change is most significant for the left arch waist and the upper left diaphragm wall in this construction step. Consequently, it is crucial to enhance monitoring efforts for the left arch waist and the upper left diaphragm wall during the excavation of the upper left 1 guide hole. After excavating the lower left 1 guide hole, the lower structure assumes a portion of the stress, resulting in a decrease in stress values for the upper structure and an increase in stress values for the lower structure. Stress values for the left arch waist and the left upper diaphragm wall decrease to 3.696 kPa and 5.353 kPa, respectively. Simultaneously, stress values for the left arch foot, left elevated arch, and left lower diaphragm wall increase to 2.812 kPa, 5.990 kPa, and 3.248 kPa, respectively.

Excavating the upper right 1 guide hole induces an increase in stress values for the right arch waist, right elevation arch, and upper right diaphragm wall, reaching 6.813 kPa, 1.112 kPa, and 5.345 kPa, respectively, with minimal impact on the structure on the left side. Following the excavation of the lower right 1 guide hole, stress values for the right arch waist and the upper right diaphragm wall experience a rapid decrease to 2.952 kPa and 4.433 kPa, while stress values for the right arch foot, right elevation arch, and lower right diaphragm wall increase to 2.957 kPa, 2.576 kPa, and 6.618 kPa, respectively. The stress values on the left side structure show small fluctuations. Post-excavation of the middle and upper 1 guide holes, stresses on both sides of the supporting structure increase. However, the overall stress rise is not significant due to the applied substructure. The left and right arch foot, left and right arch waist, left upper diaphragm wall, left lower diaphragm wall, right upper diaphragm wall, right lower diaphragm wall, and left and right elevation arches experience elevation, reaching 4.526 kPa, 3.821 kPa, 2.992 kPa, 3.218 kPa, 7.267 kPa, 7.931 kPa, 6.836 kPa, 8.262 kPa, 3.437 kPa, and 2.965 kPa, respectively. Upon the excavation of the middle and lower 1 guideway, stress within the tunnel concentrates downward, resulting in a decrease in superstructure stress and an increase in substructure stress. The stress values for the upper left diaphragm wall, upper right diaphragm wall, left elevation arch, and right elevation arch decrease to 5.169 kPa, 5.576 kPa, 1.471 kPa, and 1.451 kPa, respectively. Meanwhile, the stress values for the left arch waist, right arch waist, left arch foot, right arch foot, lower left diaphragm wall, lower right diaphragm wall, and arch bottom increase to 5.606 kPa, 5.001 kPa, 3.915 kPa, 3.605 kPa, 9.244 kPa, 10.386 kPa, and 4.683 kPa.

The excavation of the left section of the second ring tunnel predominantly affects the support structure on the left side. The stress values for the left arch waist, left arch foot, left upper diaphragm wall, left lower diaphragm wall, and left superelevation arch increase to 5.954 kPa, 4.596 kPa, 8.194 kPa, 9.380 kPa, and 5.766 kPa, respectively, while the stress value on the right side of the support structure undergoes minimal change. Subsequently, the excavation of the right section also elevates the stress value of the right supporting structure. The stress values for the right arch waist, right arch foot, right upper diaphragm wall, right lower diaphragm wall, and right superelevation arch increase to 5.047 kPa, 5.078 kPa, 6.988 kPa, 9.170 kPa, and 4.932 kPa, respectively. The stress is concentrated again on the substructure after the completion of the intermediate section excavation.

The stress pattern of the support structure during the excavation of the third ring section follows the same trend as the second ring, albeit with a lesser degree of influence. Upon completing all guide hole excavations, the stress magnitude for each structure matches that of the first group. The highest to lowest stress values are the lower diaphragm wall, upper diaphragm wall, arch waist, arch bottom, arch foot, and superelevation arch, respectively. The stress change after removing the temporary support follows the same rule as the first group, resulting in an elevated stress value for the initial support. The final stress values for the left and right arch waist, left and right arch foot, and arch base are 7.741 kPa, 8.812 kPa, 5.934 kPa, 5.233 kPa, and 7.464 kPa, respectively.

Compared with the first set of tests, the second set was conducted after excavating the upper guide tunnel on one side, allowing subsequent excavation of the lower guide tunnel on the same side. This enabled the substructure to share some of the stresses, resulting in a more evenly distributed overall structural stress. In the first group of tests, the average stress values for the left arch waist and left upper diaphragm wall during the excavation of the first ring tunnel were 5.621 kPa and 7.018 kPa, respectively. In the second group of tests, these values decreased to 4.487 kPa and 5.621 kPa, respectively, representing a 20.17% and 19.91% reduction compared to the first group. Excavating the right (left) side guide tunnel followed by the excavation of the lower guide tunnel in both groups resulted in the connection of the upper and lower structures, forming a closed loop and increasing overall stability. Construction disturbance had minimal impact on the entire structure. In the first group, after excavating the upper-left 1 guide hole and applying the supporting structure, the construction of the upper-right 1 guide hole reduced the stress value of the left arch waist from 7.174 kPa to 6.073 kPa, with a strain change of 1.101 kPa. In the second group, after the construction of the lower-left 1 guide hole, the construction of the upper-right 1 guide hole and the lower-right 1 guide hole reduced the stress value of the left arch waist from 3.696 kPa to 3.550 kPa, and then increased to 3.914 kPa, with an average stress change of 0.255 kPa. Following the construction of both side guide holes and then the middle guide hole, the stress increase value for both side structures was smaller in the second group after the substructure was applied, allowing it to share the stress of the upper structure. In the first group, excavating the middle upper 1 guide hole increased the stress value of the left arch waist from 6.073 kPa to 9.583 kPa, with a stress change of 3.510 kPa. In the second group, excavating the middle upper 1 guide hole increased the stress value of the left arch waist from 3.914 kPa to 4.526 kPa, with a stress change of 0.621 kPa.

In summary, the left-and-right excavation method and the up-and-down excavation method result in little difference in the final support stress magnitude. However, using the left-right excavation method yields a more evenly distributed and stable support structure during the excavation process, minimizing the impact of construction disturbance.

4. Conclusions

In this paper, based on modeling tests, two sets of modeling tests were carried out using two different excavation sequences, the up-and-down excavation method and the left-and-right excavation method, to determine the interaction between the surrounding rock and the supporting structure by studying the surface settlement, the surrounding rock stresses, and the lining stresses induced by the different excavation sequences:

(1) For the surface settlement law, at the same burial depth, the surface settlement is mainly related to the excavation surface approaching, penetrating, and moving away from the surface. With the excavation surface close to the surface, the settlement rate shows a trend of increasing and then decreasing. For tunnels with upper and lower multiple guide tunnels, the construction of the upper guide tunnels has a greater impact on the surface settlement. For tunnels with multiple guide tunnels on the left, center, and right, the surface in the middle is affected by the overlap of the construction of the left and right guide tunnels, which results in a greater settlement than the left and right surfaces.

(2) For the surrounding rock stress law, the initial stress state of the tunnel around the points of the surrounding rock is in a state of pressure, and the size of the stress is positively correlated with the depth of burial. After the support structure is applied, the deformation of the surrounding rock gradually decreases until the surrounding rock and the support structure reach a new equilibrium. After the removal of the diaphragm wall that provides vertical support and the temporary elevated arch that provides horizontal support, the connection between the initial support and the temporary support shrinks and deforms inwardly, and the value of the stress decreases and transfers to the surroundings.

(3) Lining the stress law, the stress value of the support structure increases because of the force given by the surrounding rock after the excavation of the guide hole. After the excavation of the lower guide hole and application of the support structure, the stress value of the lower structure increases while the stress value of the upper structure decreases. After the excavation of the middle and upper guide holes and the application of the support structure, the stress value of the two sides of the structure increases. After the middle and lower guide holes are excavated and the supporting structure is applied, the lining stress of the whole structure is redistributed and concentrated downward. When the temporary support is removed, the stress on the diaphragm wall and the temporarily elevated arch is transferred to be borne by the initial support, and the stress value of the initial support increases.

(4) Compared with the upper and lower excavation method, the surface settlement caused by the left and right excavation method is smaller, and the timely formation of a closed loop of the support structure has a certain control effect on the surface settlement. The left and right excavation method causes less disturbance to the surrounding rock, which indicates that the overall structure can better restrain the surrounding rock. The support structure is allowed to be more evenly and stably loaded during the excavation process, and the excavation disturbances have a smaller impact on the support structure.