Strain-softening Rock Mass Research Articles

Modified ground response curve (GRC) in strain-softening rock mass based on the generalized Zhang-Zhu strength criterion considering over-excavation

The ground response curve (GRC) depicts the relationship between support reaction force and ground displacement, which improves the understanding of ground-support interaction and provides important references to the tunnel design. However, it is difficult to anticipate the tunneling-induced large deformation with sufficient reliability in soft rock with high geostress since the small strain theory is not applicable. When large deformation occurs, the tunnel needs to be over-excavated. Thus, the GRC should be modified considering the enlarged excavation radius since the actual excavation radius is usually greater than the designed one. To overcome the shortcomings of small strain theory in recognizing ground-support interaction under large deformation circumstances, a new large strain numerical approach for modifying the GRC was proposed considering over-excavation in strain-softening rock masses based on the generalized Zhang-Zhu strength criterion. A case study was conducted based on the Lianchengshan tunnel in China. The modified GRC was employed to investigate the ground-support behavior for different support schemes and to explore the applicability of the stress release measures. Combined with field tests, the proposed approach was validated. By comparing with GRCs proposed by previous work, the present modified GRC was proved to be superior to others. Parametric studies were conducted and it is found that over-excavation, for example, reserving a very large clearance between the surrounding rock and the support, is necessary to reduce ground pressure to a large extent. The yielding supports which can provide high support pressure during the process of deformation are highly recommended when tunneling in high geostress environment. However, if the initial geostress is not very high, it is not necessary to pursue unwarranted over-excavation since the ground pressure applied on the support is mainly the loosening stress when the deformation is large. Ample support stiffness should be provided in the process of deformation to prevent uncontrolled large deformation of surrounding rock.

A new large strain approach for predicting tunnel deformation in strain-softening rock mass based on the generalized Zhang-Zhu strength criterion

The deformation capacity of tunnel will be overestimated by small strain theory especially in high geostress and heavily squeezing rocks, the calculated wall convergence of tunnel may even exceed the excavated radius. Based on the Generalized Zhang-Zhu (GZZ) strength criterion, a new large strain solution for tunnel excavated in strain-softening rocks under high geostress is proposed by a semi-analytical approach. During calculation, the material nodes in the plastic zone of surrounding rock are generated automatically in each unloading step. The locations of these nodes are updated after each step and the governing equations are established on the updated state. The proposed procedure allows one to predict the rock stresses, strains, and deformations in a rational and rigorous manner, and it is validated by numerical simulation. Results show that the ground displacement calculated by proposed approach is in good agreement with that obtained by GeoFBA3D, which indicates that the proposed approach is capable in predicting the large deformation of surrounding rock. As long as the unloading radial pressure of each step δp is sufficient small, i.e., the number of material nodes in the plastic zone exceeds 40, the computational error can be neglected. Compared to HB strength criterion, the GZZ criterion can take into account the intermediate principal stress, which is beneficial to tunnel stability. The applicable conditions for large strain theory and small strain theory are given by parametric studies. Parametric studies show that the calculation error produced by small strain theory can reach 30% when the deformation of surrounding rock exceeds about 10%R0, therefore, a large strain theory is necessary for calculation.

A finite strain solution for strain-softening rock mass around circular roadways

This paper presents a semi-analytical finite strain solution for circular roadways excavated in a strain-softening rock mass with a non-associated flow rule. The evolutions of both strength parameters and Young’s modulus are considered, and the finite strains are applied to describe both the elastic and plastic behaviors with the logarithmic strain in Lagrangian coordinates. By transforming the derivative of displacement with a new variable that is correlated with displacement, the stress and displacement in the elastic region are obtained in the form of integral equations. Considering the assumption of constant material parameters within a very small region, the plastic region is divided into a number of concentric annuli, whose closed-form solutions of displacement and stress can be recursively obtained. The solution is validated by similarity solutions and numerical simulation. Both the roadway wall displacement and thickness of the plastic (residual) region appear to be smaller than those of the small strain solution. For the elasto-perfectly-plastic rock mass, the finite strain solution is approximately the same as that of small strain solution. However, for the strain-softening rock mass, with the decrease of Young’s modulus, the thickness of plastic and residual regions shows the first increase and then decrease trend, finally approaching nil; the difference between the thickness of softening and residual region gradually decreases. The decreasing Young’s modulus deterioration coefficient and increasing dilation angle significantly produce the displacement. Both the displacement and the thickness of plastic and residual regions decrease with the increase of Poisson’s ratio. When Young’s modulus is large, the tangential stress gradually decreases with the increasing radius. When Young’s modulus is small, the tangential stress firstly increases to a maximum value, then decreases gradually. Different from the small strain solutions, the roadway wall displacement of finite strain solutions cannot be larger than the excavation radius, which is in compliance with the practical underground engineering condition. The predicted displacement and thickness in both plastic and residual regions are in accordance with the field test results.

Assessment of damage zone thickness and wall convergence for tunnels excavated in strain-softening rock masses

There are two fundamental issues in all underground excavations, which are safety and economy. To ensure safety and expedite excavations, level of tunnel wall convergences and damage zone thickness should be predicted before the excavation starts, should be determined accurately, and monitored during the excavation by the tunnel designer. However, accurate prediction of these two parameters is difficult unless in-situ stress and deformation measurement tools are used. In this study, damage zone thickness and tunnel wall convergence relation was investigated for horseshoe-shaped highway tunnels by using empirical methods. For this aim two-dimensional plane strain finite element models were used. Totally 9 tunnel sections were selected for the empirical analysis from 5 different ongoing tunnel excavations, which are excavated in weak and fair quality rock masses and show strain softening post-failure behavior. With the help of data gathered through in-situ convergence measurements and predicted convergences and rock mass geotechnical properties an empirical analysis was conducted. Engineering characteristics of the tunnel routes were determined by means of geological mapping, drillings and laboratory studies. Tunnel wall convergences were measured by optical measurement devices in three-dimensional space. Then, numerical models have been created for each of the tunnel sections studied. For evaluation of damaged zone thickness; yielded elements, volumetric strain, and principal stress concentrations have been used. Damage zone thickness and convergences were estimated from the numerical models and the whole data were compared with the real convergence results. Findings have been compared with previous researchers’ convergence predictions and plastic zone calculation approaches. The results are in agreement both with the field measurements and previous empirical approaches. In this way, an empirical relation has been obtained for tunnel wall convergences and damage zone thicknesses. Besides, through an analysis of the relations of convergences at each query points in plane strain finite element model, a new empirical relation has also been put forth that gives “Convergence Constant” for modelled cross-section. This constant can be used as an auxiliary tool for prediction of next section convergences, on the condition that excavation has similar geological, geotechnical properties and topography.

Numerical solutions for tunnels excavated in strain-softening rock masses considering a combined support system

In this article, an alternative numerical procedure to calculate displacements and stresses of supported circular tunnels is proposed, considering the whole process of tunnel advancement, and sequential installation of the primary and secondary support systems. In the derivation, the plastic area of the rock mass is divided into a large number of annuli around the tunnel, and then the Finite Difference Method is employed. First, the strain-softening behaviour model is taken to simulate the post-failure behaviour of the rock mass. Furthermore, the Mohr-Coulomb or the Hoek-Brown failure criteria can be chosen, a non-associated plastic flow rule is assumed and the dilatancy of the rock mass is considered. After that, the fictitious support forces concept is used to simulate the process of tunnel advancement, and thus, the three-dimensional effect of the tunnel face is considered. Finally, the solutions of displacements and stresses for the rock mass and the supports can be obtained, by using the compatibility conditions of stresses and displacements at both rock-support and support-support interfaces. The results obtained from these solutions agree well with those of the self-similar solutions for circular openings, and the compatibility conditions of supported tunnels were verified. The proposed method has been compared with the convergence-confinement method. Parametric analyses are then carried out to investigate the sensitivity of support forces and displacements to the rock mass behaviour model selection. Then, the application of the proposed solutions in the design of tunnels is presented. The proposed method provides a convenient alternative method for the preliminary design of tunnels.

A simple numerical procedure for the elasto-plastic coupling finite strain analysis of circular tunnels in strain-softening rock masses

This paper presents a numerical finite strain solution for a circular tunnel in Mohr-Coulomb and generalized Hoek-Brown strain-softening rock masses. By approximating the differential equations with a difference method in the deformed coordinates, an efficient procedure is presented to calculate the displacements and stresses. The proposed solution is verified by another numerical method for both elasto-brittle-plastic and strain-softening finite strain examples. The parametric analysis indicates that (1) with the decrease in Young’s modulus of the residual region, the displacement increases, and the thickness of the softening region decreases. The displacement and the thickness of the softening and residual regions remain relatively stable when the deterioration coefficient of Young’s modulus is less than 0.01. (2) The displacement and the thickness of the softening and residual regions decrease with the increasing Poisson’s ratio, and increase with the increasing parameter α for the generalized Hoek-Brown rock mass. (3) With the increase in the in-situ stress, the dimensionless displacement of the tunnel wall increases and tends to 1.0, and the thicknesses of plastic and residual region first increase to their maximum values and then decrease. The finite strain solution is necessary for the displacement prediction and supporting design, rather than the small strain solution.

A new semi-numerical method for elastoplastic analysis of a circular tunnel excavated in a Hoek–Brown strain-softening rock mass considering the blast-induced damaged zone

Abstract Drill and blast method is mostly used method for excavation of tunnels throughout the world. This tunneling method involves the use of explosives. Compared with bored tunneling by Tunnel Boring Machine, blasting generally results in the development of a blast-induced damaged zone around the tunnel boundary. Theoretically, the presence of this zone, with its reduced strength and stiffness, will affect the overall performance of the tunnel, as well as its construction and maintenance. In fact, the extent of the damaged zone is finite. However, the effect of this zone is traditionally considered by a damage factor D applied to the entire rock mass surrounding the tunnel. This is a common modeling method which can greatly underestimate the strength and stability of the overall rock mass. In this paper, a semi-analytical solution is proposed for analysis of tunnels considering the damaged zone. The solution is presented for circular tunnels excavated in rock masses obeying a new proposed non-linear strain-softening behavior and the non- linear Hoek–Brown failure criterion. The damaged zone is assumed to have a cylindrical shape with reduced strength and deformability parameters.

Two-stage analysis of interaction between strain-softening rock mass and liner for circular tunnels considering delayed installation of liner

A two-stage analysis of the support-rock interaction is carried out using a proposed numerical procedure. The procedure provides a simplified solution for readily obtaining the final support load and rock mass displacement that is easier to use than the conventional Convergence-Confinement Method (CCM). The procedure accounts for the strain-softening behaviour of the rock mass and the effect of delayed support installation. Based on the procedure, a method to determine the delayed distance and allowable displacement for the support installation is presented. A Modified Ground Reaction Curve (MGRC) that relates the rock mass displacement to the final support load is introduced. The effects of the rock mass quality, initial stress, support type and strain-softening, dilatancy behaviours on the delayed distance and allowable displacement are investigated. A comparison between the predictions of the MGRC and GRC is conducted. The results indicate that the influence of the rock mass quality and initial stress on the support-rock interaction is more significant than that of the strain-softening and dilatancy behaviours. An approximate support design using the GRC may be acceptable for a weak rock mass, whereas the GRC results in an overly conservative support design for an excellent rock mass.

A numerical solution of a circular tunnel in a confining pressure-dependent strain-softening rock mass

Abstract This paper presents a numerical solution for a circular tunnel excavated in a confining pressure-dependent strain-softening rock mass with linear Mohr-Coulomb (MC) and nonlinear generalized Hoek-Brown (HB) yield criteria to calculate the main geomechanical parameters, i.e., radii of plastic and residual regions, distributions of stresses and displacement. The surrounding rock is first divided into a number of thin concentric annuli with constant material parameters. The material parameters are determined by the radial stress and the plastic shear strain at the outer radius of each annulus. The equilibrium differential equation is approximated using a difference scheme to obtain the dimensionless radius of each annulus corresponding to the prior given radial stress. A simple numerical stepwise procedure is presented to recursively calculate the radius of each annulus. For elastic rock masses, a confining pressure-dependent Young’s modulus leads to that the tangent stress first increases to a maximum value and then gradually decreases. The maximum concentration factor, whose position lies inside the surrounding rock, is smaller than 2.0. For the generalized confining pressure-dependent strain-softening rock mass, about 20% increase in parameter α induces 169.14%, 56.14% and 74.31% increase in softening radius, residual radius and displacement compared to that of α = 0.5.

A fully coupled hydraulic-mechanical solution of a circular tunnel in strain-softening rock masses

This paper presents a fully coupled hydraulic-mechanical strain-softening model considering Biot’s effective stress. Both the hydraulic and mechanical parameters are considered as functions of the confining pressure and plastic shear strain. Using the proposed fully coupled hydraulic-mechanical model, the displacement, stress and pore-water pressure around a circular tunnel in both Mohr-Coulomb and Hoek-Brown strain-softening rock masses are derived using a non-associated flow rule. The proposed solutions are validated by the conventional hydraulic-mechanical elasto-brittle-plastic and strain softening rock mass using analytical and numerical methods, and the examples of the fully coupled hydraulic-mechanical strain-softening rock mass are investigated. The results show that the seepage force enlarges the displacement, residual and plastic radii. With the increase in the initial pore-water pressure, the displacement, water inflow, residual and plastic radii increase in an approximately linear manner. The increasing bulk modulus of the solid constituent increases the above four variables, which reach the approximate limit values, corresponding to the Darcy’s effective stress solutions, when Ks = 10 K0. The increasing permeability of the plastic rock mass reduces the increasing rate of the pore-water pressure but increases the water inflow. For the proposed fully coupled examples, both the hydraulic parameters of permeability and Biot’s coefficient show a non-linear decrease with the increasing radius.

Re-profiling of a squeezing tunnel considering the post-peak behavior of rock mass

In problems involving large deformation, one of main concerns in rock engineering is the occurrence of a heavily reduction in tunnel section and even shield jamming. In this paper, a rigorous theoretical model is established to characterize the process of tunnel re-profiling works in heavily squeezing ground to re-construct the desired profile, based on the finite strain approach and Lagrangian material description. The post-peak behavior of rock mass and elasto-plastic strains in plastic zone during each excavation process are taken into account. Therefore, the proposed method enables to quantify the repetitive disturbances to a plastified surrounding rock and accumulated degradation of material properties. A numerical procedure is presented, in which the history-dependent behavior and path of material point in strain-softening rock mass during the entire excavation process are determined via our previous work, in combination with incremental algorithm and spatial interpolation. The discrepancy from the accurate solution induced by the negligence of elastic strains in all plastic zones is investigated by comparing the present results with the existing study. An extensive computations are then carried out to clarify some practical questions, including the effects of post-peak behavior, ground condition and old temporary support on the repetitive re-profiling, the variation of rock pressure developing on a rigid support after excavation, and the required minimum over-excavation size to achieve the desired profile. Also the effectiveness of advancing a pilot tunnel is investigated under different post-peak and geometrical conditions, in order to illustrate the applicability of the construction method in squeezing ground.

Simple approach for solution of the quasi-plane-strain problem in a circular tunnel in a strain-softening rock mass considering the out-of-plane stress effect

The out-of-plane stress is sometimes the major or intermediate principal stress in a circular tunnel opening. The influences of the out-of-plane stress and axial strain are often neglected in the stability analyses of tunnel excavation, which can induce significant errors in the determination of surrounding rock deformations. In this paper, the use of a simple approach is proposed to solve the quasi-plane-strain problem of circular tunneling considering the effect of the out-of-plane stress, which is deformation-dependent and influenced by the in situ stress. As the intermediate principal stress is deformation-dependent, to obtain the numerical solution of the intermediate principal stress, the quasi-plane-strain problem is defined based on assumptions that the initial axial total strain is a nonzero constant (ε0) and that the axial plastic strain is nonzero. With the numerical solution for the plastic strain, obtained using the plastic potential functions based on the three-dimensional failure criteria, the formula for the intermediate principal stress can be derived using Hooke’s law. The proposed approach can be utilized to obtain the numerical solution for the intermediate principal stress, which is deformation-dependent, and the numerical results can be simplified as the solution presented by Pan and Brown. The proposed approach can also be used to obtain the solution for the strain softening of the surrounding rock. To verify its validity and accuracy, the results obtained using the proposed approach are compared with the solution of Pan and Brown. In addition, parametric studies are performed to address the influences of the out-of-plane stress on the stress and displacement in the circular tunnel.

A numerical large strain solution for circular tunnels excavated in strain-softening rock masses

This paper presents a large strain numerical solution of a circular tunnel for the ground reaction curve (GRC) in strain-softening rock masses. Both the stress equilibrium equation and deformation compatibility equation are considered in a current coordinate. A series of examples are employed to validate the proposed solutions, and the results show that: (1) the displacement, softening and residual radii of larger strain solution are smaller than that of small strain solution, and their difference significantly increases with a decrease in the Young’s modulus. (2) the increasing Poisson’s ration and critical shear plastic strain decrease the displacement, softening and residual radii.

Ground response curve of deep circular tunnel in rock mass exhibiting Hoek–Brown strain-softening behaviour considering the dead weight loading

In definition of the ground response curve for a tunnel, convergences of side wall, roof and floor may be different, because of the weight of the failed or plastic rock mass. In this paper, an analytical-numerical solution of the ground response curve for a tunnel excavated in an elastoplastic strain-softening rock mass considering the gravitational loading. In the proposed method, Hoek–Brown yield criterion and Mohr-Coulomb plastic potential function are used for the ground medium. The gravity loading is considered as a radial body force being applied to the ground medium. Two flexible and inflexible lining theories are introduced for the analysis of concrete lining. The derived differential equations cannot be integrated analytically; thus, they are solved by invoking finite difference approximations. Several illustrative examples are given to demonstrate the performance of the proposed method and to examine the effects of the gravity loading. The results obtained by the proposed method show that the gravity loads may affect the tunnel convergence, especially when the plastic region is wide.

Regression model for predicting tunnel strain in strain-softening rock mass for underground openings

Regression analysis method has been extensively used to predict tunnel during excavations. This paper applies the method to solve for the tunnel strain for a circular opening in a strain-softening rock mass. Support pressure, in-situ stress and geological strength index (GSI) are three important geological parameters that are simultaneously considered in evaluating tunnel strain. A numerical procedure of the strain-softening rock mass is incorporated to solve for tunnel strain with a series of GSI, in-situ stress and support pressure. A detailed result of the tunnel strain is solved using the repeated numerical procedures. A nonlinear regression model for predicting tunnel strain is obtained through analysing the result with the regression method. Twelve fitting equations are considered in the regression model, correlating the tunnel strain with the support pressure, GSI, initial stress and critical softening parameters. The analysis framework is validated by comparing the calculated tunnel strain to that predicted by existing studies. The influence of the critical softening parameter on tunnel strain and the radius of the plastic zone are investigated. The response surfaces of tunnel strain versus the initial stress and support pressures for different rock mass qualities with various softening behaviours are also analysed. Then a guidance of the support design is derived based on the regression model and is demonstrated in an actual tunnel case with field measurements.

A numerical stepwise approach for cavity expansion problem in strain-softening rock or soil mass

A numerical stepwise approach for cavity expansion problem in strain-softening rock or soil mass is investigated, which is compatible with Mohr–Coulomb and generalized Hoek-Brown failure criteria. Based on finite difference method, plastic region is divided into a finite number of concentric rings whose thicknesses are determined internally to satisfy the equilibrium and compatibility equations, the material parameters of the rock or soil mass are assumed to be the same in each ring. For the strain-softening behavior, the strength parameters are assumed to be a linear function of deviatoric plastic strain (yp*) for each ring. Increments of stress and strain for each ring are calculated with the finite difference method. Assumptions of large-strain for soil mass and small-strain for rock mass are adopted, respectively. A new numerical stepwise approach for limited pressure and plastic radius are obtained. Comparisons are conducted to validate the correctness of the proposed approach with Vesic\'s solution (1972). The results show that the perfectly elasto-plastic model may underestimate the displacement and stresses in cavity expansion than strain-softening coefficient considered. The results of limit expansion pressure based on the generalised H-B failure criterion are less than those obtained based on the M-C failure criterion.

A finite strain numerical procedure for a circular tunnel in strain-softening rock mass with large deformation

The reliable prediction of excavation responses for squeezing rock remains a challenging issue in rock engineering. This paper presents a numerical procedure for a strain-softening rock mass around highly deformed circular opening based on the finite strain theory, so the overall elasto-plastic analysis is a Lagrangian method which focuses on the motion of each material point and is well suited for the problems involving large deformation. The influence of axial in-situ stress is considered by introducing the initial axial stress into the elastic constitutive equations, and the axial plastic flow is realized by redefining the plastic internal variable and considering different stress distributions in the plastic zone. Thus, the numerical procedure enables prediction of the rock deformation and squeezing potential in a more rational and rigorous manner. The capability of the method for estimating the small strain and squeezing deformation is verified by being compared with the existing analytical results and the field measuring data. Negligence of the axial in-situ stress or the axial plastic flow underestimates the rock deformation, and the induced deviation essentially depends on the post-peak constitutive relation and the rock heterogeneity after rock yields. The higher level of the material homogeneity in the plastic zone, the lower effects of the axial in-situ stress on the rock responses. The stress distribution and strain-softening behavior of surrounding rock can be significantly affected by the axial in-situ stress and the critical plastic internal variable η*. Tunnel instability is independent of large deformation for the high η* but is closely associated with the squeezing problem when η* is small. As η* decreases, both of the plastic radius and wall convergence increase initially and remain constant afterwards. Lastly, the paper investigates the rock responses and ground-support interaction when the small strain theory is applied on the squeezing rock.

Dilation angle variations in plastic zone around tunnels in rocks-constant or variable dilation parameter

Dilation angle is a significant parameter needed for numerical simulation of tunnels. Even though dilation parameter is physically variable and dependent on confinement and experienced shear plastic strain based on the existing dilation models, numerical simulations of tunnels and underground openings with constant dilation parameter usually lead to satisfactory results in practical use. This study aims to find out why constant dilation angle is enough under practical conditions to simulate numerically tunnels and underground excavations in spite of the fact that dilation angle is variable in laboratory and experimental scale. With this aim, this work studies how mobilized dilation angle varies in a plastic zone surrounding a tunnel. For the circular tunnel under uniform in situ stress field, the stepwise finite difference approximation analytical solution considering strain softening rock mass behavior with mobilized dilation angle was used to study how mobilized dilation angle varies in plastic zone around tunnel under very different conditions. In practical conditions determined in this study, dilative behavior of all over the plastic zone around the tunnel can be approximated to constant dilation angle in the middle region of the plastic zone. Moreover, the plastic zone displacements for mobilized and constant dilation angle models are compared with each other. Further investigation under more general non-uniform in situ stress conditions and non-circular tunnels is performed by using the commercial finite difference software to numerically simulate the Mine-by experimental tunnel of AECL (Atomic Energy of Canada Limited) and the arched tunnel. Although the Mine-by and arched tunnels were numerically simulated based on the mobilized dilation angle model, the variability associated with dilation angle around the simulated Mine-by and arched tunnels is insignificant, and dilation angle is approximately constant in the plastic zone.

Difference solution for a circular tunnel excavated in strain-softening rock mass considering decayed confinement

Recent research regarding the strain-softening behavior of rock masses has demonstrated that the dilatancy angle ψ and the critical softening parameter η∗ are both strongly related to the confining stress. However, in many studies, ψ is assumed to be a constant or to vary linearly, and η∗ is also assumed to be a constant. The assumption of a constant ψ or η∗ is an approximation that does not correctly reflect the variable process in the plastic zone. In this paper, to describe the confinement-dependent characteristics of ψ and η∗ and their effects on the stress and displacement of tunnels in strain-softening rock masses, four dilatancy cases are defined as different combinations of ψ and η∗. First, two dilatancy models, the variable dilatancy model (VDM) and constant dilatancy model (CDM) are introduced. Then, a finite difference method for the strain-softening model is proposed to consider the variation of ψ and η∗ in analyzing the strain-softening behavior of rock masses. The accuracy of this method is verified by comparing the results with those calculated using the methods of Lee and Pietruszczak and Wang et al. Finally, using this proposed method, relevant comparisons are made among the four dilatancy cases for good-quality to poor-quality rock masses to reveal the confinement-dependent effects of ψ and η∗ on the evolution of several parameters, including the softening parameter, the critical softening parameter, the dilatancy coefficient, strength parameters, stress components, ground response curves, and plastic radii. It is concluded that in the plastic zone, ψ and η∗ varies nonlinearly with decreasing confining stress for underground tunnels excavated in different qualities of strain-softening Hoek-Brown rock masses. ψ and η∗ affect each other, and their relationship further influences the transition location from the plastic softening zone to the plastic residual zone. The effects of the confining dependency in ψ and η∗ for good-quality rock masses are less than those for poor quality rock masses. To guarantee simplicity and security in analyzing the stress and displacement of tunnel excavation problems, a constant ψ with a constant η∗ and a variable ψ with a variable η∗ are recommended as analysis models for good-quality and poor-quality rock masses, respectively.

Neural Prediction of Tunnels’ Support Pressure in Elasto-Plastic, Strain-Softening Rock Mass

The prediction of the support pressure (Pi) and the development of the ground reaction curve (GRC) are crucial elements of the convergence–confinement procedure used to design underground structures. In this paper, two different types of artificial neural networks (ANNs) are used to predict the Pi of circular tunnels in elasto-plastic, strain-softening rock mass. The developed ANNs consider the stress state, the radial displacement of tunnel and the material softening behavior. Among these parameters, strain softening is the parameter of the deterioration of the material’s strength in the plastic zone. The analysis also presents separate solutions for the Mohr–Coulomb and Hoek–Brown strength criteria. In this regard, multi-layer perceptron (MLP) and radial basis function (RBF) ANNs were successfully applied. MLP with the architectures of 15-5-10-1 for the Mohr–Coulomb criteria and 17-5-15-1 for the Hoek–Brown criteria appeared optimum for the prediction of the Pi. On the other hand, the RBF networks with the architectures of 15-5-1 for the Mohr–Coulomb criterion and 17-3-12-1 for the Hoek–Brown criterion were found to be the optimum for the prediction of the Pi.