Assessing the range of blasting-induced cracks in the surrounding rock of deeply buried tunnels based on the unified strength theory

Blasting-induced cracks in the rock surrounding deeply buried tunnels can result in water gushing and rock mass collapse,posing significant safety risks.However,previous theoretical studies on the range of blasting-induced cracks often ignore the impact of the in-situ stress,especially that of the intermediate principal stress.The particle displacement−crack radius relationship was established in this paper by utilizing the blasthole cavity expansion equation,and theoretical analytical formulas of the stress−displacement relationship and the crack radius were derived with unified strength theory to accurately assess the range of cracks in deep surrounding rock under a blasting load.Parameter analysis showed that the crushing zone size was positively correlated with in-situ stress,intermediate principal stress,and detonation pressure,whereas negatively correlated with Poisson ratio and decoupling coefficient.The dilatancy angle-crushing zone size relationship exhibited nonmonotonic behavior.The relationships in the crushing zone and the fracture zone exhibited opposite trends under the influence of only in-situ stress or intermediate principal stress.As the in-situ stress increased from 0 to 70 MPa,the rate of change in the crack range and the attenuation rate of the peak vibration velocity gradually slowed.

Ultimate end bearing capacity of rock-socketed pile based on generalized nonlinear unified strength criterion

In order to study the mechanism of bearing behavior at the tip of a pile embedded in rock, the generalized nonlinear unified strength criterion and slip line principle for resolving the differential equation systems which govern the stress field were applied to derive the ultimate end beating capacity based on some reasonable hypothesis and failure plane model. Both numerical simulation and test results were compared with the theoretic solution. The results show good consistency with each other and verify the validity of the present approach. The depth effect with respective to embedment ratio and other influence factors like geological strength index, intermediate principal stress, overburden factor, and damage on end bearing capacity were discussed in the analytical solution. The results show that the proposed yield criterion can be much better for investigating the ultimate end bearing performance of rock-socketed pile. The end bearing capacity increases with embedment ratio and the increasing degree is influenced intensely by the above parameters. Furthermore, ignoring intermediate stress effect would underestimate the strength properties of the rock material and lead to a very conservative estimation value.

Unified strength model based on the Hoek-Brown failure criterion for fibre-reinforced polymer-confined pre-damaged concrete columns with circular and square cross sections

Fibre-reinforced polymer(FRP)has the advantages of high strength,light weight,corrosion resistance and convenient construction and is widely used in repairing and strengthening damaged concrete columns.Most of the existing strength models were built by regression analysis of experimental data;however,in this article,a new unified strength model is proposed using the Hoek-Brown failure criterion.To study the strength of FRP-confined damaged and undamaged concrete columns,900 test data were collected from the published literature and a large database that contains the cross-sectional shape of each specimen,the damage type,the damage level and the FRP-confined stiffness was established.A new strength model using the Hoek-Brown failure criterion was established and is suitable for both circular and square columns that are undamaged,load-damaged and fire-damaged.Based on the database,most of the existing strength models from the published literature and the model proposed in this paper were evaluated.The evaluation shows that the proposed model can predict the compressive strength for FRP-confined pre-damaged and undamaged concrete columns with good accuracy.

Elasto-plastic analysis of the surrounding rock mass in circular tunnel based on the generalized nonlinear unified strength theory

The present paper aims to establish a versatile strength theory suitable for elasto-plastic analysis of underground tunnel surrounding rock. In order to analyze the effects of intermediate principal stress and the rock properties on its deformation and failure of rock mass, the generalized nonlinear unified strength theory and elasto-plastic mechanics are used to deduce analytic solution of the radius and stress of tunnel plastic zone and the periphery displacement of tunnel under uniform ground stress field. The results show that: intermediate principal stress coefficient b has significant effect on the plastic range,the magnitude of stress and surrounding rock pressure. Then, the results are compared with the unified strength criterion solution and Mohr–Coulomb criterion solution, and concluded that the generalized nonlinear unified strength criterion is more applicable to elasto-plastic analysis of underground tunnel surrounding rock.

New Asphalt Pavement Failure Criterion Based on Unified Strength Theory

This study aims to introduce an appropriate analytical method for asphalt pavement based upon unified strength theory （UST）. The traditional maximum shear stress strength theory （MSST） cannot describe the marked difference between tension strength and compressive strength or variable intermediate principal stress, which significantly affects the geotechnical materials. Our studies try to find a new asphalt pavement failure criterion that considers the influence of both tension-compression strength ratio and intermediate principal stress of asphalt mixture. In order to select a suitable theory on pavement material, the UST is introduced and compared with the traditional theory. Results show that the tension-compression strength ratio of asphalt mixture, which is used as a material parameter, dramatically affects the stress and stress distribution law in pavement; the pavement stress level increases dramatically after considering the intermediate principal stresses. Therefore, the UST which considers both tension-compression strength ratio and intermediate principal stress is more in line with the material characteristics of asvhalt pavement.

Analytical solutions for deep tunnels in strain-softening rocks modeled by different elastic strain definitions with the unified strength theory

This paper presents the analytical solutions for the responses of tunnels excavated in rock masses exhibiting strain-softening behavior. Since previous analyses give little consideration to the effect of the intermediate principal stress on the strain-softening rock behavior, the unified strength theory was introduced to analyze the tunnel response. Four cases of different definitions of the elastic strain in the softening and residual regions, used in the existing solutions, were considered. The tunnel displacements,stresses, radii of the softening and residual zones and critical stresses were deduced. The proposed solutions were verified by comparing with numerical simulations, model tests and existing solutions. Furthermore, the solutions of the four cases were compared with each other to investigate the influence of the elastic strain expressions on the tunnel responses. The results showed that the intermediate principal stress coefficient b has a significant effect on the tunnel displacements, stress fields, and plastic radii. Parametric studies were performed to analyze the influences of the softening and residual dilatancy coefficients,softening modulus and residual strength on the tunnel responses. The parametric analysis indicated that the existing models should be carefully evaluated in the analysis of tunnels constructed through average-quality rocks;the proposed solutions outperformed the existing models in solving the mentioned problem.

An elasto-plastic constitutive model for soft rock considering mobilization of strength

A new elasto-plastic constitutive model is presented in the framework of plasticity theory. The strength characteristics of a diatomaceous soft rock is investigated. The friction angle and cohesion of soft rock are mobilized as a function of plastic strain. A hyperbolic hardening function for the mobilized friction and a mixed parabolic and exponential equation for the mobilized cohesion are proposed. In view of the unified strength theory and the mobilizations of strength components, a yield function is given. A plastic potential function is determined by using the non-associated plastic flow rule. An elasto-plastic constitutive model is developed and verified. The results indicate that the proposed model can predict the behavior of soft rock accurately. The advantages of the proposed constitutive model are analyzed. The evidences support that the proposed constitutive model is a mixed hardening/softening model. A hump hardening/softening function for mobilized friction is extended to a more generalized condition.

Strength differential effect and influence of strength criterion on burst pressure of thin-walled pipelines

In the framework of the finite deformation theory, the plastic collapse analysis of thin-walled pipes subjected to the internal pressure is conducted on the basis of the unified strength criterion （USC）. An analytical solution of the burst pressure for pipes with capped ends is derived, which includes the strength differential effect and takes the influence of strength criterion on the burst pressure into account. In addition, a USC- based analytical solution of the burst pressure for end-opened pipes under the internal pressure is obtained. By discussion, it is found that for the end-capped pipes, the influence of different yield criteria and the strength differential effect on the burst pressure are significant, while for the end-opened pipes, the burst pressure is independent of the specific form of the strength criterion and strength difference in tension and compression.

Unified semi-analytical solution for elastic-plastic stress of deep circular hydraulic tunnel with support yielding

A unified semi-analytical solution is presented for elastic-plastic stress of a deep circular hydraulic tunnel with support yielding under plane strain conditions.The rock mass is assumed to be elastic-perfectly plastic and governed by the unified strength theory (UST).Different major principal stresses in different engineering situations and different support yielding conditions are both considered.The unified solution obtained in this work is a series of results,rather than one specific solution,hence it is suitable for a wide range of rock masses.In addition,parametric study is conducted to investigate the effect of intermediate principal stress.The result shows the major principal stress should be rationally chosen according to different engineering conditions.Finally,the applicability of the unified solution is discussed according to the critical pressures.

Unified elastoplastic finite difference and its application

Two elastoplastic constitutive models based on the unified strength the- ory （UST） are established and implemented in an explicit finite difference code, fast Lagrangian analysis of continua （FLAC/FLAC3D）, which includes an associated/non- associated flow rule, strain-hardening/softening, and solutions of singularities. Those two constitutive models are appropriate for metallic and strength-different （SD） materials, respectively. Two verification examples are used to compare the computation results and test data using the two-dimensional finite difference code FLAC and the finite element code ANSYS, and the two constitutive models proposed in this paper are verified. Two application examples, the large deformation of a prismatic bar and the strain-softening be- havior of soft rock under a complex stress state, are analyzed using the three-dimensional code FLAC3D. The two new elastoplastic constitutive models proposed in this paper can be used in bearing capacity evaluation or stability analysis of structures built of metallic or SD materials. The effect of the intermediate principal stress on metallic or SD mate- rial structures under complex stress states, including large deformation, three-dimensional and non-association problems, can be analyzed easily using the two constitutive models proposed in this paper.

An explicit formulation of the macroscopic strength criterion for porous media with pressure and Lode angle dependent matrix under axisymmetric loading

This paper aims to propose an explicit formulation of the macroscopic strength criterion for porous media with spherical voids.The matrix is assumed rigid and perfectly plastic with yield surface described by the three-parameter strength criterion,which is Lode angle and pressure dependent and capable of accounting for distinct values of the uniaxial tensile strength,uniaxial compressive strength(UCS)and equal biaxial compressive strength(eBCS).An exact upper bound of the macroscopic strength is derived for porous media subjected to purely hydrostatic loading.Besides,an estimate of the macroscopic strength profile of porous media under axisymmetric loading is obtained in parametric form.Moreover,a heuristic strength criterion in explicit form is further developed by examining limit cases of the parametric strength criterion.The developed strength criteria are assessed by finite-element based numerical solutions.Compared with the parametric strength criterion which involves cumbersome functions,the heuristic one is convenient for practical applications.For specific values of the matrix’s strength surface,the proposed heuristic strength criterion can recover the well-known Gurson criterion.The present work also addresses the effect of the ratio of matrix’s eBCS to UCS on the macroscopic strength of porous media.For matrix with distinct values of eBCS and UCS,neglecting the difference between eBCS and UCS would result in an underestimation of the macroscopic strength,especially when the pressure is large.

Basic characteristics and development of yield criteria for geomaterials

The yield criteria of geomaterials play a crucial role in studying and designing the strength of materials and structures.The basic characteristics of yield criteria for geomaterials need to be studied under the framework of continuum mechanics.These characteristics include the effects of strength difference（SD） of materials in tension and compression,normal stress,intermediate principal stress,intermediate principal shear stress,hydrostatic stress,twin-shear stresses,and the convexity of yield surface.Most of the proposed yield criteria possess only one or some of these basic characteristics.For example,the Tresca yield criterion considers only single-shear stress effect,and ignores the effect of SD,normal stress,intermediate principal stress,intermediate principal shear stress,hydrostatic stress,and twin-shear stresses.The Mohr-Coulomb yield criterion accounts for the effect of SD,normal stress,single-shear stress and hydrostatic stress,but disregards the effect of intermediate principal stress,intermediate principal shear stress,and twin-shear stresses.The basic characteristics remain to be fully addressed in the development of yield criterion.In this paper,we propose a new yield criterion with three features,that is,newly developed,better than existing criteria and ready for application.It is shown that the proposed criterion performs better than the existing ones and is ready for application.The development of mechanical models for various yield criteria and the applications of the unified strength theory to engineering are also summarized.According to a new tetragonal mechanical model,a tension-cut condition is added to the unified strength theory.The unified strength theory is extended to the tension-tension region.

Upper bound solution for active thrust of nonhomogeneous cohesive soil considering effects of intermediate principal stress

Considering the variation of cohesion along the depth,the upper bound solution of active earth pressure for a rough inclined wall with sloped backfill is formulated based on a log-spiral failure mechanism.For a more accurate prediction,the influence of intermediate principal stress is taken into consideration using the unified strength theory.Converting the search for the active pressure to an optimization problem,the most critical failure surface can be located by a natural selection-based gravitational search algorithm(GSA).The proposed method is validated compared with existing methods for noncohesive and cohesive cases and proved to be more accordance with the limit equilibrium solution.The influences of the variation of soil cohesion and intermediate principal stress on active earth pressure coefficient are then fully studied.It can be concluded that both the variations of soil cohesion and intermediate principal stress have a significant influence on the active earth pressure coefficient.

Seismic ultimate bearing capacity of strip footings on slope

The influence of earthquake forces on ultimate bearing capacity of foundations on sloping ground was studied. A solution to seismic ultimate bearing capacity of strip footings on slope was obtained by utilizing pseudo-static analysis method and taking the effect of intermediate principal stress into consideration. Based on limit equilibrium theory, the formulae for computing static bearing capacity factors, Nq, Nc, Nγ, and dynamic bearing capacity factors, Nqd, Ned, Nγd, which are associated with surcharge, cohesion and self-weight of soils respectively, were presented. A great number of analysis calculations were carried out to obtain the relationship curves of the static and dynamic bearing capacity factors versus various calculation parameters. The curves can serve as the practical engineering design. The calculation results also show that when the values of horizontal and vertical seismic coefficients are 0.2, the dynamic bearing capacity factors Nqd, Ned and Nγd, in which the effects of intermediate principal stress are taken into consideration, increase by 4%-42%, 3%-27% and 34%-57%, respectively.

Analysis of Penetration Model for Geo-Material by Rigid Projectile

Based on the cylindrical cavity expansion theory, a plastic-damage-elastic model is proposed for the penetration problem of geo-material. In the model, the unified strength criterion (Yu, 1991) is adopted as the failure criterion. The distributions of the radial stress and velocity are analyzed. According to the Newton's second law, a series results of the final penetration depth and the impedance load are obtained to different parameter b, when a rigid projectile normally impacts and penetrates a semi-infinite geo-material target with an impact velocity of 300-1200 m/s. By comparing with the test data available, it appears that the method can be used in analyzing the final depth and the impedance load of a rigid projectile penetrating into a semi-infinite target with different impact velocities.

Unified characteristics line theory of spacial axisymmetric plastic problem

The unified strength theory proposed by Yu in 1991 is extended to spacial axisymmetric problem. A unified spacial axismymmetric characteristics line theory based on the unified strength theory is proposed. This theory takes account of different effects of intermediate principal stress on yielding or failure and the SD effect (tensile-compression strength difference) of materials. Various conventional axisymmetric characteristics line theories, which are based on the Haar-von Karman plastic condition, Szczepinski hypothesis, Tresca criterion, von Mises criterion and Mohr-Coulomb theory, are special cases of the new theory. Besides, a series of new spacial axisymmetric characteristics fields for different materials can be introduced. It forms a unified spacial axisymmetric characteristics theory. Two examples are calculated with the new theory, the results are compared with those obtained by the finite element program UEPP and those based on the Mohr-Coulomb strength theory. It is shown that the new theory is reliable and feasible. The economic benefit can be obtained from the engineering application of the new theory.

Three Important Advances in Engineering Strength Theories

There are there great advances in the research on engineering strength theories in the latter half of the 20^th Century. The first advance was the devel-opment of strength theory from the single-shear strength theory including the Tresca yield criterion and Mohr-Coulomb failure criterion to theoctahe-dral-shear strength theory; the second one was that from the octahedral-shear strength theory to the twin-shear strength theory; and the third wasthe theories from the single criteria to the unifiedstrength theory. These three advances are summa-rized in this paper. It is interesting and useful for re-searchers to choose an appropriate failure criterion in studying the strength of materials and struc-tures, for engineers to correctly use it and for stu-dents to understand strength theory.

A Modified Symmetric and Antisymmetric Decomposition-Based Three-Dimensional Numerical Manifold Method for Finite Elastic-Plastic Deformations

There are relatively few studies on large rotation or deformation by means of the three-dimensional(3D)numerical manifold method(NMM).A new modified symmetric and antisymmetric decomposition(MSAD)theory is developed and implemented into the 3D NMM,eliminating the false-volume expansion and false-rotation strain/stress problems.The Jaumann rate is used to measure the material rotation,and the geometric stiffness built on the Jaumann rate is deduced.The incremental formulas of the MSAD-based 3D NMM and a practical guide on the implementation of the MSAD theory are given in detail and exemplified.The new theory and formulas can be applied to analyze both large rotation and large deformation problems.Based on the hypoelasto-plasticity theory and the unified strength theory,the unified yield criterion with associated flow rule is implemented into the MSAD-based 3D NMM.Several typical examples are studied,showing the advantage and potential of the new MSAD theory and the MSAD-based 3D NMM.