As underground engineering construction shifts from shallow to deep, rock bursts occur frequently. A large amount of strain energy is stored in deep rock masses, tunnel excavation unloading rapidly releases the strain energy, driving the dynamic fracture of rock masses. Meanwhile, structural planes also have a significant impact on the failure of rock masses. To clarify the disaster mechanism of rock burst in deep tunnels, it is imperative to investigate the combined effects of excavation unloading and structural planes. Firstly, the element partition method (EPM) is improved to model the structural plane with fillers by introducing the Mohr-Coulomb strength criterion. Then, the improved EPM is combined with Stillinger-Weber potential based discrete virtual internal bond model to investigate the rock burst. By simulating two engineering cases of rock bursts near structural planes, the effectiveness of the numerical method was verified. A tunnel excavation model with a single structural plane is generated to invetigate the influences of the structural plane, such as the inclination angle, length, and location, on rock bursts systematically. In addition, the influences of the lateral pressure coefficient and the elastic modulus of surrounding rock on rock bursts are also investigated. The simulated findings show that structural planes can preserve the surrounding rock below the structural plane while inflicting significant damage to the rock above it. As the inclination angle of the structural plane increases, the rock burst failure intensity first increases and then decreases. When the inclination angle of the structural plane is 60 degrees, the rock burst is most severe. When the structural plane is longer or it is closer to the tunnel, it has a more significant impact on the failure of surrounding rock, and the rock burst is more violent. When the lateral pressure coefficient is higher or the elastic modulus of the surrounding rock is lower, more strain energy is stored in the surrounding rock and causes a more violent rock burst. Based on the research results, the combined effect of excavation unloading and structural planes on rock bursts in deep tunnels is revealed, which helps to deepen the understanding of the disaster mechanism of rock burst in deep tunnels.

The macroscopic mechanical behavior of transversely isotropic rocks is primarily governed by the differential response and competitive interaction between two types of highly oriented internal microstructures (e.g., foliation planes and random matrix defects) under external loading. To characterize this multi-scale damage process, a new micro–macro damage constitutive model for transversely isotropic rocks is established based on wing-crack propagation theory. This model represents the foliation planes as meso-scale wing cracks with a preferred spatial orientation and the initial matrix defects as micro-scale wing cracks with random orientations, thereby providing a unified framework to describe the distribution, propagation, and interaction of these two crack sets. Crack interactions in the model are quantified through the introduction of crack space influence functions and fracture factor degradation functions. Using an incremental constitutive formulation and a return mapping algorithm, the model successfully reproduces the complete macroscopic stress–strain response of transversely isotropic rocks, including the compaction, elastoplastic hardening, peak, and post-peak softening stages. The model is validated with experimental data under various conditions and compared with existing models, demonstrating its improved capability in capturing strength and deformation anisotropy. Furthermore, the evolution of wing-crack lengths and crack opening displacements at both scales reveals that the model not only accurately describes macroscopic anisotropic behavior but also clearly elucidates the competitive propagation mechanisms between meso- and micro-scale cracks across different deformation stages. This provides a new perspective for understanding the progressive failure of transversely isotropic rocks.

Abstract The dynamic compression fracture of brittle rock under seepage pressure is a critical issue for deep underground engineering. It directly influences the stability and safety of the surrounding rock during blasting or seismic loading. However, research on the mechanisms of microcrack evolution under these coupled conditions is still lacking. The relationship between microcrack evolution and macroscopic mechanical properties also remains poorly understood. This study develops a micro–macrofracture model grounded in the wing microcrack propagation framework, integrating both mechanical and chemical interactions between free water and rock. Mechanically, it incorporates seepage pressure, dynamic Stefan force, and dynamic fracture toughness. Chemically, it accounts for the effects of saturated water on rock mechanical parameters. This model characterizes the total stress–strain constitutive behavior of brittle rock under varying seepage pressures during dynamic compression failure, encompassing both strain-hardening and strain-softening phases. This result is validated against experimental data. It accounts for the influence of seepage pressure on both the initial crack and the newly formed wing crack. The seepage pressure weakens the wedging force F W on the initial crack while enhancing the seepage tensile force F P on the wing crack, which constitutes the seepage pressure-driven crack growth mechanism. Furthermore, under the combined effects of dynamic loading and free water, the dynamic Stefan force F S and the dynamic fracture toughness K ICD serve as the mechanism for inhibiting crack growth. The combined influences of seepage pressure, confining pressure and initial crack characteristics on the dynamic mechanical behavior of brittle rock under seepage pressure are discussed.

To address the dynamic instability problem caused by the coupling of the true three-dimensional high in-situ stress and dynamic impact in deep underground engineering, this paper develops a micro-macro cross-scale mechanical model for brittle rock under combined true triaxial static and dynamic compressive loading. Based on a quasi-static microcrack mechanical model under true triaxial stress, the dynamic fracture toughness is introduced, and a toughening formula along with the applicability boundaries of the toughening effect is proposed. The rationality of the model is systematically verified by experiments. The boundary conditions for the transition from “compaction-toughening” to “damage-degradation” induced by axial pre-stress σ1pre are thoroughly investigated. Furthermore, the asymmetric regulatory function of true triaxial lateral confinement is analyzed, revealing the inhibitory effect of the intermediate principal stress σ2 on the shear slip of crack surfaces, as well as its synergistic mechanism with the minimum principal stress σ3 in regulating lateral dilatancy, elucidating the strength enhancement and anisotropic characteristics induced by σ2. Finally, the coupling laws of strain rate effects and complex stress states are summarized. The results provide a unified description of the non-linear dynamic response characteristics of deep rock under complex loading paths, offering theoretical support for dynamic stability evaluation and disaster prevention in deep tunnels subjected to high in-situ stress and strong dynamic disturbances.

During tunnel construction in weak strata, support structure failure is often encountered due to the rheological properties of the ground and the plastic behavior of the rock. Therefore, analytical approaches can be effectively employed to conduct failure analysis of tunnel support systems in such conditions. Therefore, this study proposes a viscoelastic-plastic analytical solution for composite lining tunnels considering excavation stress release and strata rheology. This method incorporates the virtual support pressure theory, classical Maxwell and Kelvin-Voigt creep models, and the Hoek-Brown yield criterion to describe stress release, rheological behavior, and plastic deformation of the surrounding rock. The effectiveness of the analytical method was validated through numerical simulation. The proposed analytical approach can accurately describe the dynamic evolution mechanism of the plastic zone during tunnel excavation in the construction phase, while also effectively analyzing the long-term mechanical behavior of the tunnel. Based on this, the influences of plastic zone parameters, support parameters, and creep parameters on the failure of the support structure were analyzed. The practical value of the method was demonstrated through its application in actual engineering projects. Finally, based on the analysis results, measures to prevent and mitigate support structure failure in weak strata were proposed. This study, proceeding from a theoretical perspective, provides a theoretical basis and guidance for the design and construction of tunnel engineering in weak strata.

The application of buffer layer provides an effective solution to the problem of secondary lining failure.Different buffer layer materials exhibit significant variations in mechanical properties,making it essential to establish a widely applicable theoretical model.For this purpose,this study firstly divides the nonlinear compressive stress-strain curve of buffer layer materials into n deformation stages,and the deformation characteristic of each stage is described by replacing with a straight line.Secondly,an interaction mechanical model between rheological surrounding rock and support considering the effect of the buffer layer is established.By using the deformation coordination in both the surrounding rock-buffer layer interface and the buffer layer-secondary lining interface during the whole interaction process,analytical solutions for tunnel displacement and contact pressures at different interfaces during various deformation stages of buffer layer materials are presented.Furthermore,the effectiveness of the proposed theoretical model is validated by comparison with previous studies and numerical results.Finally,a parametric analysis of the mechanical responses of tunnels with polyurethane and polyethylene foam buffer layers(with differing deformation characteristics)is carried out based on the theoretical model.The results show that the proposed model is applicable to different buffer layer materials.The division of deformation stages in buffer layer materials significantly impacts prediction outcomes.For polyurethane foam buffer layer,the prediction result of the secondary lining pressure without considering the deformation stage division is 35.2%higher than that under consideration,while for polyethylene foam buffer layer,the predicted value is even 96%higher than that considering the deformation stage division.For a given tunnel,the thickness of buffer layer has a reasonable range,with an optimal thickness of 25 cm for both polyurethane and polyethylene foam buffer layers under these conditions.Installing a buffer layer is more beneficial for tunnels subject to significant long-term deformation,as it effectively reduces secondary lining pressure and ensures long-term safety.

During tunnel construction in weak strata, the coupled effects of ground rheological behavior and stress release significantly influence both construction progress and safety. As a critical support measure in tunneling engineering, the time-dependent mechanical interaction between rock bolts and the surrounding rock under such complex conditions remains insufficiently understood. To elucidate the time-dependent interaction mechanism between rock bolts and surrounding rock under these challenging engineering conditions, this study develops an analytical solution for bolted tunnels that explicitly couples tunnel excavation-induced stress release and ground rheology. The rheological behavior of the ground is characterized using classical Maxwell and Kelvin-Voigt creep models, while the stress release effect is represented through the virtual support pressure method. A closed-form analytical solution is ultimately derived via integral transforms. The solution accounts for two types of rock bolts: end-anchored rock bolts and fully grouted rock bolts, which are distinguished by modifying the contact conditions at the boltrock interface. Numerical simulations verify the validity and engineering applicability of the proposed analytical method. Furthermore, parametric studies are conducted to examine the influence of bolt parameters and stress release parameters on surrounding rock deformation. The proposed analytical approach provides researchers and engineers with an improved theoretical understanding of the interaction between rock bolts and tunnel surrounding rock in weak strata.

In the design of deep soft rock tunnels, full consideration should be paid to preventing lining damage caused by time-dependent deformation of the surrounding rock throughout the entire life cycle. The composite yielding support system (deformable primary lining–buffer layer–secondary lining) has great potential in effectively ensuring the safety of tunnels during both construction and operation. In this study, a theoretical modelling attempt is conducted to predict the life-cycle mechanical responses of tunnels employing a composite yielding support system. In the established model describing the interaction between the time-dependent surrounding rock and composite yielding support system, the deformation process of both the deformable primary lining and buffer layer exhibits three-stage characteristics. The mathematical derivation is carried out in the unsupported stage, the deformable primary lining-supported stage, and the composite yielding support system-supported stage, respectively. Among them, the latter two stages are further subdivided into three stages. Analytical solutions for displacements and interface contact stresses in each stage are provided. The proposed solutions in this study can be reduced to the two simple cases provided in previous references. In addition, a numerical simulation is conducted on a tunnel using a composite yielding support system, and the consistency between the numerical simulation results and theoretical prediction results is verified. Finally, a detailed parametric investigation is performed based on the proposed analytical solutions. The supporting effects of different types of support systems are compared; the influences of several major parameters on the life-cycle safety of tunnels are determined, including important parameters of the compressible element, buffer layer, and surrounding rock. Some practical suggestions on the design of composite yielding support system are provided.

Large deformation of soft rock tunnels is an engineering and technical challenge that must be addressed to realize the ambition of becoming a leading nation in tunnel construction.However,the intricate relationship between rock deformation constraint/release,rock pressure and lining bearing capacity remains ambiguous,posing theoretical obstacles in selecting appropriate support types and determination of design parameters.To tackle this challenge,this study adopts theoretical analysis method to model and analyze the mechanism of large deformation of soft rock tunnels,attempting to establish a theoretical relationship among these factors.Firstly,theoretical formulations are presented to elucidate the relationship between rock pressure/lining bearing capacity and lining thickness,revealing the theoretical reason why,when the lining thickness is less than a certain critical value,increasing its thickness induces a greater rate of increase in surrounding rock pressure than in the bearing capacity of the lining.Secondly,the generalized Kelvin model is employed to characterize the time-dependent deformation of surrounding rock,and the deformation process of yielding lining is simplified into the deformation release stage and deformation control stage.A tunnel mechanical model describing the interaction between surrounding rock and yielding lining is established,and analytical solutions for tunnel/lining displacement and lining pressure at different deformation stages are provided.The above analytical solutions for yielding lining supported tunnels can further be degenerated to those under the strong support action.Moreover,the reliability and feasibility of the theoretical model established in this study are well verified by comparing with results in previous reference and by applying it in a practical project.Finally,based on the proposed analytical solutions,a comprehensive parametric investigation is conducted,including the deformation capacity of surrounding rock,thickness of strong support,tunnel yielding displacement,and yielding resistance.The results indicate that under some large deformation conditions,if strong support is used,the required lining thickness is excessively large,necessitating the adoption of yielding lining.There exist reasonable ranges for both the yielding displacement and yielding resistance of yielding lining,which should be determined considering the mechanical properties of surrounding rock and lining.The concise tunnel theoretical model provided in this study can play an important theoretical support for the rapid design in the preliminary stage of related projects.

The application of circumferential yielding lining proposes a good solution to the problem of overstress and failure of preliminary support in squeezing large deformation tunnels. Establishing a practical theoretical model to predict the mechanical response of tunnels using circumferential yielding lining can provide meaningful guidance for the initial design of support. This study suggests that the surrounding rock exhibits viscoelastic-plastic behaviour, and also shows plastic softening and residual characteristics after reaching a plastic state; the deformation process of circumferential yielding lining is divided into elastic, yielding and compaction stages, according to the mechanical properties of special elements. A simplified two-dimensional mechanical model is established to capture the interaction between the surrounding rock and circumferential yielding lining, taking into account the effects of tunnel face advancement and stress path. Based on the engineering reality (stress state of the surrounding rock at the time of lining installation), the interaction between the surrounding rock and lining is discussed in various cases; corresponding analytical solutions for the tunnel displacement and support pressure are proposed for each case. Furthermore, a numerical simulation is conducted using an actual tunnel, and a comprehensive comparison is performed between the theoretical prediction results, numerical simulation data, and monitored tunnel displacement. Finally, parametric sensitivity analysis is completed based on the proposed theoretical model, and the impacts of geological parameters and support parameters are discussed. By using this theoretical model, the design rationality of the circumferential yielding lining can be quickly evaluated and some design recommendations can be easily obtained.

The micro-structure of rock essentially affects its macroscopic mechanical behaviors. Based on the grain-based discretized virtual internal bond (GB-DVIB) model, an improved version of the model is developed to investigate the gain-scale, micro-cracking process. Compared with the original GB-DVIB model, a more realistic microstructure of granular rock is generated by the improved model. A micro-structure generation method is developed to generate different types of mineral grains, grain boundaries, and voids. Based on the relationship between macro-and micro-parameters in the DVIB model, the mechanical parameters of micro-structure obtained by experiments can be employed to calibrate the micro-bond parameters directly. The ability of the improved GB-DVIB model in modeling tensile and compression-shear failure is verified by the simulation of a three-point-bending test and an asymmetric compressive test, respectively. The detailed micro-cracking process of a granite sample is investigated by the simulation of uniaxial compression and tension tests, and the intra-granular and inter-granular cracks both can be reproduced. The simulated results show that the micro-cracks generated in the uniaxial compression test are much larger than the uniaxial tension test. The intra-granular and inter-granular cracks both play important roles in rock compression failure, while the inter-granular cracks play a dominant role in rock tensile failure. For the convenience of the application of the improved GB-DVIB model, the effect of mechanical parameters of micro-structure, grain size, geometric heterogeneity, and porosity on the rock macroscopic mechanical behavior is systematically investigated. Due to the different mechanisms of tension and shear failure, the influence of micro-structure on rock compression and tension failure also varies. The improved GB-DVIB model can effectively generate the micro-structure of granular rock and provides a convenient and effective tool for researching the gain-scale, micro-cracking process of granular rock.

The combined supporting system of rockbolts and linings is one of the most common methods for controlling the deformation of surrounding rock in tunnels. However, current theoretical analyses typically consider the deformation control effect of only one support type. Consequently, the bearing capacity of rockbolts or linings is not fully utilized as their combined effect is not considered. Thus, this study analyzes the mechanical responses of a "rockbolts + lining" combined supporting system for large deformation tunnels. For theoretical derivation, a viscoelastic-viscoplastic constitutive model is employed to describe the time-dependent behavior of surrounding rock. To satisfy the actual deformation development law, the effect of the stress path in the plastic zone of the surrounding rock is considered. An analytical solution is provided for predicting the tunnel behavior, where the installation time of the rockbolts and lining is considered sufficiently. Furthermore, the proposed analytical solution can be reduced to a viscoelastic solution and is well applied in a tunnel project. The superiority of the proposed solution is demonstrated by comparing it with previous solutions. Finally, a comprehensive parametric investigation is conducted, which considers the cohesion and internal friction angle of rock, the linear stiffness coefficient and installation time of rockbolts, and the stiffness and installation time of the lining. The results show that the cohesion and internal friction angle of the rock dominate the plastic deformation of the surrounding rock, thus further affecting tunnel deformation. The installation of rockbolts and lining can effectively restrict the deformation of the surrounding rock. Generally, better deformation control can be achieved by installing rock- bolts (lining) earlier or by improving the stiffness of the rockbolts (lining). However, the stiffness of the rockbolts (lining) is limited to a certain range, in which significant deformation control can be achieved. After determining the installation time of the rockbolts and lining based on the actual construction level, the reasonable design parameters of the rockbolts and lining can be determined using the proposed solution such that their bearing capacities can be fully utilized in this combined supporting system.

Ultra-high performance concrete (UHPC) has gained increasing attention in structural engineering because of its superior material properties. However, the shear failure of UHPC beams remains insufficiently understood, limiting the development of reliable design methods. This study investigates the shear failure mechanisms of UHPC beams and develops a refined theoretical method to predict their shear strength. Ten UHPC specimens were tested under varying parameters, including stirrup ratio, main reinforcement ratio, shear-span ratio, and steel fiber dosage. The experimental findings showed that augmenting fiber content meaningfully enhanced the shear strength and crack resistance of specimens. Specifically, higher fiber content reduced crack width, raised the number of cracks, and delayed the formation of a critical diagonal crack, leading to improved ductility and shear resistance. Additionally, a growth in the shear-span ratio yielded a drop in shear strength, while simultaneously enhancing the deformability. A higher stirrup ratio enhanced post-cracking strength and limited crack development. According to the test data and a thorough analysis of shear failure mechanisms, a mechanical method incorporating four primary contributors-fiber bridging-effect across critical shear crack, dowel action of longitudinal reinforcements, shear-compression zone concrete, and stirrups-was proposed. The effectiveness of the proposed method was demonstrated by its excellent agreement with test data from 144 UHPC specimens, achieving a mean prediction ratio of 0.96 with a coefficient of variation of 0.17, which significantly outperformed five commonly-used shear equations and provided valuable insights into the shear failure analysis of UHPC beams.

The application of yielding layer provides a potential good solution to the problem of large deformation in deep soft rock tunnels. Previous researches on analysis models of tunnels incorporating yielding layer have certain limitations, as one model is only applicable to one type of yielding layer material. The purpose of this work is to establish a unified analysis model of tunnels considering the yielding layer effect in order to address the limitations of existing models. Firstly, the nonlinear stress-strain curve of yielding layer materials is partitioned and multiple straight line segments are employed to approximate the original curve. A mathematical expression for elastic moduli is provided to uniformly describe the deformation characteristics of different yielding layer materials. Secondly, the tunnel construction process is divided into three stages and a viscoelastic mechanical model of tunnels considering the yielding layer effect is established. Based on stress boundary and displacement continuity conditions, analytical solutions for tunnel displacement and interface contact stresses during different deformation stage are provided. The proposed model can be used to predict the mechanical performance of tunnels incorporating yielding layer materials with arbitrary compressive characteristics, and can degrade to some simpler tunnel cases. Furthermore, the reliability of this mechanical model is verified by comparing with the numerical calculation results. Finally, a comprehensive parametric investigation is carried out based on the analytical solutions. The analysis results indicate that the tunnel supporting effect is significantly affected by the mechanical properties of yielding layer materials, the yielding layer thickness and the deformation capacity of surrounding rock.

To address the limitations of traditional steel or wooden formworks, such as complex procedures, low turnover rates, and resource waste, a novel type of permanent formwork made from steel-PP hybrid fiber reinforced cementitious composites (SPFRCC) was developed to replace the conventional formworks in construction. Fourpoint bending tests were conducted on four composite beams with SPFRCC permanent formwork and two ordinary reinforced concrete (RC) beams. The variables studied in the specimens were main reinforcement ratio and cover thickness, with a focus on the flexural properties of specimens and the slippage or delamination at the interface between the post-cast concrete and the SPFRCC formwork. The results showed that there was no slippage at the SPFRCC-concrete interface from the beginning of loading to the peak load. As the component failed, slight slippage was observed at the SPFRCC-concrete interface. And the interfacial slippage of the composite specimens with a cover thickness of 10 mm appeared earlier compared to the composite specimens with a cover thickness of 20 mm. The yield and peak load of the composite beams increased by approximately 10 %, while the cracking load was about 50 % higher than that of ordinary RC beams. Due to the enhancement contributed by the hybrid fibers after the SPFRCC formwork cracked, the flexural stiffness of the composite specimens was significantly enhanced, exceeding that of the RC beam after cracking by over 21 %. Additionally, a theoretical method for flexural strength of composite beams was established based on the material constitutive relationships and the plane section assumption. A deflection calculation method at serviceability limit state was proposed, utilizing the equivalent homogeneous material transformed section. The test results were found to closely match the calculated data derived from the developed theoretical methods.

"Radial-circumferential" combined yielding supports can tolerate extremely large deformations of the surrounding rock without being damaged. However, to date, the coordinated deformation mechanism of combined yielding supports remains unclear, and a well-established design model is still unavailable. This study analyzed the mechanical responses of tunnels with combined yielding supports using a mathematical analytical method. First, the mechanical characteristics of the compressible layer and primary lining with highly deformable elements were introduced, and their deformation processes were divided into three stages in the analytical model. Second, the deformation modes of the combined yielding supports were proposed, and their mechanical responses were classified into three cases. A mechanical model of the interaction between the surrounding rock and combined yielding supports was established. In the proposed analytical model, the rock geomaterial exhibited viscoelastic behaviour, and the effects of tunnel face advancement and support installation delay were considered. An analytical solution corresponding to each deformation mode of the combined yielding supports was provided to predict the rock displacement and interface contact stresses. Furthermore, numerical modelling was conducted for comparison with the analytically predicted results, indicating the reliability and feasibility of the proposed analytical model. Finally, a quick and convenient parametric investigation was performed to determine the sensitivity of the model output results to three design parameters: the yielding lengths of both the compressible layer and primary lining, and the yielding stress of the compressible layer. The analysis revealed that within a certain range, the tunnel displacement and interface contact stresses were highly sensitive to these three parameters. Below or beyond this range, changes in these parameters did not significantly affect the output results of the model. Based on the results of the parametric analysis, several design insights into the combined yielding supports were obtained.

Mode I fracture represents a prevalent failure mechanism in rocks, attributed to the typically significantly lower tensile strength compared to their shear strength. The cracked chevron notched Brazilian disc (CCNBD) and semi-circular bend (SCB) tests are two techniques recommended by the International Society for Rock Mechanics (ISRM) for assessing mode I fracture toughness and are commonly employed in laboratory research. The fracture toughness of a rock specimen depends on its geometric dimensions and mechanical properties. Clarifying the geometric size impacts of various types of rocks in mode I fracture toughness testing is both costly and time-consuming. Machine learning offers a predictive approach for determining the fracture toughness of rocks. This investigation leverages six sophisticated machine learning models, encompassing decision regression tree (DRT), random regression forest (RRF), generalized regression neural network (GRNN), gaussian process regression (GPR), support vector machine (SVM) and generalized additive model (GAM), to forecast the mode I fracture toughness within the CCNBD and SCB testing paradigms. The variance in input variables between the two tests is attributed to the distinct geometrical attributes of the CCNBD and SCB specimens. Tensile strength, specimen radius, specimen thickness and three dimensionless parameters related to the initial and final cracked chevron notch lengths and specimen thickness are the input variables for CCNBD tests. Tensile strength, specimen radius, specimen thickness, notch length and the span of the two loading cylindrical rollers are input variables for SCB tests. Five evaluation indicators of machine learning models, i.e., mean absolute error, mean absolute percentage error, mean square error, root mean square error and coefficient of determination, are adopted to comprehensively evaluate the predictive performance of these models. According to the evaluative metrics, the DRT and GPR models emerge as the most effective for CCNBD and SCB tests, respectively. The significance of input variables for the prediction of mode I fracture toughness was delineated employing Shapley additive explanations. The findings underscore the paramount influence of tensile strength on mode I fracture toughness within both CCNBD and SCB testing methodologies. Considering the influences of sample value differences in CCNBD and SCB datasets and taking mean absolute percentage error and coefficient of determination as the evaluation indicators, the machine learning models are more suitable in predicting mode I fracture toughness in CCNBD tests than that in SCB tests. This study delivers valuable insights for the prediction of mode I fracture toughness in rocks via machine learning techniques.

Soft rocks present some undesirable behaviors, such as low strength, high plasticity and softening. These traits pose challenges in the design and construction of soft rock tunnels. To address these issues and model plastic fracture behaviors of soft rocks, we proposed a plastic Stillinger-Weber (PSW) potential and integrated it into the discretized virtual internal bond (DVIB) model. The PSW-DVIB model combines the strengths of the plastic DVIB and the SW-DVIB models. It not only effectively reproduces the plastic fracture behavior but also accurately reflects the Poisson’s ratio. Moreover, due to the inclusion of fracture energy in the PSW potential, the simulation results are basically mesh size independent. The PSW-DVIB model is then utilized to investigate the failure behaviors of soft rock tunnels. The effects of the coefficient of lateral pressure, in-situ stress, Poisson’s ratio and tunnel shape on tunnel failure are investigated. The simulated results indicate that the coefficient of lateral pressure has significant influence on the failure zone distribution of the surrounding rock. With the coefficient of lateral pressure increasing, the failure degree of surrounding rock decreases firstly and then increases. The optimum coefficients of lateral pressure for the stability of circular, arched and square tunnels are about 1.00, 0.75 and 0.75, respectively. When the in-situ stress or Poisson’s ratio is larger, the influence of the coefficient of lateral pressure on tunnel failure is more obvious. The influence of the coefficient of lateral pressure on square tunnels are more significant than the arched tunnels, and then the circular tunnels. These findings provide valuable insights for the design and construction of soft rock tunnels.

The application of compressible layers is considered to be the most promising solution for solving the problem of large deformations in deep soft-rock tunnels. However, although significant effort has been devoted to understanding its mechanical working, the effect of the compressible layer has not been completely revealed. This study theoretically predicts the mechanical response of a deep soft-rock large deformation tunnel by applying a compressible layer. The theoretical model involves a circular tunnel, which is supported by a compressible layer and concrete lining, and subjected to a non-hydrostatic stress field. The influence of the tunnel face advancement is described by the stress release coefficient, and the three-stage deformation characteristics (elastic-yielding-compaction) of the compressible layer material are considered in this model. The entire tunnel deformation process is divided into unlined and lined (further subdivided into elastic, yielding, and compaction phases of the compressible layer material) phases. A series of complex potential functions in different media (rock, compressible layer, and concrete lining) and at different phases is provided; subsequently, the unknown coefficients in these functions are determined using the stress balance and displacement continuity conditions at different in-terfaces. Thus, the analytical solutions for tunnel displacement and support pressure at different phases are obtained. Good agreement between the numerical and analytical results is observed after performing the numerical simulation to validate the reliability and feasibility of the pro-posed analytical derivation. Finally, a parametric sensitivity investigation is conducted by including the yielding stress of the filling material, yielding length of the compressible layer, and installation time of the support. Adequate attention is paid to the tunnel displacement and sup-port pressure on the 100th day and their development laws at the positions of theta = 90 degrees, 45 degrees, and 0 degrees during the first 100 days. Some interesting findings are presented, and useful design suggestions for the compressible layer are provided.