Experimental and Numerical Investigation on the Damage Mechanism of a Loess–Mudstone Tunnel in Cold Regions

Abstract

To address loess–mudstone tunnel damage resulting from mudstone swelling induced by water absorption in cold regions, model experiments and numerical simulations were employed to study the tunnel surrounding rock pressure distribution and the stress characteristics of support structures during mudstone swelling at the tunnel base. The findings reveal that the base uplift of the tunnel leads to a rapid stress increase on the arch, and the self-supporting of the interface is insufficient, causing uneven stress distribution on the tunnel. The stress peak value at the bottom of the outer arch is 30.8% of that at the inner side. The internal force of the tunnel lining at the arch crown is the largest. The compressive stress appears at the arch feet, while the tensile stress appears at the outer side of the lining. The bending moments of the inverted arch are larger than those of the arch shoulders and arch crown. The left arch shoulder and arch bottom are primarily subjected to negative bending moments, and the maximum values are about −500 kN·m and −400 kN·m, respectively. The left side of the inverted arch is first to crack, and two main cracks then appeared at the left and right arch shoulders, respectively. The formation and development of the longitudinal cracks in the arch induced by water absorption cause the inverted arch bulge failure. This study helps understand the damage mechanism of the loess–mudstone tunnel in cold regions.

1. Introduction

Over the years, China’s rapid economic growth and the continuous promotion of the land and maritime Silk Road initiative have necessitated the construction of numerous tunnels across composite stratum areas. These composite strata exhibit significant differences in the physical and mechanical properties, as well as the engineering geology characteristics. Consequently, tunneling through such strata will potentially lead to the tunnel collapse, back-arch bottom bulging, support structure deformation, and other issues, posing serious threats to the tunnel operational safety. In loess regions, the loess–mudstone binary structure is a typical mountain structure pattern, characterized by the overlying loess and underlying bedrock (mudstone) [1]. Mudstone is a special geological body between soil and rock, which shows the characteristics of water absorption and expansion. The physical and mechanical properties of mudstone will be deteriorated when it encounters water, which can easily result in the bulging failure of the tunnel’s inverted arch [2,3]. The floor heave failure of the tunnel inverted arch is related to the geological structure, geological environment, load conditions, type design, and construction quality [4]. The substantial differences in the loess and mudstone properties result in the bearing capacity of the surrounding rock at their intersection being severely inadequate. Consequently, the deformation and damage of the tunnel surrounding rock and support structure after excavation is a pressing issue that must be addressed during the construction of loess–mudstone tunnels.

Before tunnel excavation, the surrounding rock exists in an original equilibrium stress state. Excavation disrupts this equilibrium and causes the initial rock stress to redistribute, subsequently leading to deformation and damage to the tunnel surrounding rock. The joint rock–support structure theory posits that an ideal support structure system should ensure the tunnel surrounding rock and support structure system form a secure and stable integrated entity [5]. In actual tunnel construction, accurately measuring the pressure distribution of the surrounding rock and the force exerted on the supporting structure proves challenging due to various factors. Therefore, studying the pressure distribution laws of the surrounding rock and the force characteristics of the support structure in loess–mudstone tunnels is crucial for the safe operation of the tunnels in loess regions.

Numerous scholars have employed model tests and numerical simulations to study the pressure distribution laws of the tunnel envelopes and the force characteristics of the support structures. Anagnostou [6] carried out related research on the inverted arch floor heave mechanism of tunnels with expansive surrounding rocks from micro and macro perspectives. Wilson [7] suggested that the deformation within the tunnel envelope’s plastic zone contributed to the undercurrent bulge diseases of the elevation arch, and the plastic zone’s extent, plastic strain values, and expansive envelope at the tunnel bottom were the significant influencing factors. Seki et al. [8] studied the crack expansion force law of the elevation arch and its filling layer using indoor model tests and finite difference method-based numerical analysis. Liang [9] explored the influence of local stacking positions on the large deformation of tunnels in soft strata, using reduced-scale model tests combined with finite element analysis. Afouz [10] suggested three main types of factors that contributed to the tunnel undercutting, i.e., hydrophysics, loose subgrade rock, and high geopathic stress. Kim [11] verified that the elevated arch section was superior to the slab section in terms of load resistance by the indoor model tests and numerical analyses of a high-speed railroad tunnel section in Korea. Ma [12] investigated the impact of the expansive soils on the tunnel stability, and found that the expansion effects on the tunnels were a nonlinear change under the combined action of load and strain.

Based on the aforementioned work, in composite strata, the physical and mechanical properties of individual layers vary considerably, significantly impacting the safety and stability of tunnels. However, none of these investigations explicitly focuses on tunnels in loess–mudstone composite strata. Therefore, studying the pressure distribution in tunnel envelopes and the force principles of the support structures within tunnels traversing loess–mudstone junction strata is of considerable theoretical and engineering importance.

2. Project Overview

This study focuses on the Xia-Kou Tunnel, and its engineering geological cross-section is depicted in Figure 1. The tunnel site is located in Qingshui, Gansu, China, and it comprises the separate double tunnels for the left and right lines. The overlying strata in the tunnel site area consists of the Quaternary Holocene slope deposits (Q₄^dl) containing gravel, Upper Pleistocene aeolian deposits (Q₃^eol) of loess, alluvial (Q₃^al) loess, rounded gravel, and underlying Neoproterozoic (N) sandy mudstone. The sandy mudstone is characterized as being a very soft rock with poor weathering resistance, prone to softening and disintegration in water, cracking upon water loss, collapsing in the arch post-excavation, deforming the sidewall, and exhibiting poor surrounding rock stability. Loess is marked by self-weight subsidence, poor self-stability, and a tendency for arch and sidewall collapse following excavation. Under the condition of water and air drying, the properties of the sandy mudstone and loess will change, seriously threatening the stability of tunnel support structure [13].

Taking a tunnel within loess–mudstone junction strata as an example, this study employs an indoor model test to obtain the tunnel envelope pressure, lining stress, displacement, and damage characteristics. The numerical simulations are also conducted to comprehensively analyze the distribution laws of the envelope rock and support stress characteristics in tunnels traversing loess–mudstone junction strata. This work is expected to provide an effective theoretical basis and engineering guidance for the stability and design construction of the tunnels in such strata.

3. Indoor Model Test Design

Based on the actual tunnel lining, we conducted an indoor model test of the tunnel lining in the loess–mudstone junction stratum. The object of this study is to analyze the pressure distribution laws of tunnel surrounding rock and the force deformation characteristics of the lining in tunnels crossing loess–mudstone junction strata, under the conditions involving water absorption and expansion of the underlying mudstone.

3.1. Model Test System

The model test system, as illustrated in Figure 2, comprises a test model box, a lifting system, a lifting electric control system, a data acquisition system, and a model counterweight. The model box measures 2500 × 800 × 1400 mm. Plexiglas panels are employed on the side of the model box to facilitate observation of changes in the tunnel and surrounding rock, while steel plates are utilized in other parts of the model. The lifting and lowering of the platform plate are achieved by adjusting the servo motor, enabling the realization of basement expansion loading methods. This simulates the deformation characteristics of the tunnel surrounding rock and lining under the influence of basement uplift.

Monitoring issues encompass circumferential rock pressure, lining force, and displacement. The test elements involved earth pressure boxes for collecting circumferential rock pressure at characteristic locations, such as footings, vault tops, and sidewalls, with a total of 15 monitoring points. Strain gauges were employed to gather the circumferential strain on the inner and outer sides of the liner, with 10 monitoring points arranged on both sides. Displacement gauges were utilized to capture the deformation in the radial direction of the lining and the top of the filling layer at characteristic points, with a total of 6 monitoring points. The arrangement of the measuring points is depicted in Figure 3.

3.2. Model Conditions

A tunnel lining model with a scale of 1:35 was designed based on the prototype tunnel. To ensure that the model tunnel lining exhibits similar physical properties to the actual tunnel lining concrete, particulate concrete was prepared for the construction of the tunnel lining model [14,15,16]. The finalized mass ratio of the composite lining concrete was cement (P.O 32.5)/water/sand = 1:1.5:6. The elastic modulus of the model lining was 3.019 × 10⁹ Pa. The height and width were 290 mm, 36.1 mm, and 20 mm, respectively. The lining thickness was 20 mm, and the arch height was 27 mm. Before the model filling, markings were made at 100 mm intervals within the model box to determine the mass of each layer of filled soil according to the volume of each layer. The filled soil was composed of loess in Lanzhou New District and the self-matched similar mudstone. Before the filling, the soil was first sieved, and then the density and moisture content were controlled. During the filling, the soils were added layer by layer to ensure the compaction and level of each layer.

The soil samples for this modeling test were from the site at the exit of a tunnel in Lanzhou New District. The water content of the filler, the percussion test, and the straight shear test were performed, respectively, to obtain the mechanical parameters of the material. The average natural density of the soil samples was 1.70 g/cm³, the average water content was 14.0%. The optimal water content and the maximum density are 13.2% and 1.56 g/cm³, respectively. The loess with optimal water content was used for the indoor straight shear test. The friction angle of the test soil is 18.00°, and the cohesive force is 28.70 kPa. The mudstones for this modeling test were artificially configured. The mudstones were from the manually configured similar mudstone material, which consisted of three parts (i.e., aggregate, conditioning material, and cementing material). The mass ratio of each raw material was shown as follows: river sand/bentonite/barite clay/iron powder/lime/plaster cast = 24.24%:12.12%:51.67%:2.87%:4.55%. Similar mudstone related parameters were also obtained via the compaction test and straight shear test. The optimum water content was 13.3%, and the maximum dry density was 2.11 g/cm³. The friction angle and cohesive force of the mudstone were 29.83° and 21.96 kPa, respectively.

The material parameters of the loess–mudstone junction model are presented in

Table 1. Physical and mechanical parameters of the loess and similar mudstone.

Material Name	Density g/cm3	Average Moisture Content/%	Optimum Moisture Content/%	Maximum Dry Density g/cm3	Friction Angle φ/°	Cohesion c/kPa
Loess	1.70	14.00	13.20	1.56	18.00	28.70
Similar Mudstone	-	-	13.30	2.11	29.83	21.96

. Figure 4 and Figure 5, respectively, show the picture of the completed model and the additional diagram of the test representative model.

A servo motor was utilized to control the model box lifting platform, imposing forced displacement on the substrate and simulating the substrate mudstone water absorption and expansion. Each upward jacking of 1 mm by the lifting platform represented a loading condition. After each load, the model was allowed to rest for 10 min, during which the monitoring data was observed and recorded. This loading cycle continued until the tunnel lining was damaged, at which point the test was terminated. Upon termination, the lining was destroyed and destabilized, with the loading platform having risen a total of 20 mm, encompassing 20 loading conditions.

4. Analyses of the Test Results

4.1. Analysis of the Surrounding Rock Pressure

4.1.1. Variation in the Surrounding Rock Pressure

Surrounding rock pressure indicates the force causing deformation or damage to the rock and support structures around the excavation space. This includes the surrounding rock pressure due to geo-stress and the force acting on the support structure resulting from obstructed deformation. The lining pressure directly reflects the load magnitude of the surrounding rock, which can elucidate the lining’s role in sharing the surrounding rock pressure [17]. To investigate the variation pattern of the rock pressure under different loading conditions in the loess–mudstone stratum, the process curves of the surrounding rock pressure with changing conditions were extracted from eight measurement points around the tunnel opening.

The surrounding rock pressure curve is depicted in Figure 6. In the loess–mudstone stratum, the surrounding rock pressure at each characteristic point exhibits a growing trend with the increase in basement uplift height. The growth rate of pressure around the hole at location P2 (i.e., at the foot of the right arch) is considerably larger than that at other locations. This may be attributed to the fact that at the final stage of the test, the rock at the foot of the right arch was not destabilized and still possessed load-bearing capacity. Thus, the surrounding rock pressure did not reach its peak. The lithology differences in the loess and mudstone results in an uneven distribution of rock pressure around the tunnel hole. The tunnel lining structure in the bottom drum of the upward arch under the action of the right arch foot of the peripheral rock slippage, the tunnel shear response increases, presenting a stress concentration.

The pressure of the rock at the bottom of the central arch of the inverted arch P1 did not develop apparently, with a maximum value of 0.2 kPa at the end of the test. Upon analysis, it is inferred that this is due to the substrate not being compacted during tunnel filling, resulting in a gap between the bottom of the tunnel lining and the rock. The gap was compressed when the loading platform was jacked up, thereby releasing the rock pressure. Consequently, in actual projects, an appropriate amount of deformation should be reserved between the surrounding rock and supporting structure during tunnel excavation. Voids should be backfilled with slurry promptly, and proper deformation of the rock is permitted. This can release the rock pressure to prevent damage to the supporting structure from pressure [18].

4.1.2. Distribution of Surrounding Rock Pressure

Pressure values of the surrounding rock under five loading conditions (from working condition 4 to 20) were extracted from eight measurement points around the tunnel. These values correspond to the pressure distribution of the rock under different working conditions, as illustrated in Figure 7.

As illustrated in Figure 7, the surrounding rock pressure in the loess–mudstone junction, except for the right arch foot, generally exhibits a symmetrical distribution. Stress concentration occurs at the tunnel perimeter rock pressure at the right arch foot. This may be attributed to the loess–mudstone laminated interface, where the expansion of the substrate could result into a non-uniform distribution of rock pressure and deformation.

In the cases where the overburden above the tunnel is restricted, the effect of the basement’s bottom drumming causes the stress of the rock range to increase rapidly, with stress concentration occurring at the left and right arch shoulders and the right arch foot. The surrounding rock pressure distribution is as follows: right arch foot > arch shoulder > arch waist > arch top ≈ arch bottom. In the vertical direction, the step-by-step loading has a more significant impact on the earth pressure of the rock at the bottom of the tunnel, the back arch, and the arch shoulder, while that has a lesser effect on the pressure of the tunnel arch and the overburden above.

It can be observed that the pressure distribution around the tunnel cavern of the loess–mudstone stratum was notably uneven. This is due to the strength and bearing capacity of the loess stratum being weaker than those of the mudstone. When subjected to vertical pressure at the base, the self-supporting capacity of the rock at the intersection is very poor. The loess stratum becomes compressed and deformed, and the bearing capacity of the mudstone stratum is larger than that of the loess stratum. The rock at the intersection was damaged, resulting in the physical and mechanical properties deteriorating and thus reducing or even eliminating the bearing capacity. This leads to a complex pressure distribution and significant stratigraphic effects.

4.2. Analyses of Lining Stress and Bending Moment

To investigate the stresses experienced by the tunnel lining during the basement uplift, the strain values during the model test loading were utilized to analyze. The peak strains of the tunnel lining vault, arch shoulders, arch feet, and arch bottom were extracted from the strain gauges when the model test loading completed, as presented in

Table 2. Peak internal and external strain of the tunnel lining.

Acquisition Location	Upper Side of the Arch	Arch Left Shoulder	Arch Right Shoulder	Left Side of the Arch Foot	Right Side of the Arch Foot	Arch Bottom
Inside	770.73	2439.02	331.70	−1699.44	−138.54	3500.00
Outer side	−165.80	−378.48	−50.26	291.16	292.95	−1078.48

. In this context, the tension is considered positive, and compression is negative. The strain values obtained at each characteristic point of the lining were converted into the peak lining stress at the corresponding location (Figure 8). Subsequently, the peak lining moment at each location of the tunnel lining model was derived from the stress values (Figure 9). The corresponding calculation equations are as follows [19,20]:

$$\sigma =E·\epsilon ,$$

(1)

$$\Delta \epsilon ={\epsilon }_2-{\epsilon }_1,$$

(2)

$$I=b{h}^3/12,$$

(3)

$$M=EI\Delta \epsilon /h=E({\epsilon }_2-{\epsilon }_1)b{h}^2/12,$$

(4)

where $\sigma$ is the lining stress value; $E$ is the lining material elastic modulus, 3.019 × 10⁹ Pa; $I$ is the interface moment of inertia; $b$ is the lining longitudinal unit length, 1 m; $h$ is the lining thickness, 0.02 m; $M$ is the lining bending moment; ${\epsilon }_1$ is the tunnel lining model inside strain, ${\epsilon }_2$ is the tunnel lining model outside strain, $\epsilon$ is the tunnel lining surface strain value; and $\Delta \epsilon$ is the bending strain.

From Table 2 and Figure 8, it is evident that in the loess–mudstone stratum, the tunnel lining is characterized by compression at the two arch feet on the inner side of the liner, and is characterized by tension at the top, shoulders, and bottom of the arch. Conversely, the outer side of the liner experiences tension at the left and right arches, while it experiences compression at the top, shoulders, and bottom of the arches. The peak stresses are depicted in Figure 7. It can be observed that the peak stresses on the inside of the tunnel liner at each characteristic point are higher than those on the outside, under the effect of the substrate expansion. The peak stresses on both the inner and outer sides of the arch bottom are the largest, with the magnitude of the peak stress on the outer side being 30.8% of that on the inner side. The magnitude of the peak stress on the outer side of the arch shoulder is 15.5% of that on the inner side.

The development of the arch lining stress is not pronounced, and it is likely due to the fact that when the force is transferred to the loess–mudstone intersection, destabilization damage occurs due to the poor bearing performance of the intersection and its interaction with the lining. This results in the loss of the restraining effect on the lining, leading to a smaller stress on the arch.

From the peak distribution of the lining moment in Figure 9, it is evident that the maximum bending moment at each characteristic point of the tunnel lining is prominent in the inverted arch part. The overall bending moment of the inverted arch is larger than that of the arch shoulder and the arch roof. The arch bottom and the left arch shoulder primarily experience negative bending moments, with maximum values close to −500 kN·m and −400 kN·m, respectively, while the left and right arch feet undergo positive bending moments. Given the overall distribution, it can be observed that the lining elevation arch and the left and right arch shoulders represent the unfavorable positions of the force. Consequently, it is necessary to strengthen the lining structure in a targeted manner to address these vulnerabilities.

The stress characteristics of the loess–mudstone tunnel lining structure are thus obtained. The left and right sides of the tunnel lining and the inner side of the lining are subjected to the compressive stress, while the outer side of the lining is subject to the tensile stress. The tunnel arch shoulder, the arch base area, and the inner side of the lining are subjected to the tensile stress, while the outer side of the lining is subjected to the compressive stress. Therefore, the left arch shoulder, the outside of the left arch foot of the loess–mudstone junction tunnel lining, and the inside of the arch foot on both sides of the lining are the weak areas of the tunnel. The targeted reinforcement measures should be carried out.

4.3. Analysis of the Tunnel Perimeter Displacement

To investigate and analyze the development and evolution of the deformation process in the tunnel surrounding rock, the deformation monitoring data from six measurement points around the tunnel were extracted. Figure 10 illustrates the variation and distribution curves of the tunnel perimeter displacement with loading conditions in loess–mudstone strata.

From Figure 10a, it is evident that as the height of the footing bulge increases, the displacement of each characteristic point around the cave exhibits an overall trend of increment. At the time of model destruction, the maximum displacement of D1 of the left footing of the inverted arch reaches 12 mm, while the displacement of D3 of the right footing reaches 10.8 mm. The maximum displacement of D2 of the arch bottom reaches 17.35 mm, while the displacement of D6 of the arch top reaches 10.32 mm. The displacement values indicate that the entire inverted arch tends to deform due to the uplifting of the footing, with the largest displacement occurring at the center of the inverted arch, suggesting a pronounced deformation of the bottom drum.

The poor self-supporting ability of the surrounding rock at the intersection leads to destabilization, and the lining restraint ability becomes inadequate. The positive displacement value of the arch waist implies a tendency to deform outward, away from the tunnel center. From the displacement distribution curve in Figure 10b, it can be observed that the effect of tunnel substrate expansion on the horizontal convergence of the cavern perimeter is relatively small, with the settlement of the arch in the vertical direction being dominant. As the basement bulge increases, both the displacement growth rate and displacement of the inverted arch are the largest, indicating that the basement expansion is the primary factor which contributed to the damage of the bottom bulge of the inverted arch of the tunnel at the loess–mudstone intersection.

5. Numerical Simulation

Given that the volume expansion of mudstone, caused by variations in the mudstone moisture fields, is similar with the rise and shrinkage of the surrounding rock induced by temperature field variations [21,22], the “temperature comparison method” was employed. A corresponding numerical calculation model was established using the ABAQUS software to simulate the water absorption and expansion of the mudstone, with the expansion depth set at 6 m. This model facilitated the investigation of the pressure and lining force, as well as deformation characteristics of the tunnel surrounding rock at the midpoint of the step in the tunnel at the loess–mudstone intersection.

5.1. Material Parameters

During the simulation of the water absorption and expansion of the basement mudstone, the stress–strain relationship of a material may become quite complex due to various factors (e.g., rate of deformation, strain history, etc.). For the sake of simplicity, the model was simplified as follows: (1) the stress–strain relationship of the moisture field was assumed to be linear elastic; (2) the expansion of the basement mudstone was modeled using isotropic heat transfer thermodynamics; (3) the expansion occurred solely in the surrounding rock. All model boundaries were adiabatic boundaries, and the excavation of the tunnel and the implementation of the support structure remained unaffected by temperature field changes.

Based on the principle of St. Venant, considering the accuracy of the numerical simulation, on-site stratigraphy, and calculation cost, the width, height, and longitudinal length of the model size were 100.96 m, 99.1 m, and 24 m, respectively. The form of tunnel section was determined according to the construction drawings, in which the span and height were 12.62 m and 10.22 m, respectively. The thickness of the initial support was 0.26 m, and C25 shotcrete was adopted, while the thickness of the lining was 0.45 m, and the C30 molded concrete was adopted. When establishing the model, the parts of the surrounding rock and tunnel structure were first created separately, and the combination of the parts was then realized via assembly. When meshing, the cell type was C3D8R six-surface solid cell. The numbers of mesh cells for the surrounding rock, primary support, secondary lining, and fill layer were 85,632, 1782, 1872, and 1224, respectively. The total number of mesh cells was 90,456, and the mesh division of each part is shown in Figure 11. The numerical model is shown in Figure 12, in which the loess–mudstone adopted the Mohr–Coulomb strength criterion (Mohr–Coulomb), while the tunnel lining and supporting structure adopted the linear-elastic principal model. The material parameters and boundary conditions of the numerical model determined based on the indoor model test are shown in

Table 3. Numerical model of the material parameters.

Material	Severe γ/(kN/m3)	Modulus of Elasticity E/GPa	Poisson’s Ratio /μ	Cohesion c/kPa	Angle of Friction φ/°
Loess	19	0.5	0.28	50	25
Mudstone	22	1.1	0.25	2960	41
Primary lining	23	28.9	0.20	-	-
Secondary lining	24	33.6	0.20	-	-
Filling layer	23	22.0	0.20	-	-
Steel arch	78	210.0	0.30	-	-

and

Table 4. Boundary condition.

Border Surface	X Axial Displacement	Y Axial Displacement	Z Axial Displacement
top surface	free state	free state	free state
left side	stationary state	free state	free state
right side	stationary state	free state	free state
front side	free state	free state	stationary state
rear side	free state	free state	stationary state
bottom side	stationary state	stationary state	stationary state

.

5.2. Analysis of the Maximum Principal Stress in the Elevation Arch

Figure 13a illustrates the maximum principal stress cloud of the inverted arch, while Figure 13b presents the corresponding maximum principal stress curve of the inverted arch.

As evident from Figure 13, the numerical results reveal that the maximum principal stress in the tunnel lining occurs at the base of the arch. The maximum principal stress at the center of the inverted arch reaches 1367.56 kPa, indicating that the base of the inverted arch is the most unfavorable location for stress. This aligns with the model test lining stress peak. The maximum principal stress distribution is symmetrically distributed, reaching its peak at the base of the arch, while the stress at the left and right arch foot is smaller. Consequently, for loess tunnels with overlying loess and underlying mudstone, the expansion effect of basement mudstone has the most significant impact on the safety of the inverted arch. Therefore, the location of the inverted arch base necessitates particular attention in tunnel design and construction.

5.3. Displacement and Plastic Strain Results

Figure 14 displays the vertical displacement cloud of the rock surrounding the tunnel cavern, while Figure 15 presents the vertical displacement curve of the inverted arch.

The vertical displacement cloud diagram of the rock of the tunnel cavern, as illustrated in Figure 14, reveals that the maximum displacement occurs at the base of the inverted arch and the left and right arch foot. Figure 15a demonstrates the numerical simulation of the vertical displacement for each node of the inverted arch, exhibiting a symmetrical distribution with the maximum vertical displacement (13.782 mm) appearing at the base of the inverted arch. Mudstone absorption of water and liquid water migration cause rapid expansion and deformation of the tunnel basement rock. A comparison of the inverted arch base in the loess–mudstone tunnel lining, obtained from model tests and numerical simulations, is shown in Figure 15b. These figures indicate that the elevation height of the arch base increases with the expanding height of the mudstone, and the development trend of the arch base elevation from the model test and numerical simulation is fundamentally consistent.

When the loess–mudstone interface is situated at the midpoint of the excavation’s mid-step, the plastic strain zone of the tunnel surrounding rock emerges above the mid-step of the tunnel excavation, as depicted in Figure 16a. The plastic strain is symmetrically distributed along the tunnel’s central axis, with the maximum plastic strain appearing at the left and right arch shoulders, the damage results of the lined arch shoulder in the corresponding model test are shown in Figure 16b,c above. In the construction and operation of the loess–mudstone tunnel in frozen soil regions, special attention should be paid to the safety of the tunnel drainage system and reinforcement structure in operation [23,24,25,26], thereby preventing the swelling of mudstone at the bottom of the tunnel, which leads to the deformation of the inverted arch at the base. This thus results in the damage of the lining system and directly threatens the safety of tunnel structure and operation. The equivalent plastic strain of the rock around the cavern and the model lining damage results are depicted in Figure 16.

This implies that the lining and surrounding rock at the left and right arch shoulders are in the most unfavorable position. The numerical calculation results are fundamentally consistent with the model test results. In practical engineering applications, when the tunnel intersects the loess–mudstone junction, it is essential to enhance the strength of the support structure at the left and right arch shoulders of the tunnel lining, thereby resisting the deformation of the rock around the tunnel. However, it is worth noting that there is a discrepancy between the numerical simulation and model test results in the analysis of the tunnel surrounding rock pressure. This may be due to the fact that the numerical simulation was calculated as an ideal state and was unable to simulate the voids existing in the surrounding rock and soil around the tunnel lining in the model test, thus resulting in the inconsistent location of the maximum stress.

6. Conclusions

In this study, taking a loess–mudstone interface tunnel in cold regions as the research object, the pressure distribution law of surrounding rock and the stress and deformation characteristics of the supporting structure of the loess–mudstone interface tunnel are studied via a model test and numerical simulation. The following conclusions are preliminarily obtained:

(1)

With the increase in basement uplift, the stress of the inverted arch surrounding rock increases rapidly due to the floor heave effect. Because the strength and bearing capacity of loess are weaker than those of mudstone and the self-bearing capacity of surrounding rock at the interface is poor, the pressure distribution of the surrounding rock is complex, and the stress distribution is uneven when subjected to the vertical pressure of the basement. The peak stress at the bottom of the outer arch is 30.8% of that of the inner arch. The internal force of the tunnel lining at the vault is the largest. The compressive stress appears at the arch foot, while the tensile stress appears outside the lining. The stratum effect is significant.

(2)

The internal force of the tunnel lining is the largest at the inverted arch. The maximum principal stress at the inverted arch bottom reaches 1367.56 kPa via numerical simulation. The left arch shoulder and arch bottom mainly bear a negative bending moment, and the maximum values are close to −500 kN·m and −400 kN·m. The left and right arch feet bear a positive bending moment. Therefore, the lining’s inverted arch bottom and the left and right arch feet are all unfavorable positions.

(3)

As the height of the elevated arch base elevation increases, both numerical simulations and model tests show an overall increasing trend of perimeter displacements of the cave. The arch bottom displacement experiences the highest growth rate and displacement. At the point of model failure, the maximum displacement of the numerical simulation arch bottom bulge is 13.782 mm, while the maximum displacement of the model test arch bottom bulge reaches 17.35 mm, representing a 25.9% increase. Furthermore, the center of the inverted arch displays a prominent bottom bulge deformation.

(4)

Longitudinal penetration cracks emerged in the inverted arch and the left and right arch shoulders, which was consistent with the plastic strain results. The expansion of the basement mudstone contributed to the deformation of the bottom of the inverted arch, and the formation and development of longitudinal cracks in the inverted arch were the primary factors leading to the damage of the bottom drum. In the loess–mudstone regions, special attention should be paid to the safety of the tunnel drainage system and the reinforced structure in operation, which can prevent the uplift of the mudstone at the bottom of the tunnel, the deformation of the inverted arch’s bottom, and the stress damage of the vault and thus ensure the safety of the tunnel structure.