Enhanced Hoek-Brown(H-B)criterion for rocks exposed to chemical corrosion

Underground constructions often encounter water environments,where water–rock interaction can increase porosity,thereby weakening engineering rocks.Correspondingly,the failure criterion for chemically corroded rocks becomes essential in the stability analysis and design of such structures.This study enhances the applicability of the Hoek-Brown(H-B)criterion for engineering structures operating in chemically corrosive conditions by introducing a kinetic porosity-dependent instantaneous mi(KPIM).A multiscale experimental investigation,including nuclear magnetic resonance(NMR),X-ray diffraction(XRD),scanning electron microscopy(SEM),pH and ion chromatography analysis,and triaxial compression tests,is employed to quantify pore structural changes and their linkage with the strength responses of limestone under coupled chemical-mechanical(C-M)conditions.By employing ion chromatography and NMR analysis,along with incorporating the principles of free-face dissolution theory accounting for both congruent and incongruent dissolution,a kinetic chemical corrosion model is developed.This model aims to calculate the kinetic porosity alterations within rocks exposed to varying H+concentrations and durations.Subsequently,utilizing the generalized mixture rule(GMR),the kinetic porositydependent mi is formulated.Evaluation of the KPIM-enhanced H-B criterion using compression test data from 5 types of rocks demonstrated a high level of consistency between the criterion and the experimental results,with a coefficient of determination greater than 0.96,a mean absolute percentage error less than 4.84%,and a root-mean-square deviation less than 5.95 MPa.Finally,the physical significance of the porosity-dependent instantaneous mi is clarified:it serves as an indicator of a rock’s capacity to leverage the confining pressure effect.

Fatigue Resistance of RCA Modified Asphalt Based on Dielectric Properties

In order to study the anti-fatigue performance of RCA modified asphalt (RMA),the performance of RMA and 90#matrix asphalt with different modifier content were measured by asphalt penetration,ductility,softening point,Brookfield viscosity,rheological index,infrared spectrum and dielectric constant test.This paper discusses the changes of asphalt basic indexes,fatigue properties and asphalt components based on dielectric properties under different modifier contents,and analyzes the grey correlation degree between components and asphalt pavement performance indexes.The results show that the optimum content of RCA modifier is 16.7%of the asphalt quality according to the penetration,ductility,softening point,Brockfield viscosity,viscosity temperature curve and fatigue life.In the phase angle-strain curve,there is disorder in the latter part of the curve.According to the strain (ε_(d)) corresponding to the disorder point,a new fatigue failure criterion is proposed and proved.Based on the new asphalt fatigue failure criterion,the fatigue prediction model of asphalt mixture is improved,and the fatigue life predicted by the improved fatigue model is compared with the fatigue life obtained by four-point bending fatigue test.The results show that the proposed new asphalt fatigue failure criterion is reasonable,and the fatigue life predicted by the improved asphalt mixture fatigue prediction model is accurate.The research method of classifying asphalt components based on dielectric properties is simple and effective,and the components have a high correlation with the road performance of base asphalt and modified asphalt.

Three-dimensional limit variation analysis on the ultimate pullout capacity of the anchor cables based on the Hoek-Brown failure criterion

Only simplified two-dimensional model and a single failure mode are adopted to calculate the ultimate pullout capacity(UPC)of anchor cables in most previous research.This study focuses on a more comprehensive combination failure mode that consists of bond failure of an anchorage body and failure of an anchored rock mass.The three-dimensional ultimate pullout capacity of the anchor cables is calculated based on the Hoek-Brown failure criterion and variation analysis method.The numerical solution for the curvilinear function in fracture plane is obtained based on the finite difference theory,which more accurately reflects the failure state of the anchor cable,as opposed to that being assumed in advance.The results reveal that relying solely on a single failure mode for UPC calculations has limitations,as changes in parameter values not only directly impact the UPC value but also can alter the failure model and thus the calculation method.

A modified Hoek-Brown failure criterion considering the damage to reservoir bank slope rocks under water saturation-dehydration circulation

After water is impounded in a reservoir,rock mass in the hydro-fluctuation belt of the reservoir bank slope is subject to water saturationdehydration circulation(WSDC). To quantify the rate of change of rock mechanical properties, samples from the Longtan dam area were measured with uniaxial compression tests after different numbers(1,5, 10, 15, and 20) of simulated WSDC cycles. Based on the curves derived from these tests, a modified HoekBrown failure criterion was proposed, in which a new parameter was introduced to model the cumulative damage to rocks after WSDC. A case of an engineering application was analyzed, and the results showed that the modified Hoek-Brown failure criterion is useful.Under similar WSDC-influenced engineering and geological conditions, rock mass strength parameters required for analysis and evaluation of rock slope stability can be estimated according to this modified Hoek-Brown failure criterion.

Two-dimensional face stability analysis in rock masses governed by the Hoek-Brown strength criterion with a new multi-horn mechanism

The face stability problem is a major concern for tunnels excavated in rock masses governed by the Hoek-Brown strength criterion.To provide an accurate prediction for the theoretical solution of the critical face pressure,this study adopts the piecewise linear method(PLM)to account for the nonlinearity of the strength envelope and proposes a new multi-horn rotational mechanism based on the Hoek-Brown strength criterion and the associative flow rule.The analytical solution of critical support pressure is derived from the energy-work balance equation in the framework of the plastic limit theorem;it is formulated as a multivariable nonlinear optimization problem relying on 2m dependent variables(m is the number of segments).Meanwhile,two classic linearized measures,the generalized tangential technique(GTT)and equivalent Mohr-Coulomb parameters method(EMM),are incorporated into the analysis for comparison.Surprisingly,the parametric study indicates a significant improvement in support pressure by up to 13%compared with the GTT,and as expected,the stability of the tunnel face is greatly influenced by the rock strength parameters.The stress distribution on the rupture surface is calculated to gain an intuitive understanding of the failure at the limit state.Although the limit analysis is incapable of calculating the true stress distribution in rock masses,a rough approximation of the stress vector on the rupture surface is permitted.In the end,sets of normalized face pressure are provided in the form of charts for a quick assessment of face stability in rock masses.

Triaxial strength behaviour of rockmass satisfying Modified Mohr-Coulomb and Generalized Hoek-Brown criteria

The triaxial strength of twenty rockmass types was predicted using two non-linear triaxial strength criteria for rockmass i.e. Modified Mohr-Coulomb(MMC) criterion and Generalized Hoek-Brown(GHB)criterion. Four different rockmass classification systems were used for the calculation of MMC criterion parameters while only GSI classification system has been used for calculation of GHB parameters. The representative value of the uniaxial compressive strength and elastic modulus of rockmass have been estimated using probabilistic approach. A hypothetical case of an unsupported tunnel has been analyzed considering both MMC and GHB criteria. The analysis was done using the convergence-confinement method with two different approaches. The first approach predicts the tunnel response using GHB criterion directly. The second approach predicts the tunnel response using equivalent Mohr-Coulomb parameters obtained by linearization of triaxial data points obtained from MMC and GHB criteria. The tunnel response has been estimated in terms of radius of plastic zone, tunnel convergence and tunnel convergence strain. For very poor rockmasses the tunnel response predicted by MMC criterion is less than that predicted by GHB criterion. For poor and fair rockmass, the tunnel response estimated considering both the criteria are comparable except for few cases. Squeezing condition in rockmass has been also evaluated.

An approximate nonlinear modified Mohr-Coulomb shear strength criterion with critical state for intact rocks

In this paper, the Mohr-Coulomb shear strength criterion is modified by mobilising the cohesion and internal friction angle with normal stress, in order to capture the nonlinearity and critical state concept for intact rocks reported in the literature. The mathematical expression for the strength is the same as the classical form, but the terms of cohesion and internal friction angle depend on the normal stress now,leading to a nonlinear relationship between the strength and normal stress. It covers both the tension and compression regions with different expressions for cohesion and internal friction angle. The strengths from the two regions join continuously at the transition of zero normal stress. The part in the compression region approximately satisfies the conditions of critical state, where the maximum shear strength is reached. Due to the nonlinearity, the classical simple relationship between the parameters of cohesion, internal friction angle and uniaxial compressive strength from the linear Mohr-Coulomb criterion does not hold anymore. The equation for determining one of the three parameters in terms of the other two is supplied. This equation is nonlinear and thus a nonlinear equation solver is needed. For simplicity, the classical linear relationship is used as a local approximation. The approximate modified Mohr-Coulomb criterion has been implemented in a fracture mechanics based numerical code FRACOD,and an example case of deep tunnel failure is presented to demonstrate the difference between the original and modified Mohr-Coulomb criteria. It is shown that the nonlinear modified Mohr-Coulomb criterion predicts somewhat deeper and more intensive fracturing regions in the surrounding rock mass than the original linear Mohr-Coulomb criterion. A more comprehensive piecewise nonlinear shear strength criterion is also included in Appendix B for those readers who are interested. It covers the tensile, compressive, brittle-ductile behaviour transition and the critical state, and gives smooth transitions.

Rockburst criterion and evaluation method for potential rockburst pit depth considering excavation damage effect

Excavation-induced disturbances in deep tunnels will lead to deterioration of rock properties and formation of excavation damaged zone(EDZ).This excavation damage effect may affect the potential rockburst pit depth.Taking two diversion tunnels of Jinping II hydropower station for example,the relationship between rockburst pit depth and excavation damage effect is first surveyed.The results indicate that the rockburst pit depth in tunnels with severe damage to rock masses is relatively large.Subsequently,the excavation-induced damage effect is characterized by disturbance factor D based on the Hoek-Brown criterion and wave velocity method.It is found that the EDZ could be further divided into a high-damage zone(HDZ)with D=1 and weak-damage zone(WDZ),and D decays from one to zero linearly.For this,a quantitative evaluation method for potential rockburst pit depth is established by presenting a three-element rockburst criterion considering rock strength,geostress and disturbance factor.The evaluation results obtained by this method match well with actual observations.In addition,the weakening of rock mass strength promotes the formation and expansion of potential rockburst pits.The potential rockburst pit depth is positively correlated with HDZ and WDZ depths,and the HDZ depth has a significant contribution to the potential rockburst pit depth.

Limit load and failure mechanisms of a vertical Hoek-Brown rock slope

The problem considered in this short note is the limit load determination of a vertical rock slope.The classical limit theorem is employed with the use of adaptive finite elements and nonlinear programming to determine upper and lower bound limit loads of a Hoek-Brown vertical rock slope.The objective function of the mathematical programming problem is such as to optimize a boundary load,which is known as the limit load,resembling the ultimate bearing capacity of a strip footing.While focusing on the vertical slope,parametric studies are carried out for several dimensionless ratios such as the dimensionless footing distance ratio,the dimensionless height ratio,and the dimensionless rock strength ratio.A comprehensive set of design charts is presented,and failure envelopes shown with the results explained in terms of three identified failure mechanisms,i.e.the face,the toe,and the Prandtl-type failures.These novel results can be used with great confidence in design practice,in particularly noting that the current industry-based design procedures for the presented problem are rarely found.

Modified Burzynski criterion with non-associated flow rule for anisotropic asymmetric metals in plane stress problems

The Burzynski criterion is developed for anisotropic asymmetric metals with the non-associated flow rule （NAFR） for plane stress problems. The presented pressure depending on the yield criterion can be calibrated with ten experimental data, i.e., the tensile yield stresses at 0°, 45°, and 90°, the compressive yield stresses at 0°, 15°, 30°, 45°, 75°, and 90° from the rolling direction, and the biaxial tensile yield stress. The corresponding pressure independent plastic potential function can be calibrated with six experimental data, i.e., the tensile R-values at 0°, 15°, 45°, 75°, and 90° from the rolling direction and the tensile biaxial R-value. The downhill simplex method is used to solve these ten and six high nonlinear equations for the yield and plastic potential functions, respectively. The results show that the presented new criterion is appropriate for anisotropic asymmetric metals.

Pseudo-static stability analysis of rock slopes reinforced by passive bolts using the generalized Hoek-Brown criterion

The stability analysis of passive bolt-reinforced rock slopes under seismic loads is investigated within the framework of the kinematic approach of limit analysis theory.A pseudo-static method is adopted to account for the inertial forces induced in the rock mass by seismic events.The strength properties of the rock material are described by a modified Hoek-Brown strength criterion,whereas the passive bolts are modeled as bar-like inclusions that exhibit only resistance to tensile-compressive forces.Taking advantage of the ability to compute closed-form expressions for the support functions associated with the modified Hoek-Brown strength criterion,a rotational failure mechanism is implemented to derive rigorous lower bound estimates for the amount of reinforcement strength to prevent slope failure.The approach is then applied to investigating the effects of relevant geometry,strength and loading parameters in light of a preliminary parametric study.The accuracy of the approach is assessed by comparison of the lower bound estimates with finite element limit analysis solutions,thus emphasizing the ability of the approach to properly predict the stability conditions and to capture the essential features of deformation localization pattern.Finally,the extension of the approach to account for slipping at the interface between reinforcements and surrounding rock mass is outlined.

Simplifying Triangular Mesh Model by Modified Distance Criterion

Model simplification is used in a variety of disciplines, such as vir'tUal reality, CAD anddynamic simulation. The method of model simplification is an important problem. This paperpresents a new method to delete vertex from mesh model for simplification, in which the modifieddistance actS as deletion criterion. In order to improve the mesh quality, the poyer uses an optimalmethod based on swapping diagonal for retriangulating the local polygon. By the method. thesimplified model can approximate original model very well. An example to illustrate the efficiencyof the method is given.

A new three-dimensional Hoek-Brown strength criterion

The Hoek-Brown （HB） strength criterion has been widely applied to the estimation of strength of intact rock and rock mass, while evolving ever since. However, negligence of the effect of the intermediate principal stress still remains in the criterion＇s latest version. At the same time, several three-dimensional （3D） HB strength, which can takes into account the influence of the intermediate principal stress, have already been proposed, among which the 3D HB criterion proposed by Zhang and Zhu seems to be the most reasonable one. However, the Zhang 3D HB criterion may have problems with some stress path close to triaxial extension state because of the non-convexity characteristic of its failure surface. In this paper, a new 3D HB strength criterion is presented based on a generalized form of the HB criterion, which also considers the effect of the intermediate principal stress and inherits all the merits of the original version of the HB criterion. In addition, this new criterion can remedy to some extent the shortcomings observed in the Zhang 3D HB criterion. Polyaxial tests for five different rocks from pub- lished literatures are used for evaluating this new criterion and comparing it with the Zhang 3D HB criterion. The re- sults show that this new criterion may over-predict or under- predict the polyaxial strength of rocks but the errors are rela- tively small, and similar results are also found for the Zhang 3D HB criterion, which one is better depends on the type of the rock under estimation.

Limit analysis for the seismic stability of three-dimensional rock slopes using the generalized Hoek-Brown criterion

The parameters that influence slope stability and their criteria of failure are fairly understood but over-conservative design approaches are often preferred,which can result in excessive overburden removal that may jeopardize profitability in the context of open pit mining.Numerical methods such as finite element and discrete element modelling are instrumental to identify specific zones of stability,but they remain approximate and do not pinpoint the critical factors that influence stability without extensive parametric studies.A large number of degrees of freedom and input parameters may make the outcome of numerical modelling insufficient compared to analytical solutions.Existing analytical approaches have not tackled the stability of slopes using non-linear plasticity criteria and threedimensional failure mechanisms.This paper bridges this gap by using the yield design theory and the Hoek-Brown criterion.Moreover,the proposed model includes the effect of seismic forces,which are not always taken into account in slope stability analyses.The results are presented in the form of rigorous mathematical expressions and stability charts involving the loading conditions and the rock mass properties emanating from the plasticity criterion.

A simplified three-dimensional extension of Hoek-Brown strength criterion

The Hoek-Brown(HB)strength criterion has been applied widely in a large number of projects around the world.However,this criterion ignores the intermediate principal stress s2.Many evidences have demonstrated that the rock strength is dependent on s2.Thus it is necessary to extend the HB criterion into a three-dimensional(3D)form.In this study,the effect of s2 on the strength of rocks is identified by reviewing the true triaxial tests of various rock types reported in the literature.A simple 3D strength criterion is developed.The modified criterion is verified by the true triaxial tests of 13 rock types.The results indicate that the modified criterion can achieve a good fit to most of rock types.It can represent a series of criteria as b varies.For comparisons,several existing 3D versions of the HB criterion are selected to predict the strengths of these rock types.It is indicated that the proposed criterion works better than other criteria.A substantial relationship between parameter b and the unconfined compressive strength is established,which guarantees that the proposed criterion can still work well even in the absence of true triaxial test data.

Validation of Hoek-Brown failure criterion charts for rock slopes

Although stability charts suggested by Hoek and Bray on the basis of Mohr-Coulomb criterion are used for rock slopes,but complete and precise recognition is required for distinguishing cohesive strength and Mohr-Coulomb equivalent internal friction angle for rock mass.The paper by Lia et al.[6]is the only one that introduced rock slope charts according to Hoek-Brown failure criterion.In this paper,at first,this type of charts is introduced.Then,Mohr-Coulomb failure criterion charts[2]are compared and validated with Hoek-Brown failure criterion ones[6].Next,Bishop method utilizing Slide software is compared with Hoek-Brown failure criterion stability charts.Average standard deviation(ASD),root mean square error(RMSE)and variance account for(VAF)were used for the comparison.According to the results,because of high distribution and very low correlation among the comparisons,Hoek-Brown failure criterion charts are not efficient.

Upper bound solution for supporting pressure acting on shallow tunnel based on modified tangential technique

Based on the nonlinear failure criterion and the upper bound theorem, the modified tangential technique method was proposed to derive the expression of supporting pressure acting on shallow tunnel. Instead of the same stress state, different normal stresses on element boundaries were used. In order to investigate the influence of different factors on supporting pressures, the failure mechanism was established. The solution of supporting pressure, with different parameters, was obtained by optimization theory. The corresponding failure mechanism and numerical results were presented. In comparison with the results using the single tangential technique method, it is found that the proposed method is effective, and the good agreement shows that the present solution of supporting pressure is reliable.

3D limit analysis of rock slopes based on equivalent linear failure criterion with tension cut-off

Hoek-Brown (HB) failure criterion is widely used to predict the strength of intact or heavily jointed rock mass. For stability analysis of rock slopes governed by the HB failure criterion, the equivalent linearity to Mohr-Coulomb (MC) criterion is often adopted, leading to the well-known equivalent Mohr-Coulomb method (EMCM). Existing studies on EMCM analysis mainly consider the shear strength of rock material, while consideration of the tensile strength is rare. This contradicts the fact that the underlying tensile strength of rock mass has considerable impact on the rock slope stability in real world. In this regard, this paper proposes a limit analysis-based approach that can account for tension in the three-dimensional (3D) stability analysis of HB rock slope. This approach is established on the equivalent linearity of the HB criterion with consideration of tensile strength, known as the equivalent tension cut-off MC method (ETMCM), and using a horn-like 3D mechanism of limit analysis. The safety factor solutions given by the proposed approach are validated by previous studies and numerical results. Parametric studies are conducted to investigate the effect of rock tensile strength on slope stability. Results show that the consideration of tension leads to a more conservative safety factor and a sharper curvature of the failure surface, and these impacts tend to be more obvious with the increases in slope inclination and slope width. Finally, the stability of the HB rock slope under seepage conditions is studied using the proposed approach. The results indicate that the effect of tensile strength is highly remarkable in seepage circumstances.

基于Hoek-Brown准则等效强度参数的工程应用

为研究重庆至长沙省际公路共和隧道层状围岩稳定性,减小模拟值与实测值误差,并充分考虑倾角效应、静水压力效应和罗德角效应,将适用于层状岩体的修正Hoek-Brown(H-B)准则在I_(1)-√J_(2)平面与Mohr-Coulomb(M-C)准则进行瞬时等效,推导出用于层状岩体的等效强度参数公式,计算得到不同倾角下砂质页岩等效c、φ值,然后输入FLAC^(3D)遍布节理模型中对原岩体参数进行修正。结果表明:1)修正岩体参数法所得关键点位移变化规律与修正前一致,且位移量大于修正前,但当倾角大于60°后,该法适用性有所降低;2)修正后围岩各关键点偏应力(σ_(1)-σ_(3))始终大于修正前,且二者塑性区随倾角变化趋势一致;3)当岩体内摩擦角小于节理内摩擦角时,围岩塑性区面积较大;反之,当岩体内摩擦角大于节理内摩擦角时,塑性区面积较小。

基于上限定理确定隧道式锚碇极限抗拔承载力

隧道式锚碇作为一种新型的悬索桥锚碇结构,因具有因地制宜、经济环保的优点在多山的西南地区得到了广泛应用。已有研究表明,锚塞体围岩性质较差、埋深较浅,锚塞体与围岩接触界面结合程度较好的隧道式锚碇极易发生倒楔形冲切破坏。将破坏体视为以锚塞体中心线为轴线的旋转楔形体,假定破坏面为最小旋转曲面,利用变分法经典欧拉方程求解破坏体最小旋转曲面问题,确定旋转曲面母线方程;基于改进的Mohr-Coulomb强度准则,由主缆拉拔荷载和楔形体自重所做的外功率与楔形体沿滑移面所消耗的内功率相等的条件建立虚功方程,推导隧道式锚碇极限抗拔承载力上限解。开展隧道式锚碇室内模型试验,研究了拉拔承载过程中的坡面位移的变化规律及隧道式锚碇的破坏模式。研究结果表明,拉拔作用点的荷载-位移曲线可分为4个阶段:克服重力阶段、弹性阶段、弹塑性阶段以及破坏阶段;隧道式锚碇破坏模式为围岩倒楔形冲切破坏,破坏体可近似视为以锚塞体中心线为轴线的旋转楔形体;由推导公式得到的隧道式锚碇极限抗拔承载力计算值与实测值一致性较好,具有一定的可靠性,可为隧道式锚碇的设计提供参考。