Method and system suitable for tunnel gushing water surrounding rock staged failure semi-analytical solution

Abstract

The invention provides a surrounding rock staged failure semi-analytical solution method and system suitable for tunnel water gushing, and belongs to the technical field of tunnel engineering. The method comprises the steps that according to test data under different water contents, all surrounding rock mechanical parameters are fitted, and a surrounding rock mechanical parameter fitting equation considering the water contents is obtained; the three-dimensional arch effect in the tunnel excavation process is considered, and the surrounding rock damage process caused by tunnel excavation is divided into two stages, namely the first stage and the second stage; in the first stage, the surrounding rock failure mode is that the first stress of the excavation effect is redistributed; in the second stage, the surrounding rock failure mode is that stress is redistributed again under the combined action of the excavation effect and the water weakening effect; and for the second stage, establishing a circular tunnel calculation model considering the water weakening effect, and performing mechanical calculation on the surrounding rock failure process by adopting a semi-analytical method. Through two-stage division, the excavation effect and the water weakening effect are considered, and the progressive failure characteristics of the surrounding rock under the water gushing condition are described more accurately.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of tunnel engineering, in particular to a method and system for semi-analytical solution of stage destruction of surrounding rock suitable for tunnel water gushing. BACKGROUND

[0002] Weakly cemented sandstone strata are widely distributed in western China. The strata are mainly sedimentary sandstone formed by granular material and cementing material through dissolution, compaction and other effects, with characteristics of low strength, easy disintegration, water cementation, weak cementation, high swelling and the like, which poses a serious challenge to the stability of surrounding rock of underground engineering such as tunnels and mines.

[0003] At present, research on weakly cemented sandstone has involved multiple aspects, such as analyzing mineral composition and spatial structure through X-ray diffraction (XRD), scanning electron microscopy, CT and the like; exploring the correlation between mudification, water absorption and disintegration process and physical and mechanical parameters through indoor disintegration test; and studying the strength and deformation characteristics through conventional uniaxial and triaxial compression tests. However, there is little research on the failure mechanism of weakly cemented sandstone strata under water-rich conditions, and the existing research does not consider the influence of stress redistribution after excavation, water swelling and softening on the plastic zone and stress of surrounding rock, which cannot effectively optimize and guide the support design.

[0004] Therefore, it is necessary to provide an improved technical solution to overcome the above-mentioned deficiencies of the prior art. SUMMARY

[0005] The present application aims to provide a method and system for semi-analytical solution of stage destruction of surrounding rock suitable for tunnel water gushing, to solve or alleviate the problems existing in the prior art.

[0006] In order to achieve the above-mentioned purpose, the present application provides the following technical solution: In a first aspect, the present application provides a method for semi-analytical solution of stage destruction of surrounding rock suitable for tunnel water gushing, comprising: Fitting each surrounding rock mechanical parameter according to the test results of the samples under different water contents to obtain a fitting equation of the surrounding rock mechanical parameter considering water content; Considering the three-dimensional arch effect in the tunnel excavation process, the surrounding rock destruction process caused by tunnel excavation is divided into two stages, i.e. the first stage and the second stage. In the first stage, the surrounding rock destruction mode is the first stress redistribution of excavation effect. In the second stage, the surrounding rock destruction mode is the stress redistribution caused by the combined action of excavation effect and water weakening effect; For the second stage, a circular tunnel calculation model considering water weakening effect is established based on the fitting equation of the surrounding rock mechanical parameter considering water content, and a semi-analytical method is used to perform mechanical calculation on the surrounding rock destruction process.

[0007] In the technical solution, a two-stage failure model is proposed: in the first stage (excavation effect dominates), after tunnel excavation, stress redistribution leads to an increase in tangential stress of the surrounding rock, the surrounding rock enters the plastic zone, and the first failure zone is formed. In the second stage (combined effect of excavation and water weakening), the advancement of the working face causes the development of cracks in the surrounding rock, and the water inflow increases. The outer boundary of the first failure zone becomes the new "equivalent excavation boundary", and the stress transfers to the deep part, forming the second failure zone. By dividing the two stages, the effects of excavation and water weakening are considered, the failure processes of different mechanisms are separated, the progressive failure characteristics of the surrounding rock under water inflow conditions are more accurately described, and the actual failure mode of the water inflow tunnel is more consistent. Based on the test data under different water contents, a fitting equation of the mechanical parameters of the surrounding rock (such as elastic modulus, cohesion, and internal friction angle) with water content is established, i.e., a fitting equation of the mechanical parameters of the surrounding rock considering water content, which provides dynamic mechanical parameters related to water content for subsequent analysis, so that the model can reflect the differences in mechanical response under different water conditions; a circular tunnel calculation model considering water weakening effect is established, and the water weakening effect is coupled for mechanical calculation. The model input is dynamically corrected by the parameter fitting equation, so that the calculation results match the actual water content state.

[0008] In combination with the first aspect, in a possible implementation, according to the test data under different water contents, each surrounding rock mechanical parameter is fitted to obtain a fitting equation of the surrounding rock mechanical parameter considering water content, including: according to the test results of the samples under different water contents, a linear equation is used to fit the change of the elastic modulus with the water content to obtain a fitting equation of the elastic modulus; The peak stress and residual stress of the surrounding rock are fitted based on the Mohr-Coulomb strength criterion, and according to the stress fitting results, a linear equation is used to fit the change of the cohesion at the peak strength, the cohesion at the residual strength, the friction angle at the peak strength, and the friction angle at the residual strength with the water content, respectively, to obtain the fitting equations of the cohesion at the peak strength, the cohesion at the residual strength, the friction angle at the peak strength, and the friction angle at the residual strength; A linear equation is used to fit the change of the dilatancy angle with the water content to obtain a fitting equation of the dilatancy angle.

[0009] In the technical solution, the change law of each mechanical parameter with the water content is fitted by a linear equation, which provides a clear mathematical relationship between each mechanical parameter and the water content, simplifies the parameter input process, and is easy to implement and has high calculation efficiency. Linear fitting is performed based on the Mohr-Coulomb strength criterion to clearly distinguish the water weakening laws of the peak strength and the residual strength, and to more accurately describe the whole failure process of the surrounding rock.

[0010] In combination with the first aspect, in a possible implementation, the stress release rate at the position of the working face is used to represent the three-dimensional arching effect in the tunnel excavation process; When the stress release ratio at the position of the tunnel face is greater than a preset stress release ratio threshold, it is determined that the tunnel is in the second phase of the excavation process, and when the stress release ratio at the position of the tunnel face is less than or equal to the preset stress release ratio threshold, the tunnel is in the first phase of the excavation process.

[0011] In the technical solution, the stress release coefficient at the position of the tunnel face is used as a quantitative index of the three-dimensional arching effect, the excavation phases are divided by using the preset stress release coefficient threshold, an objective and quantifiable phase conversion determination criterion is established, a clear numerical criterion is provided to evaluate the influence degree of the three-dimensional arching effect, the subjectivity of artificial experience judgment is avoided, and the reliability of the analysis result is improved.

[0012] In combination with the first aspect, in a possible implementation manner, the circular tunnel calculation model considering the water weakening effect includes: The plastic softening zone and the plastic residual zone are uniformly regarded as a plastic zone by establishing the circular tunnel calculation model. The solving problem of the stratum response of the circular tunnel considering the water weakening effect is simplified as a plane strain problem. Uniform initial ground stress is applied to the surrounding rock The tunnel excavation radius is set as The hole wall support pressure is set as . The critical pressure at which the plastic zone is generated in the surrounding rock is calculated and determined When , it is determined that the hole wall surrounding rock only has an elastic zone, and when , it is determined that the hole wall surrounding rock has a plastic zone. In the plane strain problem, the radial stress is used as the minimum principal stress of the surrounding rock, the tangential stress is used as the maximum principal stress of the surrounding rock, and is the displacement of the surrounding rock.

[0013] In the technical solution, the plastic softening zone and the residual zone are uniformly regarded as a single plastic zone, which is beneficial to simplify the complexity of the calculation model and maintain the basic description ability of the plastic deformation. The three-dimensional problem is simplified as a plane strain problem, which greatly reduces the calculation amount and can maintain the description ability of the main mechanical behavior. The critical pressure is used as a plastic zone generation criterion, which can provide a clear plastic zone generation standard and is beneficial to realize automatic judgment in the calculation process.

[0014] In combination with the first aspect, in a possible implementation manner, based on the fitting equation of the mechanical parameter of the surrounding rock considering the water content, a circular tunnel calculation model considering the water weakening effect is established, and a semi-analytical method is used for mechanical calculation of the failure process of the surrounding rock, including: solving the elastic state solution of the surrounding rock, and the calculation process is as follows: According to the difference between the initial ground stress and the critical pressure , combined with the tunnel excavation radius , the radial stress , tangential stress of any point in the elastic zone range is calculated by using the Lame solution. Without considering the strain and displacement caused by the initial ground stress , the radial strain, tangential strain and displacement at the position of any point in the elastic zone range are calculated by considering the shear modulus of water content, wherein the shear modulus of water content is calculated by a shear modulus fitting equation, and the shear modulus fitting equation is one of the fitting equations of the surrounding rock mechanical parameters considering water content.

[0015] In the above technical solution, the Lame solution is used to calculate the stress field of the elastic zone, which can obtain accurate elastic zone stress analytical solution and has high calculation efficiency without numerical discretization. The shear modulus related to water content is calculated by using the fitting equation, so that the quantitative consideration of the water weakening effect is realized. Without considering the strain caused by the initial ground stress, the calculation process is simplified, and the influence of excavation disturbance is highlighted.

[0016] In combination with the first aspect, in some possible implementation manners, based on the fitting equation of the surrounding rock mechanical parameters considering water content, a circular tunnel calculation model considering the water weakening effect is established, and a semi-analytical method is used to perform mechanical calculation on the failure process of the surrounding rock, including: solving the plastic state solution of the surrounding rock, and the calculation process is as follows: For the elastic zone in the plastic state, according to the difference between the initial ground stress and the critical pressure , combined with the plastic zone radius , the mechanical characteristics of the elastic zone in the plastic state are calculated; At the boundary of the elastic-plastic zone, according to the initial ground stress and the pressure of any point at the boundary of the elastic-plastic zone, combined with a preset strength criterion, the critical pressure of the elastic-plastic boundary is calculated; based on the critical pressure of the elastic-plastic boundary, the shear modulus of water content is considered to calculate the mechanical characteristics at the boundary of the elastic-plastic zone; Wherein, the shear modulus of water content is calculated by a shear modulus fitting equation, and the shear modulus fitting equation is one of the fitting equations of the surrounding rock mechanical parameters considering water content. For the plastic zone, the stress, strain and displacement of the surrounding rock are solved by using the finite difference method.

[0017] In the above technical solution, based on the initial ground stress and the critical pressure The elastic zone mechanical characteristics are calculated, the elastic zone in the plastic state is analytically solved, continuity with the elastic zone solution in the elastic state is maintained, and a connection condition is provided for the elastic-plastic boundary. The shear modulus related to the water content is introduced, the boundary critical pressure is calculated by using the strength criterion, and the influence of water weakening on the boundary position can be accurately reflected. The finite difference method is used to solve the plastic zone, the nonlinear problem can be effectively handled, and the calculation accuracy is improved.

[0018] With reference to the first aspect, in a possible implementation manner, for the plastic zone, the stress, strain and displacement of the surrounding rock are solved by using the finite difference method, including: The plastic zone is divided into a plurality of concentric circular rings, and the radius of each circular ring is normalized; The radial stress increment of each circular ring is assumed to be equal, the radial stress at each circular ring is calculated by using the difference between the support pressure of the hole wall and the critical pressure The tangential stress at each circular ring is calculated by substituting the radial stress into the yield equation; The elastic strain increment at each circular ring is calculated according to Hooke's law under the plane strain condition; The balance equation is established for each calculation node in the plastic zone, to ensure that the stress distribution meets the static equilibrium condition; The plastic strain is calculated based on the plastic flow theory, considering the change of the friction angle and the cohesion of the surrounding rock; The displacement of the plastic zone is calculated by combining the elastic strain and the plastic strain; When the plastic shear strain of the calculation node exceeds the residual strength of the surrounding rock, the mechanical behavior of the surrounding rock is described by using a linear weakening function. In the above technical solution, the plastic zone is divided into a plurality of concentric circular rings and normalized, the spatial discretization of the complex plastic zone is realized, the equal-increment stress is assumed, the yield equation is applied, the stress is decomposed and calculated, and the behavior after the residual strength is described by using a linear function, so that the mechanical characteristics of the plastic zone are efficiently and accurately solved.

[0019] With reference to the first aspect, in a possible implementation manner, for the first stage, the stress and strain characteristics of the surrounding rock are solved based on the mechanical parameters of the surrounding rock corresponding to the natural water content. Thus, the initial mechanical state of the surrounding rock can be reflected.

[0020] The second aspect, the embodiments of the present application provide a computer system, comprising a memory, a processor and a computer program stored on the memory, the processor executes the computer program to realize the steps of the method provided by any of the above embodiments.

[0021] The second aspect, the embodiments of the present application provide a computer system, comprising a memory, a processor and a computer program stored on the memory, the processor executes the computer program to realize the steps of the method provided by any of the above embodiments.

[0022] ​In a third aspect, the embodiments of the present application provide a computer readable storage medium, which stores computer programs / instructions, and the computer programs / instructions are executed by a processor to implement the steps of the method provided by any of the above embodiments.

[0023] The beneficial effects of the technical solutions provided by the second aspect and the third aspect of the present application can refer to the description of the beneficial effects of the first aspect, and will not be repeated here. BRIEF DESCRIPTION OF DRAWINGS

[0024] Figure 1 A schematic diagram of two-stage evolution of tunnel excavation is provided according to some embodiments of the present application, in which (a) is a schematic diagram of plastic zone formation in the first stage (stage I), and (b) is a schematic diagram of plastic zone formation in the second stage (stage II).

[0025] Figure 2 A schematic diagram of the process of surrounding rock failure is provided according to some embodiments of the present application.

[0026] Figure 3 A schematic diagram of a circular tunnel calculation model considering the water weakening effect.

[0027] Figure 4 A schematic diagram of the calculation principle of the solving process of the plastic zone.

[0028] Figure 5 A schematic diagram of the stress redistribution of surrounding rock considering the two-stage evolution process.

[0029] Figure 6 A schematic diagram of the displacement redistribution of surrounding rock considering the two-stage evolution process.

[0030] Figure 7 A schematic diagram of the convergence constraint curve of surrounding rock considering the two-stage evolution process. DETAILED DESCRIPTION

[0031] In the process of tunnel excavation, water gushing will cause the water content of surrounding rock to increase, triggering the deterioration of mechanical parameters (such as reduction of elastic modulus and cohesion), and further aggravating the deformation and failure of surrounding rock. The existing methods for analyzing the stability of surrounding rock do not consider the coupling effect of water weakening effect and excavation stress redistribution, and are insufficient in describing the stage characteristics of “excavation-water gushing-re-failure” of surrounding rock under water-rich conditions, resulting in large deviation between the calculation results and the actual engineering, and being difficult to guide the design and construction of tunnels in water-rich and weakly cemented sandstone strata.

[0032] Therefore, the embodiment aims to solve the problem that the deterioration and stage damage characteristics of the surrounding rock mechanics parameters are difficult to be quantitatively analyzed when water gushes in the tunnel of water-rich and weakly cemented sandstone stratum, and provides a method for stage damage semi-analytical solution of surrounding rock suitable for tunnel water gushing. The method obtains the fitting equation of the surrounding rock mechanics parameters considering the water content, establishes the quantitative relationship between the water content and the weakly cemented sandstone mechanics parameters, and determines the influence law of the water weakening effect. The method divides the stage damage mode (two-stage mode) of the surrounding rock in the tunnel excavation process, reveals the two-stage damage mechanism of the surrounding rock "excavation effect→water weakening+excavation effect", and makes up for the deficiency of the existing method in describing the stage characteristics. The method establishes a circular tunnel calculation model considering the water weakening effect, combines the analytical method and the numerical calculation method, realizes efficient calculation of the surrounding rock stress and displacement under water-rich conditions, and provides a theoretical basis for tunnel support design.

[0033] The embodiments of the application are described below with reference to the drawings.

[0034] Embodiment 1 The embodiment of the application provides a method for stage damage semi-analytical solution of surrounding rock suitable for tunnel water gushing, which comprises the following steps: Step S1, according to the test data under different water contents, fitting each surrounding rock mechanics parameter to obtain the fitting equation of the surrounding rock mechanics parameters considering the water content.

[0035] The water content refers to the percentage of the mass of water in the surrounding rock to the total mass of the surrounding rock, which is used to reflect the saturation degree of water in the internal pores of the surrounding rock. According to the different water contents, the state of the surrounding rock can be divided into the following several states: dry state, saturated state, natural state and other states, and the other states can be expressed by different percentages. Further, the mechanical parameters (such as elastic modulus, peak internal friction angle, peak cohesion, residual internal friction angle, residual cohesion and expansion angle) of the rock under different confining pressures and different water contents can be analyzed through triaxial compression test.

[0036] In the embodiment, based on the test data of the mechanical properties of the surrounding rock under different water contents, the multiple key mechanical parameters affecting the stability of the surrounding rock are systematically analyzed. Through statistical and regression processing of the test data, the change law of each mechanical parameter with the change of the water content is established. On this basis, a fitting equation of the surrounding rock mechanics parameters reflecting the influence of the water content is constructed by using a mathematical fitting method. The fitting equation can be used in the subsequent calculation model to more accurately simulate the mechanical response of the surrounding rock under actual engineering conditions.

[0037] Step S2, considering the three-dimensional arching effect in the tunnel excavation process, the surrounding rock failure process caused by tunnel excavation is divided into two stages, namely the first stage and the second stage; in the first stage, the surrounding rock failure mode is: the first stress redistribution of excavation effect; in the second stage, the surrounding rock failure mode is: stress redistribution caused by the combined action of excavation effect and water weakening effect.

[0038] In the process of tunnel excavation, considering the existence of three-dimensional arching effect in the stratum, the failure process of surrounding rock is divided into two main stages, which correspond to different stress redistribution mechanisms and failure characteristics.

[0039] In the first stage, the failure mode of surrounding rock is mainly caused by the initial stress field disturbance caused by tunnel excavation. With the advancement of tunnel face, the original stress balance state of surrounding rock is broken, which causes the first redistribution of stress. In this stage, the preliminary stress release zone and stress concentration zone are formed in the surrounding rock, and part of the area may begin to appear micro-cracks or local yield, but the whole is still in a relatively stable stress state.

[0040] In the second stage, the failure mode of surrounding rock is characterized by the combined action of excavation effect and water weakening effect. With the extension of the exposure time of surrounding rock, groundwater gradually seeps into the surrounding rock cracks, resulting in the decrease of the mechanical properties of surrounding rock, especially the significant decrease of cohesion and shear strength. At this time, on the basis of the original stress redistribution, due to the aggravation of water weakening effect, the surrounding rock further adjusts the stress and forms more complex secondary stress redistribution. This stage is often accompanied by large-scale plastic zone expansion, displacement increase and structure surface slip, which is an important stage affecting the long-term stability of the tunnel.

[0041] By dividing the surrounding rock failure process into the above two stages, the actual response of the surrounding rock in the tunnel excavation process can be more accurately reflected, and a theoretical basis for support design and construction control is provided.

[0042] Step S3, for the second stage, based on the surrounding rock mechanical parameter fitting equation considering water content, a circular tunnel calculation model considering water weakening effect is established, and a semi-analytical method is used to calculate the mechanical calculation of the surrounding rock failure process.

[0043] In the second stage of tunnel excavation, the surrounding rock failure mode exhibits the combined effects of excavation and water weakening, leading to stress redistribution. To accurately simulate the surrounding rock response in this stage, this embodiment establishes a circular tunnel calculation model considering the water weakening effect and employs a semi-analytical method to perform mechanical analysis of the surrounding rock failure process. First, the influence of water content on the mechanical parameters of the surrounding rock is examined: based on the relationship equation between the surrounding rock mechanical parameters (such as compressive strength, elastic modulus, cohesion, and friction angle) obtained from previous experimental data and the water content, the mechanical properties of the surrounding rock are dynamically adjusted. The tunnel is considered a circular structure, and the surrounding rock is divided into multiple concentric annular regions. The mechanical parameters of each annulus are updated according to the water content at its location. Based on the updated mechanical parameters, the weakening effect of water seepage on the mechanical properties of the surrounding rock is quantified.

[0044] To efficiently solve for the stress, strain, and displacement distribution of the surrounding rock, this embodiment combines the advantages of analytical solutions and numerical calculations, employing a semi-analytical method. Specifically, within the elastic region of the surrounding rock, the radial stress, tangential stress, and displacement distribution are quickly calculated using the classic Lame solution or similar analytical formulas. Within the plastic region, the changes in stress, strain, and displacement are gradually solved using the finite difference method or finite element method, combined with the yield criterion of the surrounding rock (such as the Mohr-Coulomb criterion).

[0045] In this embodiment, by establishing a circular tunnel calculation model that considers the water weakening effect and employing a semi-analytical method to perform mechanical calculations on the surrounding rock failure process, the complex mechanical behavior of the surrounding rock undergoing staged failure due to water inrush during tunnel excavation is effectively solved. This method can accurately simulate the stress redistribution process of the surrounding rock in the second stage, providing strong technical support for the safety and economy of tunnel engineering.

[0046] According to a preferred embodiment of the aforementioned method, the process of fitting the surrounding rock mechanical parameters based on experimental data at different water contents specifically includes modeling and analyzing the relationship between multiple key mechanical parameters and water content. Specifically, step S1 involves fitting each surrounding rock mechanical parameter based on experimental data at different water contents to obtain a fitting equation for the surrounding rock mechanical parameters considering water content, including: Step S11: Based on the test results of the samples under different moisture contents, a linear equation is used to fit the change of elastic modulus with moisture content to obtain the fitting equation of elastic modulus.

[0047] Step S12: Fit the peak stress and residual stress of the surrounding rock based on the Mohr-Coulomb strength criterion, and according to the fitting results, use linear equations to fit the changes of cohesion at peak strength, cohesion at residual strength, friction angle at peak strength and friction angle at residual strength with water content, and obtain the fitting equations for cohesion at peak strength, cohesion at residual strength, friction angle at peak strength and friction angle at residual strength.

[0048] Step S13: Use a linear equation to fit the change of the dilatation angle with the water content to obtain the fitting equation of the dilatation angle.

[0049] By fitting equations for the above mechanical parameters, the influence of water content on the mechanical behavior of surrounding rock can be more comprehensively reflected, providing a more accurate calculation basis for subsequent surrounding rock failure analysis, solution and support design.

[0050] In some embodiments, in order to more accurately reflect the stress state and failure stage of the surrounding rock during tunnel excavation, the stress release degree at the tunnel face is introduced as a criterion to characterize the development of the three-dimensional arch effect of the tunnel.

[0051] Specifically, during tunnel excavation, the stress release level in the tunnel face area is monitored or calculated and compared with a preset stress release coefficient threshold. When the stress release coefficient at the tunnel face is greater than the threshold, it indicates that the surrounding rock has undergone significant stress adjustment and the three-dimensional arch effect is significantly enhanced. At this point, the tunnel is determined to be in the second stage of the excavation process, and a circular tunnel calculation model considering the water weakening effect should be introduced to perform mechanical calculations on the surrounding rock failure process. Conversely, when the stress release coefficient at the tunnel face is less than or equal to the threshold, it indicates that the surrounding rock is still in the initial stress redistribution stage, and the three-dimensional arch effect has not yet fully developed. At this point, the tunnel is determined to be in the first stage of the excavation process.

[0052] The stress release coefficient refers to the proportion of the original stress state of the surrounding rock that is released under excavation disturbance, reflecting the degree of stress redistribution within the surrounding rock. The preset stress release coefficient threshold can be pre-set based on geological conditions, engineering experience, or numerical simulation results to distinguish the response characteristics of the surrounding rock at different stages.

[0053] In some embodiments, in the first stage of the tunnel excavation process, i.e. the initial stress redistribution stage where the surrounding rock failure is mainly caused by the excavation effect, the stress and strain characteristics are solved using the surrounding rock mechanical parameters under the natural water content condition. That is, for the first stage, the stress and strain characteristics of the surrounding rock are solved based on the surrounding rock mechanical parameters corresponding to the natural water content.

[0054] During this stage, groundwater has not yet significantly affected the surrounding rock, and its physical and mechanical properties remain largely stable. Therefore, the surrounding rock mechanical parameters used in the computational model are all based on experimental data or fitting results under natural water content conditions, without considering the influence of water weakening effects.

[0055] In some embodiments, the model structure is reasonably simplified when establishing a circular tunnel calculation model that considers the water weakening effect, in order to improve computational efficiency and applicability. Specifically, the circular tunnel calculation model considering the water weakening effect includes: A circular tunnel calculation model was established, and the plastic softening zone and the plastic residual zone were uniformly regarded as the plastic zone; The problem of solving the formation response of a circular tunnel considering the water weakening effect is simplified into a plane strain problem; Apply uniform initial geostress to the surrounding rock. The tunnel excavation radius is set as The pressure of the tunnel wall support is ; Calculate the critical pressure for determining whether the surrounding rock has formed a plastic zone. ;when At that time, it was determined that only an elastic zone existed in the surrounding rock of the tunnel wall. At that time, it was determined that a plastic zone had appeared in the surrounding rock of the tunnel wall; In plane strain problems, radial stress is... As the minimum principal stress of the surrounding rock, the tangential stress As the maximum principal stress of the surrounding rock This represents the displacement of the surrounding rock.

[0056] Among them, initial geostress That is, hydrostatic pressure. By treating the plastic softening zone and the plastic residual zone as the same plastic zone, the amount of calculation can be effectively reduced.

[0057] Furthermore, the critical pressure value for determining whether the surrounding rock has undergone plastic failure is calculated through theoretical derivation or numerical methods. When the support pressure at the tunnel wall Greater than this critical pressure When the support pressure is less than or equal to the critical pressure, the surrounding rock is determined to be in an elastic state, with only an elastic zone present; however, when the support pressure is less than or equal to the critical pressure, the surrounding rock is determined to have undergone localized plastic failure, resulting in a plastic zone.

[0058] The above modeling can effectively simulate the mechanical behavior of the surrounding rock under the influence of water weakening effect after tunnel excavation, providing theoretical support for the stability analysis and support design of the surrounding rock.

[0059] In some optional embodiments, based on the fitting equation of the surrounding rock mechanical parameters considering water content, a circular tunnel calculation model considering the water weakening effect is established. A semi-analytical method is used to perform mechanical calculations on the surrounding rock failure process, including: solving for the elastic state solution of the surrounding rock. The calculation process is as follows: According to the tunnel wall support pressure With initial geostress The difference relationship, combined with the tunnel excavation radius The radial stress at any point within the elastic region under elastic conditions is calculated using the Lame solution. tangential stress ; Ignoring initial ground stress The resulting strain and displacement are calculated based on the shear modulus considering water content. The radial strain, tangential strain, and displacement at any point within the elastic zone under elastic conditions are calculated. The shear modulus considering water content is obtained by a shear modulus fitting equation, which is one of the equations in the fitting equation of the surrounding rock mechanical parameters considering water content.

[0060] In this embodiment, under the condition that the surrounding rock is in an elastic state, based on the difference between the support pressure at the tunnel wall and the initial ground stress, and combined with the known tunnel excavation radius, the stress distribution at any location within the elastic zone is calculated using the basic principles of the Lame solution. Specifically, the radial stress and tangential stress at this location are solved, serving as the basic parameters for subsequent stability analysis. Based on this, the strain and displacement response of the surrounding rock under elastic conditions are further calculated. To more realistically reflect the influence of groundwater on the mechanical properties of the surrounding rock, the shear modulus, calculated using a shear modulus fitting equation considering the influence of water content, is used in the calculation. This shear modulus fitting equation is a component of the surrounding rock mechanical parameter fitting equation constructed based on previous experimental data.

[0061] In the calculation process, the initial strain and displacement caused by the initial in-situ stress alone are ignored; only the additional strain and displacement changes caused by stress redistribution due to excavation disturbance are considered. Based on this, the specific values ​​of radial strain, tangential strain, and radial displacement at any point in the surrounding rock under elastic conditions can be obtained. Using this method, it is possible to quickly and accurately calculate the elastic response of the surrounding rock while considering the influence of water content, providing reliable data support for subsequent analysis of plastic zone development and stress assessment of the support structure.

[0062] In other alternative embodiments, based on the established circular tunnel calculation model considering the water weakening effect, a semi-analytical method is used to solve the mechanical response of the surrounding rock in the plastic state, so as to more comprehensively simulate the failure process and deformation characteristics of the surrounding rock under different water content conditions after tunnel excavation. That is, based on the fitting equation of the surrounding rock mechanical parameters considering water content, a circular tunnel calculation model considering the water weakening effect is established, and a semi-analytical method is used to perform mechanical calculations on the failure process of the surrounding rock, including: solving the plastic state solution of the surrounding rock, the calculation process is as follows: For the elastic region in the plastic state, based on the initial ground stress Critical pressure The difference relationship, combined with the radius of the plastic zone Calculate the mechanical characteristics of the elastic region under plastic conditions; At the boundary of the elastic-plastic region, based on the initial geostress at any point at the boundary of the elastic-plastic region... Combined with the preset strength criteria, the critical pressure at any point on the elastic-plastic boundary is calculated; based on the critical pressure at any point on the elastic-plastic boundary, and combined with the shear modulus considering the moisture content, the mechanical characteristics at the boundary of the elastic-plastic region are calculated. The shear modulus considering water content is calculated by a shear modulus fitting equation, which is one of the equations in the fitting equation of the surrounding rock mechanical parameters considering water content. For the plastic zone, the finite difference method is used to solve for the stress, strain and displacement of the surrounding rock.

[0063] Specifically, when the surrounding rock enters a plastic state, for the elastic zone, based on the difference between the initial in-situ stress and the critical pressure, and combined with the determined influence range of the plastic zone (i.e., the radius of the plastic zone), the stress distribution and deformation characteristics exhibited by the elastic zone in the plastic state are calculated. Further, at the elastoplastic boundary region, i.e., the junction of the elastic and plastic zones, based on the initial in-situ stress and boundary pressure at any point on this boundary, and combined with a preset strength criterion, the critical pressure value corresponding to any point on this boundary is derived. On this basis, the shear modulus, considering the influence of water content, calculated through a shear modulus fitting equation, is introduced to further analyze and calculate the mechanical characteristics such as stress, strain, and displacement at the elastoplastic boundary. The shear modulus fitting equation is a component of the surrounding rock mechanical parameter fitting equation constructed based on previous experimental data. For the plastic zone in the surrounding rock, the finite difference method is used to numerically solve for the stress distribution, strain development, and displacement changes of the surrounding rock. This method can effectively handle nonlinear constitutive relations and complex boundary conditions, and is suitable for simulating the plastic flow and failure evolution of surrounding rock caused by excavation disturbance under the effect of water weakening.

[0064] Specifically, when modeling the plastic zone, the surrounding rock plastic region is divided into multiple concentric ring structures, and the radius of each ring is normalized to unify the calculation scale between different nodes, thereby improving calculation efficiency and stability. Within each ring, assuming a consistent radial stress increment, and considering the difference between the support pressure and critical pressure at the tunnel wall, the radial stress distribution at each ring location is calculated sequentially. Subsequently, the calculated radial stress is substituted into the preset yield equation to further solve for the tangential stress value at the corresponding ring location, thus constructing a complete stress field distribution. Under plane strain conditions, based on the fundamental principles of Hooke's law, the elastic strain increment at each ring location is calculated, and the elastic strain value is obtained accordingly. To further ensure the model's rationality, corresponding equilibrium equations are established for each calculation node within the plastic zone, ensuring that the obtained stress distribution satisfies the static equilibrium condition, thereby guaranteeing the continuity and stability of the overall stress system. Furthermore, considering the plastic deformation of the surrounding rock, plastic flow theory is introduced, and the plastic strain at each node is calculated by combining the actual friction angle and cohesion variation trends of the surrounding rock. Finally, by integrating the calculation results of elastic strain and plastic strain, the displacement distribution at each point within the plastic zone is obtained, which is used to assess the overall deformation development trend of the surrounding rock. When the plastic shear strain at a certain calculation node exceeds the residual strength that the surrounding rock can withstand, it indicates that the region has entered a significant softening stage. At this time, a linear weakening function is used to describe the mechanical behavior of the surrounding rock in this region to reflect the process of its strength gradually decreasing with deformation. Through the above method, the entire process of stress, strain, and displacement in the plastic zone of the surrounding rock can be simulated under the premise of considering the influence of water content, providing strong technical support for the dynamic assessment of the stability of the surrounding rock during tunnel excavation.

[0065] The linear weakening function is used to describe the changes in mechanical parameters of the surrounding rock in the post-peak stage of water-rich, weakly cemented sandstone formations. When the plastic shear strain of the surrounding rock has not reached the critical value corresponding to the residual strength, this function causes the cohesion and internal friction angle of the surrounding rock to decrease linearly with increasing plastic shear strain. When the plastic shear strain exceeds the critical value, the cohesion and internal friction angle no longer change and remain at the values ​​corresponding to the residual strength.

[0066] In summary, this embodiment quantitatively analyzes the correlation between water content and various surrounding rock mechanical parameters based on experimental data at different water contents. It also fits these parameters, providing the relationships between each mechanical parameter and water content (i.e., fitting equations for surrounding rock mechanical parameters considering water content). Based on these fitting equations and the finite difference principle, a semi-analytical solution for the staged failure of the surrounding rock in weakly cemented sandstone tunnel excavation, considering the water weakening effect, is derived. The results show that the surrounding rock parameters gradually deteriorate from the natural state to the water-saturated state, with significant changes in both the peak tangential stress and the surrounding rock displacement, revealing a two-stage, staged failure phenomenon in the surrounding rock.

[0067] The technical solution of this application will be described in detail below with specific examples.

[0068] Step 1: Obtain experimental data Based on the study of physical properties, the mechanical properties of weakly cemented sandstone were analyzed by triaxial compression tests. Before the test, in accordance with the provisions of the water absorption test in the "Standard for Test Methods of Engineering Rock Mass" (GBT50266-2013), the rock sample was placed in a drying oven. After 24 hours, it was removed and placed in a dry environment to cool to room temperature before weighing, which is the dry weight of the rock sample. Due to the disintegration of the sample, in this embodiment, the water content was determined after forced saturation by vacuum pumping.

[0069] The experiment first recorded the moisture content of the rock samples under natural conditions. Then, the rock samples used to test the dry-state characteristics were dried. Afterward, the dried samples were cooled to room temperature and placed in a saturator under vacuum. Distilled water was then introduced to submerge the samples, and the samples were soaked for different times to control different moisture content gradients. Once the desired soaking time and moisture content were achieved, the rock samples were removed, wiped dry, and weighed. The moisture content of the rock samples was calculated by combining the dry and wet weights. Samples with different moisture contents (dry and saturated) were prepared using the drying oven and vacuum extraction method, combined with the original naturally saturated samples, to form three moisture content samples, as shown in Table 1, preparing for subsequent conventional triaxial compression tests at different moisture contents.

[0070] Table 1. Sample moisture content

[0071] Triaxial compression failure tests under different confining pressures were conducted using the TZW-3000 fully automatic triaxial rock testing system developed by Changchun Chaoyang Testing Instrument Co., Ltd. This equipment has a maximum normal load of 3000 kN with a control accuracy of ±1% FS, a maximum confining pressure of 100 MPa with a control accuracy of ±2% FS, an axial displacement range of 10 mm with a measurement accuracy of ±1% FS (compatible with diameters of 50 mm and 100 mm), a circumferential displacement range of 5 mm with a measurement accuracy of ±1% FS (compatible with diameters of 50 mm and 100 mm), and a control mode that allows for both load and displacement control with smooth switching. Standard specimens were prepared according to requirements, with dimensions of 50 mm × 100 mm (diameter × height). The specimens were wrapped in latex sleeves and placed between two pads, then compacted using a hot air blower.

[0072] At the beginning of the test, axial pressure and confining pressure were applied at a loading rate of 0.05 MPa / s to the predicted values. Axial load was then applied at a loading rate of 0.005 mm / s, with the confining pressure remaining constant during the axial loading process. Different confining pressure values ​​were used in this test, corresponding to the support forces provided in actual engineering projects. The design confining pressures were 0 MPa, 5 MPa, and 10 MPa. Each confining pressure value corresponded to three different moisture contents: dry, natural, and saturated. A total of nine sets of tests were conducted to obtain test data under different moisture contents.

[0073] Stress-strain curves under different confining pressures were plotted based on experimental data. Analysis of these curves revealed that the stress-strain curves of weakly cemented sandstone can be divided into five stages: compaction, elasticity, plasticity, strain softening, and residual. Further analysis of the stress-strain curves showed that the characteristics of the stress-strain curves varied under different water content conditions. For dry samples, the curve developed from the linear elastic stage to the peak strength and then suddenly dropped rapidly, showing a sharp inflection, indicating that the dry rock sample underwent brittle failure. As the water content increased, the stress-strain curve became increasingly flat, with a smaller overall inclination, indicating that the rock gradually transitioned from brittle to ductile failure. Furthermore, with increasing confining pressure, the initial increase in lateral strain was small. When the load was small, the sample was in a compressed state; when the load reached its critical value, volume expansion occurred. When the stress reached 70% of the peak strength, internal damage gradually began, and microcracks evolved, developed, and connected with increasing stress. When the stress exceeds the peak strength and enters the failure stage, the bearing capacity of the specimen shows a rapid downward trend. At this time, the rate of increase of transverse strain far exceeds that of axial strain. From the stress-strain curve, the strain reduction at 0MPa and 5MPa is significantly greater than that at 10MPa.

[0074] The mechanical parameters of the specimen were obtained from the stress-strain curves, as shown in Table 2.

[0075] Table 2 Mechanical parameters of the specimen

[0076] Substituting the above calculation results into the following formula, the cohesion and internal friction angle can be calculated: (1) In the formula, The maximum principal stress (stress at failure) is expressed in MPa. It is the confining pressure, and the unit is MPa; It is the angle of internal friction, and the unit is °; It is cohesion, and the unit is MPa.

[0077] Based on equation (1) and experimental data, the cohesion and internal friction angle of the rock mass under three conditions—dry, natural, and saturated—can be obtained, as shown in Table 3.

[0078] Table 3. Cohesion and internal friction angle of the samples

[0079] Based on the foregoing analysis, it is evident that the surrounding rock of weakly cemented sandstone strata exhibits significant water-induced softening properties, with both rock strength and elastic modulus decreasing substantially with increasing water content. Rock mass strength is greatly influenced by water content and variations in the rock's microstructure. When the rock mass has numerous and large pores, and the cohesion between rock particles is poor, groundwater will seep into the rock mass along these pores, leading to softening, expansion, and disintegration. This reduction in the mechanical strength of the surrounding rock due to water content is even more pronounced in weakly cemented sandstone strata. When groundwater seeps into the surrounding rock around the tunnel excavation area, it significantly reduces the stability of the surrounding rock, making it more prone to large deformations, and the degree of deformation will be more intense.

[0080] Step 2: Analyze the water-induced softening effect on weakly cemented sandstone. The elastic modulus of samples under different moisture contents was summarized and analyzed. The elastic modulus of samples with the same moisture content was averaged, and the elastic modulus of samples under different moisture contents was plotted. It can be seen from the figure that the elastic modulus decreases with increasing moisture content. A linear equation can be used to fit the change of elastic modulus with moisture content. The fitting equation for the elastic modulus is as follows: (2) In the formula, Indicates moisture content, , These are different moisture contents The elastic modulus under dry conditions and the elastic modulus under dry conditions.

[0081] The Mohr-Coulomb strength criterion is commonly used to describe the variation of peak stress and residual stress in surrounding rock with confining pressure. Its expression is as follows: (3) in: The maximum principal stress (stress at failure) is expressed in MPa. It is the confining pressure, in MPa; To be related to moisture content The relevant cohesion (determined by the fitted equation); The coefficient related to the internal friction angle is calculated as follows: (4) In the formula, To be related to moisture content The relevant internal friction angle (determined by the fitted equation).

[0082] The Mohr-Coulomb strength criterion was used to fit the peak stress and residual stress of the surrounding rock. Scatter plots of cohesion, internal friction angle, and dilatation angle at different water contents were plotted based on experimental data to statistically analyze the effect of different water contents on cohesion and internal friction angle. Analysis of the scatter plots shows that with increasing water content, the cohesion at the peak strength decreases. Cohesion at residual strength All gradually decrease, with the internal friction angle at the peak intensity. and the internal friction angle at the residual strength The values ​​also gradually decrease, indicating that the surrounding rock parameters gradually decrease and the surrounding rock deteriorates with increasing water content. A linear equation can be used to fit the changes in cohesion and internal friction angle with water content, resulting in the following fitted equation: (5) (6) (7) (8) In the formula, subscript and These represent the mechanical parameter values ​​under dry and moist conditions, respectively. , These are the cohesive forces at the peak strength and residual strength under dry conditions, respectively. , These are the conditions under which water content is (water content is 100%). (The same applies below) Cohesion at peak strength and residual strength; , These are the internal friction angles at the peak strength and residual strength under dry conditions, respectively. , These are the internal friction angles at the peak strength and residual strength under water-containing conditions, respectively. Similarly, the dilatation angle of the surrounding rock under different water contents was statistically analyzed. This is manifested by the dilatation angle gradually increasing with moisture content. Using a linear equation for fitting, the fitted equation is as follows: (9) In the formula, The shear dilatation angle under water-bearing conditions. This is the shear dilatation angle under dry conditions.

[0083] In summary, the above analysis and research show that with the increase of water content, the surrounding rock exhibits a significant water-induced softening effect, and the elastic modulus, cohesion, and internal friction angle decrease according to a certain law, which has an important impact on the deformation and failure of the surrounding rock in weakly cemented sandstone strata.

[0084] Step 3: Analysis of the Stage-by-Stage Failure Process of Surrounding Rock During tunnel excavation, the slope and excavation radius are fixed. When the tunnel reaches a certain depth, the plastic zone of the surrounding rock is mainly affected by cohesion and internal friction angle. However, the water content of the surrounding rock is different, and the cohesion and internal friction angle are also different. As a result, the range of the plastic zone of the surrounding rock after tunnel excavation is different, and even the failure mode of the surrounding rock will be different.

[0085] Studies have shown that after tunnel excavation, the surrounding rock undergoes elastoplastic deformation as stress is released. When local stress and water content are low, the surrounding rock can reach a stable state after the formation of a loosened zone. However, during the excavation of weakly cemented sandstone under water-rich conditions, the stress will redistribute in the initial stage of tunnel excavation, and the tangential pressure on the tunnel wall surrounding rock will suddenly increase, causing it to be in a plastic or elastoplastic state. Under tangential pressure, the tunnel wall, as a free surface, has a maximum deviatoric stress between the tangential and radial directions. Under the maximum tangential support pressure, the surrounding rock can only undergo lateral tensile expansion towards the free surface. When this tensile deformation reaches the ultimate strain, the surrounding rock undergoes brittle deformation, leading to the formation of the first failure zone around the tunnel wall. Under the action of pore water pressure, there is a situation where the stress that was not fully released is redistributed again. After the rock stress under the combined pressure of ground stress and pore water pressure is released, since the tunnel construction location is in a weak cemented sandstone stratum with low rock strength, the outer boundary of the first failure zone is equivalent to the new excavation boundary. The surrounding rock stress is transferred to the depth and redistributed again. When the new stress field meets the failure conditions, the stress is released again, forming the second failure zone. Figure 1 This is a schematic diagram of the two-stage evolution of tunnel excavation according to some embodiments of this application, which can schematically illustrate the tunnel excavation process.

[0086] Considering the three-dimensional arch effect during tunnel excavation, such as Figure 2 As shown, the excavation process is divided into two stages: Phase I (First Phase): such as Figure 2 In part (a), the tunnel is divided into an excavation zone, a plastic residual zone (1), a plastic softening zone (0→1), and an elastic zone (0). , , These are the tangential stresses in the elastic region, the plastic softening region, and the plastic residual region, respectively. , These represent the radial stresses in the elastic zone and the plastic softening zone, respectively. At infinity from the tunnel face, the tunnel is in a state of in-situ rock stress. As the tunnel face advances, the core rock mass at the face deforms, causing the first stress release in the surrounding rock ahead of the tunnel face. This first stress release is completed when the tunnel section reaches the face. Assume the stress release coefficient at the face location is... During this stage, the surrounding rock remains in a state of natural water content, and the fissures within the surrounding rock have not yet been connected. Only the excavation effect of the tunnel exists at this stage. Figure (a) shows a schematic diagram of the formation of the plastic zone in stage I, where 0 indicates that the surrounding rock is in the elastic zone and is in the original stress state, 1 indicates that the surrounding rock lacks radial stress due to excavation and is in the residual failure zone, and 0→1 indicates that the surrounding rock is in the plastic softening zone, developing from the elastic zone to the residual failure zone; Stage II (Second Stage): As the tunnel face continues to advance, internal fissures in the surrounding rock develop and connect, increasing the water inflow within the tunnel. This stage is called Stage II, and both the tunnel excavation effect and the weakening effect of water on the surrounding rock must be considered simultaneously. Figure (b) shows a schematic diagram of the formation of the plastic zone in Stage II. In the plastic zone, the surrounding rock undergoes radial deformation under the influence of pore water pressure and water expansion, resulting in a redistribution of stress. The surrounding rock in the failure zone changes from 1 to 2, further exacerbating the damage.

[0087] Step 4: Semi-analytical solution of surrounding rock response considering water weakening effect To perform mechanical calculations on the surrounding rock failure process, a calculation model for a circular tunnel considering the water weakening effect is established, such as... Figure 3 As shown, to simplify the calculation process, the plastic softening zone and the plastic residual zone are treated as a single plastic zone. The solution problem for the formation response of a circular tunnel considering the water weakening effect is a plane strain problem, assuming that a uniform hydrostatic pressure acts on the surrounding rock. The tunnel excavation radius is The pressure of the tunnel wall support is , The critical pressure for determining whether the surrounding rock has formed a plastic zone. When Greater than At that time, the surrounding rock of the cave wall only had an elastic zone. Less than At this time, a plastic zone will appear in the surrounding rock of the tunnel wall. In plane strain problems, radial stress... and tangential stress These are often considered to be the minimum principal stress and the maximum principal stress experienced by the surrounding rock, respectively. This represents the displacement of the surrounding rock. Step 41, Elastic State Solution When the initial geostress When the size is small, the support force of the tunnel wall after excavation Greater than The surrounding rock is in the elastic stage. Based on the Lame solution, the stress calculation results in the elastic zone are as follows: (10) (11) In the formula: The radius of the surrounding rock at different locations. Ignoring the initial geostress The resulting strain and displacement can be obtained as follows: (12) (13) (14) In the formula, Shear modulus considering the effect of moisture content; and These are the radial strain and tangential strain of the surrounding rock, respectively.

[0088] Step 42, Solution of Plastic State (1) Elastic zone As the excavation depth gradually increases, when the support pressure decreases, the tunnel wall will exhibit a radius of... The circular plastic region. The solution for the elastic region under plastic conditions is as follows: (15) (16) (17) (18) (19) Step 43, Boundary of the Elastic-Plastic Zone At the boundary of the elastic-plastic zone, the stress state of the elastic zone satisfies the strength criterion (Equation (3)). Substituting Equations (15) and (16) into Equation (3), the critical support pressure can be solved. : (20) in, , All are with The relevant parameters are calculated using the following formulas: (twenty one) (twenty two) Will Substituting into equations (15) to (19), the stress and strain at the elastoplastic boundary can be obtained as follows: (twenty three) (twenty four) (25) (26) (27) In the formula, the minor subscript Represents the location of the elastoplastic interface. , These represent the radial stress and tangential stress at the elastoplastic interface, respectively. , , These represent the radial strain, tangential strain, and displacement at the elastoplastic interface, respectively.

[0089] Step 44, Plastic Zone Decomposition For the solution in the plastic region, the finite difference method is used. The calculation principle is as follows: Figure 4 As shown, the plastic region is divided into We obtain the following by taking the radius of each of the three annular rings and normalizing it: (28) In the formula, the subscript 𝑖 represents the ring number, which is also the number of different calculation nodes. Let be the radius at different computation node locations. The normalized radius is used at different computation nodes. Consider the radial stress increment of each ring If they are the same, then: (29) Therefore, the first Radial stress at each ring This can be expressed as follows: (30) In the formula, .

[0090] when Increase from 1 to At this point, radial stress components can be calculated from the elastoplastic interface to the tunnel wall. It should be noted that although the values ​​of each ring... Same, but its thickness Different. The stress state within the plastic zone satisfies the yield equation, and the radial stress... Substituting into the yield equation, we can obtain the first... Tangential stress at the location of the ring for: (31) in: (32) In the formula, For the first Plastic shear strain at each calculation node. Therefore, we have: (33) Under plane strain conditions, according to Hooke's law, the elastic strain increment can be solved by the following formula: (34) (35) In the formula, and These represent the increments of elastic radial strain and elastic tangential strain at the calculation nodes, respectively. It is Poisson's ratio. The stress state at each node of the surrounding rock within the plastic zone must satisfy the equilibrium equation, expressed using the normalized radius as follows: (36) Substituting equation (31) into equation (36), in the first... Equation (36) at each computation node can be approximately solved as follows: (37) In the formula, This represents the average radial stress between two adjacent calculation nodes. .

[0091] Then the first Normalized radius of the ring It can be explicitly expressed as: (38) To solve for plastic strain, the displacement compatibility equation can be expressed as follows: (39) Considering that strain in the plastic region can be decomposed into elastic strain and plastic strain: (40) (41) In the formula, and The first The radial elastic strain and radial plastic strain at each calculated location; and They are respectively Tangential elastic strain and tangential plastic strain at each calculation node. Equation (39) can then be rewritten as: (42) The difference form of equation (42) is: (43) Considering plastic flow, the plastic radial strain and plastic tangential strain can satisfy the following equation: (44) in, The coefficients related to the plastic potential function are the dilatation angle under water-bearing conditions. The relevant calculation formula is as follows: (45) According to equations (43) and (44), the plastic strain increment can be expressed as follows: (46) (47) Where, is the mean of the normalized radii between two adjacent computation nodes: The increment of plastic shear strain can be calculated as follows: (48) The post-peak stage of the surrounding rock is described using a linear weakening function. At each computing node Plastic shear strain at the point where it is less than the residual strength of the surrounding rock hour: (49) (50) At the compute node Greater than hour: (51) (52) The displacement of each node can be calculated using the following formula: (53) in: (54) (55) Step 5: Analysis of Calculation Results Based on the surrounding rock mechanics parameters, a semi-analytical solution is used to analyze the two-stage response of the tunnel from three aspects: stress redistribution, displacement distribution, and convergence constraint curve of the surrounding rock after excavation. Assuming the stress relief factor for stage I is 0.3, Figure 5A schematic diagram of the stress redistribution in the surrounding rock considering the two-stage evolution process is shown, illustrating the stress redistribution of the tunnel under Stage I and Stage II conditions. During the excavation of Stage I, the surrounding rock is in a natural state with good mechanical properties. With the increase of radius, the radial stress gradually increases, while the tangential stress gradually decreases, indicating that the surrounding rock is in an elastic state. During the excavation of Stage II, the excavation effect causes the tangential stress in the tunnel wall to accumulate further, and the surrounding rock enters the plastic zone. The tangential stress exhibits a distribution pattern of first increasing, then rapidly increasing, and finally decreasing. Considering the gradual increase in water content during the excavation process, the water weakening effect causes the surrounding rock parameters to gradually deteriorate. The peak tangential stress gradually decreases from 12.32 MPa to 11.51 MPa, and the peak tangential stress gradually moves towards the interior of the surrounding rock, indicating that the plastic zone of the tunnel wall gradually increases, while the residual failure zone gradually increases.

[0092] Figure 6 To illustrate the redistribution of surrounding rock displacement during the two-stage evolution process, the diagram summarizes the displacement distribution of surrounding rock under different water content conditions during the two stages. Since the surrounding rock is in an elastic state in stage I, the water content only affects the displacement of the surrounding rock by changing the elastic modulus. Therefore, the displacement of the surrounding rock at the same radius under different water content conditions in stage I is almost the same. The displacement at the tunnel wall location from dry to natural and finally to saturated state is 0.016m, 0.02m, and 0.025m, respectively. Considering the excavation effect in stage II, the displacement of the tunnel wall surrounding rock in the natural state increases from 0.02m to 0.14m. The water weakening effect causes the displacement of the surrounding rock to increase sharply. From the natural state to the saturated state, the displacement of the tunnel wall surrounding rock increases from 0.14m to 0.57m, indicating that the increase in water content causes a sharp increase in the displacement of the tunnel wall.

[0093] Figure 7 The diagram illustrates the convergence constraint curve of the surrounding rock considering the two-stage evolution process. It shows the convergence constraint curve of the surrounding rock considering the two-stage process. The excavation effect causes the convergence constraint curve of stage I to decrease approximately linearly. Considering the water weakening effect, the elastic modulus of the surrounding rock decreases, and the convergence constraint curve shows a plateau segment. In stage II, under the combined effect of the excavation effect and the water weakening effect, the mechanical parameters such as the elastic modulus and cohesion of the surrounding rock decrease, and the displacement of the surrounding rock of the tunnel wall increases sharply.

[0094] Based on the above analysis, considering both the three-dimensional spatial effects of the tunnel during excavation and the weakening effect of water on the rock, the surrounding rock exhibits a phased failure phenomenon. In the first stage, the excavation effect of the tunnel is mainly considered. The radial stress of the surrounding rock is gradually released, while the tangential stress concentrates, and the surrounding rock may experience excavation-induced damage. As excavation progresses and the tunnel face continues to advance, water continuously flows into the tunnel. The surrounding rock is affected by the water weakening effect, and its strength continuously decreases. Simultaneously, considering the tunnel excavation effect, the deformation of the surrounding rock increases sharply, resulting in the second stage of failure.

[0095] In summary, the stability of the surrounding rock in weakly cemented sandstone formations is closely related to its physical and mechanical parameters. This embodiment addresses the issue of high water inflow at the tunnel face during tunnel construction in this formation. Considering the impact of water content on the weakly cemented sandstone, the scheme quantitatively analyzes the correlation between water content and the mechanical parameters of the weakly cemented sandstone. The correlations between the elastic modulus, peak internal friction angle, peak cohesion, residual internal friction angle, residual cohesion, and expansion angle with water content are presented. Based on these water content correlations and the finite difference principle, a semi-analytical solution for the staged failure of the surrounding rock in weakly cemented sandstone formations considering the water weakening effect is derived. The results show that the surrounding rock parameters gradually deteriorate from the natural state to the saturated state. The peak tangential stress decreases from 12.32 MPa to 11.51 MPa, while the surrounding rock displacement increases from 0.14 m to 0.57 m. The surrounding rock ultimately exhibits a two-stage, graded failure phenomenon.

[0096] Triaxial tests were conducted on weakly cemented sandstone under different confining pressures and water contents to quantitatively analyze the correlation between water content and the mechanical parameters of weakly cemented sandstone. Relationships between elastic modulus, peak internal friction angle, peak cohesion, residual internal friction angle, residual cohesion, and expansion angle with water content were given. To investigate the influence mechanism of water on the overall stability of the surrounding rock of weakly cemented sandstone strata, based on the given relationships and combined with the finite difference principle, a semi-analytical solution for the staged failure of the surrounding rock during tunnel excavation in weakly cemented sandstone strata considering the water weakening effect was derived. The results show that the surrounding rock parameters gradually deteriorate from the natural state to the water-saturated state, with the peak tangential stress decreasing from 12.32 MPa to 11.51 MPa and the surrounding rock displacement increasing from 0.14 m to 0.57 m. This reveals a two-stage staged failure phenomenon of the surrounding rock, which can provide effective optimization guidance for support design.

[0097] Example 2 Based on the same inventive concept, this embodiment provides a computer system including a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of any of the methods described above.

[0098] Example 3 Based on the same inventive concept, a computer-readable storage medium is provided that stores a computer program / instructions thereon, which, when executed by a processor, implements the computer program to perform the steps of any of the methods described above.

[0099] The above description is merely a preferred embodiment of this application and is not intended to limit this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the protection scope of this application.

Claims

1. A method for a semi-analytical solution of staged failure of surrounding rock in tunnel water inrush, characterized in that, include: Based on the test data at different water contents, the mechanical parameters of the surrounding rock were fitted to obtain the fitting equation of the mechanical parameters of the surrounding rock considering the water content. Considering the three-dimensional arch effect during tunnel excavation, the surrounding rock failure process caused by tunnel excavation is divided into two stages: the first stage and the second stage. In the first stage, the surrounding rock failure mode is the initial stress redistribution due to the excavation effect. In the second stage, the surrounding rock failure mode is the stress redistribution caused by the combined effect of the excavation effect and the water weakening effect. For the second stage, based on the fitting equation of the surrounding rock mechanical parameters considering water content, a circular tunnel calculation model considering the water weakening effect is established, and a semi-analytical method is used to perform mechanical calculations on the surrounding rock failure process.

2. The method according to claim 1, characterized in that, Based on experimental data at different water contents, various surrounding rock mechanical parameters were fitted to obtain fitting equations for surrounding rock mechanical parameters considering water content, including: Based on the test results of the samples under different moisture contents, a linear equation was used to fit the change of elastic modulus with moisture content, and the fitting equation of elastic modulus was obtained. Based on the Mohr-Coulomb strength criterion, the peak stress and residual stress of the surrounding rock were fitted. Based on the fitting results, linear equations were used to fit the changes of cohesion at peak strength, cohesion at residual strength, friction angle at peak strength and friction angle at residual strength with water content, respectively, and the fitting equations for cohesion at peak strength, cohesion at residual strength, friction angle at peak strength and friction angle at residual strength were obtained. The variation of the dilatation angle with water content was fitted using a linear equation to obtain the fitted equation for the dilatation angle.

3. The method according to claim 1, characterized in that, The stress release coefficient at the tunnel face is used to characterize the three-dimensional arch effect during tunnel excavation. When the stress relief coefficient at the tunnel face is greater than the preset stress relief coefficient threshold, the tunnel is determined to be in the second stage of the excavation process. When the stress relief coefficient at the tunnel face is less than or equal to the preset stress relief coefficient threshold, the tunnel is in the first stage of the excavation process.

4. The method according to claim 1, characterized in that, The circular tunnel calculation model considering the water weakening effect includes: A circular tunnel calculation model was established, and the plastic softening zone and the plastic residual zone were uniformly regarded as the plastic zone; The problem of solving the formation response of a circular tunnel considering the water weakening effect is simplified into a plane strain problem; Apply uniform initial geostress to the surrounding rock. The tunnel excavation radius is set as The pressure of the tunnel wall support is ; Calculate the critical pressure for determining whether the surrounding rock has formed a plastic zone. ;when At that time, it was determined that only an elastic zone existed in the surrounding rock of the tunnel wall. At that time, it was determined that a plastic zone had appeared in the surrounding rock of the tunnel wall; In plane strain problems, radial stress is... As the minimum principal stress of the surrounding rock, the tangential stress As the maximum principal stress of the surrounding rock This represents the displacement of the surrounding rock.

5. The method according to claim 4, characterized in that, Based on the fitting equations for the mechanical parameters of the surrounding rock considering water content, a calculation model for a circular tunnel considering the water weakening effect is established. A semi-analytical method is used to perform mechanical calculations on the failure process of the surrounding rock, including solving for the elastic state solution of the surrounding rock. The calculation process is as follows: According to the tunnel wall support pressure With initial geostress The difference relationship, combined with the tunnel excavation radius The radial stress at any point within the elastic region under elastic conditions is calculated using the Lame solution. tangential stress ; Ignoring initial ground stress The resulting strain and displacement are calculated based on the shear modulus considering water content. The radial strain, tangential strain, and displacement at any point within the elastic zone under elastic conditions are calculated. The shear modulus considering water content is obtained by a shear modulus fitting equation, which is one of the equations in the fitting equation of the surrounding rock mechanical parameters considering water content.

6. The method according to claim 4, characterized in that, Based on the fitting equations for the mechanical parameters of the surrounding rock considering water content, a calculation model for a circular tunnel considering the water weakening effect is established. A semi-analytical method is used to perform mechanical calculations on the failure process of the surrounding rock, including solving for the plastic state solution of the surrounding rock. The calculation process is as follows: For the elastic region in the plastic state, based on the initial ground stress Critical pressure The difference relationship, combined with the radius of the plastic zone Calculate the mechanical characteristics of the elastic region under plastic conditions; At the boundary of the elastic-plastic region, based on the initial geostress at any point at the boundary of the elastic-plastic region... Combined with the preset strength criteria, the critical pressure at any point on the elastic-plastic boundary is calculated; based on the critical pressure at any point on the elastic-plastic boundary, and combined with the shear modulus considering the moisture content, the mechanical characteristics at the boundary of the elastic-plastic region are calculated. The shear modulus considering water content is calculated by a shear modulus fitting equation, which is one of the equations in the fitting equation of the surrounding rock mechanical parameters considering water content. For the plastic zone, the finite difference method is used to solve for the stress, strain and displacement of the surrounding rock.

7. The method according to claim 6, characterized in that, For the plastic zone, the finite difference method is used to solve for the stress, strain, and displacement of the surrounding rock, including: The plastic region is divided into multiple concentric rings, and the radius of each ring is normalized. Assuming the radial stress increment is equal for each ring, the support pressure through the tunnel wall of each ring in the plastic zone... and critical pressure The difference is used to calculate the radial stress at each ring; Substitute the radial stress into the preset yield equation to calculate the tangential stress at each ring. Under plane strain conditions, the elastic strain increment at each ring is calculated according to Hooke's law, and then the elastic strain is calculated. For each calculation node in the plastic zone, establish equilibrium equations to ensure that the stress distribution satisfies the static equilibrium condition; Based on the theory of plastic flow, considering the changes in the friction angle and cohesion of the surrounding rock, the plastic strain is calculated; Calculate the displacement of the plastic zone by combining elastic strain and plastic strain; When the plastic shear strain of the calculation node exceeds the residual strength of the surrounding rock, a linear weakening function is used to describe the mechanical behavior of the surrounding rock.

8. The method according to claim 1, characterized in that, For the first stage, the stress and strain characteristics of the surrounding rock are solved based on the mechanical parameters of the surrounding rock corresponding to the natural water content.

9. A computer system comprising a memory, a processor, and a computer program stored in the memory, characterized in that, The processor executes the computer program to implement the steps of the method according to any one of claims 1 to 7.

10. A computer-readable storage medium having a computer program / instructions stored thereon, characterized in that, When the computer program / instructions are executed by the processor, they implement the steps of the method described in any one of claims 1 to 7.

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