Seismic bearing capacity of strip footings on rock masses using the Hoeke Brown failure criterion

In this paper,the bearing capacity of strip footings on rock masses has been studied in the seismic case.The stress characteristics or slip line method was used for analysis.The problem was analyzed in the plane strain condition using the Hoeke Brown failure criterion.First,the equilibrium equations along the stress characteristics were obtained and the rock failure criterion was applied.Then,the equations were solved using the finite difference method.A computer code has been provided for analysis.Given the footing and rock parameters,the code can calculate the stress characteristics network and obtain the stress distribution under the footing.The seismic effects have been applied as the horizontal and vertical pseudo-static coefficients.The results of this paper are very close to those of the other studies.The seismic bearing capacity of weightless rock masses can be obtained using the proposed equations and graphs without calculating the whole stress characteristics network.

The Hoeke-Brown failure criterion and GSI-2018 edition

The HoekeBrown criterion was introduced in 1980 to provide input for the design of underground excavations in rock.The criterion now incorporates both intact rock and discontinuities,such as joints,characterized by the geological strength index(GSI),into a system designed to estimate the mechanical behaviour of typical rock masses encountered in tunnels,slopes and foundations.The strength and deformation properties of intact rock,derived from laboratory tests,are reduced based on the properties of discontinuities in the rock mass.The nonlinear HoekeBrown criterion for rock masses is widely accepted and has been applied in many projects around the world.While,in general,it has been found to provide satisfactory estimates,there are several questions on the limits of its applicability and on the inaccuracies related to the quality of the input data.This paper introduces relatively few fundamental changes,but it does discuss many of the issues of utilization and presents case histories to demonstrate practical applications of the criterion and the GSI system.

Elasto-plastic Analysis of Circular Tunnels in Jointed Rock Masses Satisfy the Hoek-Brown Failure Criterion

The relationship between the Hoek-Brown parameters and the mechanical response of circular tunnels is il-lustrated. Closed-form and approximate solutions are given for the extent of the plastic zone and the stress and dis-placement fields under axisymmetrical and asymmetric stress conditions. For the same rock masses and under axisym-metrical stress conditions,the radius of the plastic zone in terms of Hoek-Brown criterion is generally an approximation of the radius in terms of the Mohr-Coulomb criterion. The radius in terms of the Hoek-Brown criterion is larger under low stress conditions. For poor quality rock masses (GSI<25),measures (such as grouting,setting rock bolts,etc.) that improve the GSI of rock masses are effective in improving the stability of tunnels. It is not advisable to improve the sta-bility of the tunnels by providing a small support resistance p through shotcrete,except for very poor quality jointed rock masses. Without reference to the quality of the rock mass,the disturbance factor D should not less than 0.5. Meas-ures which disturb rock masses during tunnel construction should be taken carefully when the tunnel depth increases.

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.

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.

A simplified approach to directly consider intact rock anisotropy in Hoek——Brown failure criterion

Many rock types have naturally occurring inherent anisotropic planes, such as bedding planes, foliation,or flow structures. Such characteristic induces directional features and anisotropy in rocks＇ strength anddeformational properties. The HoekeBrown （HeB） failure criterion is an empirical strength criterionwidely applied to rock mechanics and engineering. A direct modification to HeB failure criterion toaccount for rock anisotropy is considered as the base of the research. Such modification introduced a newdefinition of the anisotropy as direct parameter named the anisotropic parameter （Kb）. However, thecomputation of this parameter takes much experimental work and cannot be calculated in a simple way.The aim of this paper is to study the trend of the relation between the degree of anisotropy （Rc） and theminimum value of anisotropic parameter （Kmin）, and to predict the Kmin directly from the uniaxialcompression tests instead of triaxial tests, and also to decrease the amount of experimental work. 2014 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Production and hosting byElsevier B.V. All rights reserved.

基于约束收敛法的Hoek-Brown岩体巷道大变形分析

轴对称圆形巷道的弹塑性理论分析是深部软岩巷道施工过程的基础问题和重要问题。基于约束收敛法、有限变形次弹塑性理论、Hoek-Brown破坏准则、应变软化本构模型等基本理论,开展了深埋软弱围岩圆形巷道开挖诱致挤压大变形现象的基础研究。在相关大变形研究的基础上,以巷道开挖后围岩脆塑性解析解来表征岩体应变软化区划分圆环岩体响应解析解的方法,简述Hoek-Brown岩体深埋软岩巷道围岩各分区应力与变形解析解求解思路。通过现场监测数据和不同力学模型的计算结果分别进行模型有效性对比验证,并对m、s、a等岩体强度相关参数进行了影响分析。基于大变形和小变形理论下围岩特征曲线差别,提出软弱破碎岩体的支护建议,为深部不利赋存条件下软弱围岩支护工程设计提供理论分析手段和指导。

一种改进的真三轴Hoek–Brown强度准则

Hoek–Brown强度准则已经广泛应用于岩石与岩体力学分析、岩石边坡稳定性分析、岩石隧道设计等领域,但常规Hoek–Brown强度准则未考虑中间主应力对岩石强度的影响,应用上不能反映岩石的真三轴力学性能,因此有必要对Hoek–Brown强度准则进行改进。通过分析岩石的真三轴试验结果,明确了岩石中间主应力对岩石强度的影响存在增强和抑制两种特征,当中间主应力大于临界值σ*2时,岩石强度被增强;当中间主应力小于临界值σ*2时,岩石强度被减弱。基于中间主应力的临界应力状态,引入中间主应力系数β,将一种2维Hoek–Brown强度准则改进为真三轴Hoek–Brown强度准则。采用非线性拟合方法确定了模型中的参数,通过对比8种岩石类型的真三轴试验数据,对改进后强度准则的精确性和普适性进行验证,并与其他3种真三轴强度准则做对比。结果表明:改进的真三轴强度准则的最佳参数m取值均能落在Hoek和Brown建议的取值区间,能够继承Hoek–Brown强度准则的优点。改进后的强度准则对8种岩石类型的均方根差(RMSE)均低于另外3种准则,能够准确预测岩石强度,且适用于大多数岩石类型,较好地体现了中间主应力对岩石强度的影响;Pan–Hudson准则总是在低σ2条件下高估岩石强度值,在高σ2条件下低估岩石强度值;Zhang–Zhu和Priest准则对岩石类型具有较强依赖性,描述精度较差。因此,改进的真三轴Hoek–Brown强度准则具有重要的应用推广价值。

基于Hoek-Brown准则的地下洞室围岩稳定性分析

基于Hoek-Brown准则,针对该准则中与围岩稳定性相关联因素,如最大主应力σ1、最小主应力σ3、岩石强度指标GSI和岩石单轴抗压强度σci,对水电站大型地下洞室围岩稳定性的影响开展分析,建立相关数值计算模型和方案,分析σ1、σ3、GSI和σci影响下大型地下洞室围岩变形、塑性区深度的变化规律。研究结果表明:根据不同σ1、σ3、GSI和σci条件下地下洞室围岩变形、塑性区深度的变化规律,可将围岩变形和塑性区深度划分为3个阶段:基本不变阶段、缓变阶段、陡变阶段。根据洞室围岩的塑性区特征,并结合洞室变形趋势等可将围岩变形和塑性区划分为自稳域、可控域、不可控域,得到基于Hoek-Brown准则的水电站地下洞室地应力-岩体强度-围岩稳定关系。自稳域对应地下洞室围岩处于稳定或基本处于稳定状态;可控域对应围岩有一定的变形或松弛破坏,但在一定支护策略下可控制变形或维持围岩稳定;不可控域对应围岩变形或松弛破坏较为明显,在一般支护策略下无法控制围岩变形或维持围岩稳定。根据研究成果可对Hoek-Brown准则下不同地应力大小、不同岩体强度的地下洞室进行围岩稳定性综合评判,用于系统指导地下洞室群的全过程设计和建设。

基于Hoek-Brown准则的层理岩石强度模型研究

为了提高Hoek-Brown准则对层状岩的适用性,减少对层状岩地质强度指标(GSI)取值的主观性,提出了考虑层状岩石GSI值随层理倾角β变化的修正Hoek-Brown屈服准则。首先收集不同层理角的层状岩在不同围压下的三轴试验数据,结果显示,层状岩石峰值强度与层理角β呈U形曲线关系。然后定义层理倾角β=0°的岩样为完整岩石,采用Hoek-Brown准则得到完整岩石的单轴抗压强度σc与参数mi,以此反算其他层理倾角下对应的GSI值。基于GSI随层理倾角β的变化趋势,采用高斯函数对GSI与β的变化关系进行拟合,从而建立基于Hoek-Brown准则的含层理岩石强度模型。最后对比GSI弱化模型所得峰值强度,验证了提出的修正Hoek-Brown准则对预测不同倾角与围压下层状岩强度具有较好的适用性,并对屈服准则中引入的新参数的意义进行了讨论。

基于Hoek-Brown准则的岩石地基承载力

确定岩体地基承载力的方法主要有岩基荷载试验方法、对岩石饱和单轴抗压强度乘以折减系数的规范法和查表法等。其中岩基荷载试验法结果较准确,但试验设备要求高,试验周期长,费用比较大,仅对少数重要建筑勘察采用。规范法比较简单方便,费用低,但折减系数的确定缺乏理论依据,精度不高。本文依据Hoek-Brown准则,利用岩石的单轴抗压强度,确定了岩体在不同质量程度下的地基极限承载力,并对此做出了说明。同时利用这一方法计算了部分岩石的岩体地基极限承载力表。

基于Hoek-Brown强度折减法的隧道开挖面稳定分析

在隧道开挖过程中,当泥水盾构通过岩层时刀盘磨损加快,需定点开舱检查及更换刀具,此时开挖面的稳定情况对工程安全至关重要。依托南京市江宁区新济洲供水管线廊道工程,采用PLAXIS~(3D)有限元软件建立数值模型,并与现场监测结果进行对比,基于霍克布朗(H-B,Hoek-Brown)准则的强度折减法,计算不同支护应力下隧道开挖面的安全系数,得到各工况下的破坏模式。结果表明:在该工程中,开挖面在各工况下均处于稳定状态,常压开舱安全系数2.9,带压开舱最大安全系数17.2,可优先选择常压开舱;开舱点开挖面附近岩土体破坏模式分为4类:中心内侵型、两侧内侵型、滑落型和外侵型;随着支护压力的增大,安全系数先增大后减小,最大安全系数对应支护压力约为1.35倍的开挖面水土压力。

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.

A generalized three-dimensional failure criterion for rock masses

The smooth convex generalized failure function, which represents 1/6 part of envelope in tile deviatoric plane, is proposed. The proposed function relies on four shape parameters （L, a, b and c）, in which two parameters （a and b） are dependent on the others. The parameter Ls is called extension ratio. The proposed failure function could be incorporated with any two-dimensional （2D） failure criteria to make it a three-dimensional （3D） version. In this paper, a mathematical formulation for incorporation of Hoek-Brown failure criterion with the proposed function is presented. The Hoek-Brown failure criterion is the most suited 2D failure criterion tbr geomaterials. Two types of analyses for best-fitting solution of published true tri-axial test data were made by considering （1） constant extension ratio and （2） variable extension ratio. The shape and strength parameters for different types of rocks have been determined by best-fitting the published true tri-axial test data for both the analyses. It is observed from the best-fitting solution by considering uniform extension ratio （L~） that shape constants have a correlation with Hoek-Brown strength parameters. Thus, only two parameters （c~. and m） are needed for representing the 3D failure criterion for intact rock. The statistical expression between shape and Hoek-Brown strength parameters is given. In the second analysis, when considering varying extension ratio, another parameterfis introduced. The modified extension ratio is related tofand extension ratio. The results at minimum mean misfit for all the nine rocks indicate that the range off varies from 0.7 to 1.0. It is found that mean misfit by considering varying extension ratio is lower than that in the first analysis. But it requires three parameters. A statistical expression betweenfand Hoek-Brown strength parameters has been established. Though coefficient of correlation is not reasonable, we may eliminate it as an extra parameter. At the end of the paper, a methodology has also been given for its application to isotropic jointed rock mass, so that it can be implemented in a numerical code for stability analysis of jointed rock mass structures.

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.

考虑Hoek-Brown准则的盾构隧道掌子面稳定性分析

为了研究Hoek-Brown准则下盾构隧道的稳定性,依据南昌地铁1号线东延段盾构区间隧道工程背景,采用极限分析上限法构建主动坍塌和被动挤出2种破坏模式,推导了盾构隧道掌子面外功率和内能耗散率表达式,通过MATLAB软件算法求解了掌子面达到破坏极限状态时的盾构支护力范围。并通过监测盾构掘进期间的地表位移量,发现地表最大沉降量和最大隆起量均不超过2 mm,地表变形控制良好。

基于Hoek-Brown的双向不等压隧道支护估算及工程应用

现行隧道塑性区分析中常基于轴对称荷载建立分析模型,忽略侧压力带来的影响。增加了对围岩侧压力的考虑,基于Hoek-Brown准则推导了双向不等压圆形隧道的塑性半径及应力计算式。依托滇中引水工程板凳山隧洞的监测数据,结合滑移剪切模型对隧道的极限位移和极限支护应力进行计算。结果表明:在确定围岩材料参数的条件下,塑性边界上的径向应力为恒值;环向应力在θ为0~30°范围内与侧压力成正比,在θ为30°~90°范围内与侧压力成反比,当θ取30°时环向应力为最大值,最终形成蝴蝶状的曲线。隧洞塑性区范围随着侧压力系数的降低呈现出上下端部小,中间部分大的椭圆形,在λ<0.38后,塑性区不再是可完整包裹开挖截面的椭圆形。基于滑移剪切模型对隧洞极限位移和极限支护应力进行计算,完善具有滇中红层特性的隧洞支护特征曲线。根据以上的计算结果对支护方案进行修正,并通过监测结果验证了方案的合理性。

Limit equilibrium analysis for rock slope stability using basic Hoek–Brown strength criterion

Hoek–Brown(HB)strength criterion can reflect rock’s inherent failure nature,so it is more suitable for analyzing the stability of rock slopes.However,the traditional limit equilibrium methods are at present only suitable for analyzing the rock slope stability using the linear equivalent Mohr–Coulomb(EMC)strength parameters instead of the nonlinear HB strength criterion.Therefore,a new method derived to analyze directly the rock slope stability using the nonlinear HB strength criterion for arbitrary curve slip surface was described in the limit equilibrium framework.The current method was established based on certain assumptions concerning the stresses on the slip surface through amending the initial normal stressσ0 obtained without considering the effect of inter-slice forces,and it can satisfy all static equilibrium conditions of the sliding body,so the current method can obtain the reasonable and strict factor of safety(FOS)solutions.Compared with the results of other methods in some examples,the feasibility of the current method was verified.Meanwhile,the parametric analysis shows that the slope angleβhas an important influence on the difference of the results obtained using the nonlinear HB strength criterion and its linear EMC strength parameters.Forβ≤45°,both of the results are similar,showing the traditional limit equilibrium methods using the linear EMC strength parameters and the current method are all suitable to analyze rock slope stability,but forβ>60°,the differences of both the results are obvious,showing the actual slope stability state can not be reflected in the traditional limit equilibrium methods,and then the current method should be used.

基于Hoek-Brown准则和Sarma法的海外水电工程边坡稳定性评价

在海外水利水电工程勘察中,由于中国规范与国外规范的差别,导致岩体力学参数的合理取值一直都是难点,难以得到业主及咨询方的认可。文章以老挝南俄4水电站10#坝段开挖边坡为例,利用基于GSI法的Hoek-Brown强度准则岩体力学参数估计方法,结合开挖地质资料和室内岩石力学试验结果,估算边坡岩体力学参数,分析对比GSI法和中国规范经验取值的差异,综合提出边坡稳定计算力学参数值,并采用Sarma法对坝基边坡的稳定性进行定量计算与分析。研究成果对类似海外水利水电工程地质勘察具有一定的指导意义。

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。