Retrospective and prospective review of the generalized nonlinear strength theory for geomaterials

Strength theory is the basic theory for calculating and designing the strength of engineering materials in civil,hydraulic,mechanical,aerospace,military,and other engineering disciplines.Therefore,the comprehensive study of the generalized nonlinear strength theory(GNST)of geomaterials has significance for the construction of engineering rock strength.This paper reviews the GNST of geomaterials to demonstrate the research status of nonlinear strength characteristics of geomaterials under complex stress paths.First,it systematically summarizes the research progress of GNST(classical and empirical criteria).Then,the latest research the authors conducted over the past five years on the GNST is introduced,and a generalized three-dimensional(3D)nonlinear Hoek‒Brown(HB)criterion(NGHB criterion)is proposed for practical applications.This criterion can be degenerated into the existing three modified HB criteria and has a better prediction performance.The strength prediction errors for six rocks and two in-situ rock masses are 2.0724%-3.5091%and 1.0144%-3.2321%,respectively.Finally,the development and outlook of the GNST are expounded,and a new topic about the building strength index of rock mass and determining the strength of in-situ engineering rock mass is proposed.The summarization of the GNST provides theoretical traceability and optimization for constructing in-situ engineering rock mass strength.

Failure mechanism of bolting support and high-strength bolt-grouting technology for deep and soft surrounding rock with high stress

In deep underground mining, the surrounding rocks are very soft with high stress. Their deformation and destruction are serious, and frequent failures occur on the bolt support. The failure mechanism of bolt support is proposed to solve these problems. A calculation theory is established on the bond strength of the interface between the anchoring agent and surrounding rocks. An analysis is made on the influence law of different mechanical parameters of surrounding rocks on the interfacial bond strength. Based on the research, a new high-strength bolt-grouting technology is developed and applied on site. Besides, some helpful engineering suggestions and measures are proposed. The research shows that the serious deformation and failure, and the lower bond strength are the major factors causing frequent failures of bolt support. So, the bolt could not give full play to its supporting potential. It is also shown that as the integrity, strength, interface dilatancy and stress of surrounding rocks are improved, the bond strength will increase. So, the anchoring force on surrounding rocks can be effectively improved by employing an anchoring agent with high sand content, mechanical anchoring means, or grouting reinforcement. The new technology has advantages in a high strength, imposing pre-tightening force, and giving full play to the bolt supporting potential. Hence, it can improve the control effect on surrounding rocks. All these could be helpful references for the design of bolt support in deep underground mines.

Cohesive Strength and Seismogenic Stress Pattern along the Active Basement Faults of the Precordillera-Sierras Pampeanas Ranges,Western Argentina:An Experimental Analysis by Means of Numerical Model

A two-dimensional finite element method (FEM) model that incorporates faults,elastic rock physical properties,topographical load due to gravity and far-field plate velocity boundary conditions was used to recognize the seismogenic stress state along the fold-and-thrust belt of the Precordillera-Sierras Pampeanas ranges of western Argentina. A plane strain model with nine experiments was presented here to examine the fault strength with two major rock phyical properties:cohesion and angle of internal friction. Mohr-Coulomb failure criterion with bulk rock properties were applied to analyse faults. The stress field at any point of the model was assumed to be comprised of gravitational and tectonic components. The analysis was focused to recognize the seismogenic shear strain concentrated in the internal-cristaline domain of the orogene shown by the modeling. Modeling results are presented in terms of four parameters,i. e.,(i) distributions,orientations,and magnitudes of principal stresses (σ1 and σ3),(ii) displacement vector,(iii) strain distribution,and (iv) maximum shear stress (τmax) contour line within the model. The simulation results show that the compressive stress is distributed in and around the fault systems. The overall orientation of σ1 is in horizontal directions,although some stress reorientations do occur within weaker parts,especially subsequent to the faults. A large-scale shear stress is accumulating along the active faults of Tapias-Villicum Fault (TVF),Salinas-Berros Fault (SBF),Ampacama-Niquizanga Fault (ANF) and Las Charas Fault (CF),which could act as local stress and strain modulators to localize the earthquakes occurrence.

A true triaxial strength criterion for rocks by gene expression programming

Rock strength is a crucial factor to consider when designing and constructing underground projects.This study utilizes a gene expression programming(GEP)algorithm-based model to predict the true triaxial strength of rocks,taking into account the influence of rock genesis on their mechanical behavior during the model building process.A true triaxial strength criterion based on the GEP model for igneous,metamorphic and magmatic rocks was obtained by training the model using collected data.Compared to the modified Weibols-Cook criterion,the modified Mohr-Coulomb criterion,and the modified Lade criterion,the strength criterion based on the GEP model exhibits superior prediction accuracy performance.The strength criterion based on the GEP model has better performance in R2,RMSE and MAPE for the data set used in this study.Furthermore,the strength criterion based on the GEP model shows greater stability in predicting the true triaxial strength of rocks across different types.Compared to the existing strength criterion based on the genetic programming(GP)model,the proposed criterion based on GEP model achieves more accurate predictions of the variation of true triaxial strength(s1)with intermediate principal stress(s2).Finally,based on the Sobol sensitivity analysis technique,the effects of the parameters of the three obtained strength criteria on the true triaxial strength of the rock are analysed.In general,the proposed strength criterion exhibits superior performance in terms of both accuracy and stability of prediction results.

Experimental study on the mechanical and failure behaviors of deep rock subjected to true triaxial stress:A review

It has become an inevitable trend of human development to seek resources from the deep underground.However,rock encountered in deep underground engineering is usually in an anisotropic stress state(σ_(1)>σ>σ_(3))due to the influences of geological structures and engineering disturbances.It is therefore essential to study the mechanical,seepage,and dynamic disaster behaviors of deep rock under true triaxial stress to ensure the safe operation of deep rock engineering and the efficient exploitation of deep resources.In recent years,experimental techniques and research on true triaxial rock mechanics have achieved fruitful results that have promoted the rapid development of deep rock mechanics;thus,it is necessary to systematically review and summarize these developments.This work first introduced several typical true triaxial testing apparatus and then reviewed the corresponding research progress on rock deformation,strength,failure mode,brittleness,and energy as well as the 3D volumetric fracturing(dynamic disaster)properties of deep rocks under true triaxial stress.Then,several commonly used true triaxial rock strength criteria and their applicability,the permeability characteristics and mathematical models of deep reservoir rocks,and the disaster-causing processes and mechanisms of disturbed volumetric fracturing(rockburst,compound dynamic disasters)in deep rock engineering were described.This work may provide an essential reference for addressing the true triaxial rock mechanics issues involved in deep rock engineering,especially regarding the stability of surrounding rock at depth,disaster prevention and control,and oil and gas exploitation.

Failure criterion for soft rocks considering intermediate principal stress

The significant differences between hard rocks(more brittle)and soft rocks(more ductile)may suggest the use of different failure criteria.A strength criterion for soft rocks that includes intermediate principal stress was proposed.The new criterion includes two independent parameters:the uniaxial compressive strength(σ_(ci)),which can be obtained from common laboratory tests or indirectly estimated by alternative index tests in the laboratory or field;and f(joint),which is used to characterize the rock mass quality and can be easily estimated.The authors compared the predictive capabilities of the new criterion with other criteria using the database of soft rocks under two conditions:with and without triaxial data.For the estimation of triaxial and true-triaxial strengths,the new criterion generally produced a better fit.The proposed criterion is practical for an approximate first estimation of rock mass strength,even without triaxial data,as it balances accuracy(lower prediction error)and simplicity(fewer independent parameters).

Experimental study and stress analysis of rock bolt anchorage performance

A new method was developed to apply pull-and-shear loads to the bolt specimen in order to evaluate theanchorage performance of the rebar bolt and the D-Bolt. In the tests, five displacing angles （0°, 20°, 40°,60°, and 90°）, two joint gaps （0 mm and 30 mm）, and three kinds of host rock materials （weak concrete,strong concrete, and concrete-granite） were considered, and stressestrain measurements were conducted.Results show that the ultimate loads of both the D-Bolt and the rebar bolt remained constantwith any displacing angles. The ultimate displacement of the D-Bolt changed from 140 mm at the0 displacing angle （pure pull） to approximately 70 mm at a displacing angle greater than 40. Thedisplacement capacity of the D-Bolt is approximately 3.5 times that of the rebar bolt under pure pull and50% higher than that of the rebar bolt under pure shear. The compressive stress exists at 50 mm from thebolt head, and the maximum bending moment value rises with the increasing displacing angle. The rebarbolt mobilises greater applied load than the D-Bolt when subjected to the maximum bending. Theyielding length （at 0） of the D-Bolt is longer than that of the rebar bolt. The displacement capacity of thebolts increased with the joint gap. The bolt subjected to joint gap effect yields more quickly with greaterbending moment and smaller applied load. The displacement capacities of the D-Bolt and the rebar boltare greater in the weak host rock than that in the hard host rock. In pure shear condition, the ultimateload of the bolts slightly decreases in the hard rock. The yielding speed in the hard rock is higher thanthat in the weak rock. 2014 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Production and hosting byElsevier B.V. All rights reserved.

Full-scale pullout tests of rock anchors in a limestone quarry focusing on bond failure at the anchor-grout and grout-rock interfaces

Rock anchors are a common safety measure for stabilising large-scale infrastructure,such as bridge towers,retaining walls,rock slopes and windmills.There are four principal failure modes for rock anchors:(a)tensile failure of the steel anchor,(b)anchor-grout interface failure,(c)grout-rock interface failure,and(d)rock mass uplift.Field tests were performed in a limestone quarry.These tests were designed to test failure modes B and C through pullout.In the tests of failure mode B,the shear stress on the anchor-grout interface is the largest at the top of the grout column and attenuates towards the distal end for small loads.The shear stress becomes uniformly distributed when the applied load is approximately 50%of the ultimate pullout load.The anchors designed to test failure mode C were installed with an endplate and had a higher toughness than the straight bar anchors.The shear stress on the grout-rock interface is the largest at the endplate and attenuates upward before slip starts along the interface.When the ultimate pullout load is reached,and the grout column starts to slip,the shear stress is approximately constant.The bond shear strength on the anchor-grout interface was approximately 20%of the uniaxial compressive strength of the grout,and the bond strength of the grout-rock interface was around 5%for that of the grout.The grout-rock interface is likely determined by whichever is weaker,the grout or the rock.

Effect of intermediate principal stress on strength of soft rock under complex stress states

A series of numerical simulations of conventional and true triaxial tests for soft rock materials using the three-dimensional finite difference code FLAC3D were presented. A hexahedral element and a strain hardening/softening constitutive model based on the unified strength theory(UST) were used to simulate both the consolidated-undrained(CU) triaxial and the consolidated-drained(CD) true triaxial tests. Based on the results of the true triaxial tests simulation, the effect of the intermediate principal stress on the strength of soft rock was investigated. Finally, an example of an axial compression test for a hard rock pillar with a soft rock interlayer was analyzed using the two-dimensional finite difference code FLAC. The CD true triaxial test simulations for diatomaceous soft rock suggest the peak and residual strengths increase by 30% when the effect of the intermediate principal stress is taken into account. The axial compression for a rock pillar indicated the peak and residual strengths increase six-fold when the soft rock interlayer approached the vertical and the effect of the intermediate principal stress is taken into account.

Crustal Stress Measurement for Significant Project Construction and Its Application in Design

The hydrofracturing technique has developed into a reliable and practical method for determining the original three-dimensional crustal stress state of underground caverns,the load-bearing capacity of a high pressure cavern itself,and the high pressure hydraulic permeability of rock masses,and has also been extensively used in disposal of nuclear waste,long and deeply-buried traffic channels and high-pressure cavern engineering for hydraulic power plants.The practice shows that the comprehensive measurement of the physical parameters of the rock mass and taking full use of the wall rock load-bearing capacity to optimize the engineering design hold are very useful in ensuring the engineering safety and improving the design level.

Shear strength criteria for rock,rock joints,rockfill and rock masses:Problems and some solutions

Although many intact rock types can be very strong,a critical confining pressure can eventually be reached in triaxial testing,such that the Mohr shear strength envelope becomes horizontal.This critical state has recently been better defined,and correct curvature or correct deviation from linear Mohr-Coulomb（MC） has finally been found.Standard shear testing procedures for rock joints,using multiple testing of the same sample,in case of insufficient samples,can be shown to exaggerate apparent cohesion.Even rough joints do not have any cohesion,but instead have very high friction angles at low stress,due to strong dilation.Rock masses,implying problems of large-scale interaction with engineering structures,may have both cohesive and frictional strength components.However,it is not correct to add these,following linear M-C or nonlinear Hoek-Brown（H-B） standard routines.Cohesion is broken at small strain,while friction is mobilized at larger strain and remains to the end of the shear deformation.The criterion ＇c then σn tan φ＇ should replace ＇c plus σn tan φ＇ for improved fit to reality.Transformation of principal stresses to a shear plane seems to ignore mobilized dilation,and caused great experimental difficulties until understood.There seems to be plenty of room for continued research,so that errors of judgement of the last 50 years can be corrected.

Upper Limit for Rheological Strength of Crust in Continental Subduction Zone:Constraints Imposed by Laboratory Experiments

The transitional pressure of quartz coesite under the differential stress and highly strained conditions is far from the pressure of the stable field under the static pressure. Therefore, the effect of the differential stress should be considered when the depth of petrogenesis is estimated about ultrahigh pressure metamorphic (UHPM) rocks. The rheological strength of typical ultrahigh pressure rocks in continental subduction zone was derived from the results of the laboratory experiments. The results indicate the following three points. (1) The rheological strength of gabbro, similar to that of eclogite, is smaller than that of clinopyroxenite on the same condition. (2) The calculated strength of rocks (gabbro, eclogite and clinopyroxenite) related to UHPM decreases by nearly one order of magnitude with the temperature rising by 100 ℃ in the range between 600 and 900 ℃. The calculated strength is far greater than the faulting strength of rocks at 600 ℃, and is in several hundred to more than one thousand mega pascals at 700-800 ℃, which suggests that those rocks are located in the brittle deformation region at 600 ℃, but are in the semi brittle to plastic deformation region at 700-800 ℃. Obviously, the 700 ℃ is a brittle plastic transition boundary. (3) The calculated rheological strength in the localized deformation zone on a higher strain rate condition (1.6×10 -12 s -l ) is 2-5 times more than that in the distributed deformation zone on a lower strain rate condition (1.6×10 -14 s -1 ). The average rheological stress (1 600 MPa) at the strain rate of 10 -12 s -1 stands for the ultimate differential stress of UHPM rocks in the semi brittle flow field, and the average rheological stress (550-950 MPa) at the strain rate of l0 -14 - 10 -13 s -l stands for the ultimate differential stress of UHPM rocks in the plastic flow field, suggesting that the depth for the formation of UHPM rocks is more than 20-60 km below the depth estimated under static pressure condition due to the effect of the differential stress.

Stress analysis of single joint rock mass under triaxial compression

Based on the fundamental principle of rock mechanics, the stresses of single joint rock mass under three-dimensional compression were analyzed. The effect of the in-termediate principle stress on the strength of single joint rock mass were discussed in par-ticular. It is found that the strength of single joint rock are affected by the intermediate principal stress, which may be the main factor in some conditions.

多因素影响下巷道围岩稳定性分析及优化设计研究

针对深部煤层巷道矿压显现剧烈且巷道变形难以控制的问题,基于Kastner公式对巷道高宽比、侧压系数、埋深、断面形状、围岩强度5种影响巷道围岩稳定性的因素展开正交数值模拟实验,通过方差和直观分析图法研究了各因素对巷道变形破坏的敏感性。采用平面弹性复变函数理论分析了不同侧压系数与巷道高宽比下椭圆和矩形巷道围岩的应力分布规律,对椭圆形和矩形巷道宽高比和形状进行了优化设计。研究结果表明:围岩强度与侧压系数是影响巷道围岩稳定性的主要因素,埋深、断面形状、巷道高宽比为次要因素;椭圆形巷道在等轴应力比下围岩应力差值最小;矩形巷道宽度为5 m、高宽比为0.6左右时,应力集中程度较小;针对矩形巷道应力快速增高区,在考虑承压特性和断面利用率的基础上设计了圆角矩形优化巷道,确立了圆角半径的计算公式,通过数值模拟验证了其良好的性能。

考虑中间主应力效应的修正Hoek-Brown真三轴强度准则

为改善Hoek-Brown强度准则未考虑中间主应力对岩石强度的影响,通过岩石真三轴试验结果分析了岩石强度的演化规律,引入中间主应力系数,量化分析主应力系数对岩石真三轴强度的影响,考虑Hoek-Brown强度准则中的参数和岩石应力水平间的关联性,提出了基于拉格朗日插值方法的修正岩石真三轴Hoek-Brown强度准则,分析了其空间包络特征。最后,利用7种岩石的真三轴试验数据与其它3种真三轴强度准则进行最优拟合误差分析,探讨了修正强度准则的合理性。研究结果表明:岩石强度随着最小主应力的增加逐渐增大,随着中间主应力的增加则呈现先增大后减小的变化规律,表现出显著的区间效应;修正强度准则不仅能够继承Hoek-Brown强度准则在子午面上的非线性优点,且能够表征岩石强度在应力空间中的基本特性;线性和非线性插值形式的修正强度准则空间包络面分别为非等边的六棱锥面以及能够满足拉压子午面区间连续光滑要求的圆锥面;修正强度准则能够较好地预测岩石真三轴试验强度,较为合理地反映中间主应力对岩石强度的影响;相比于线性插值形式强度准则,二次插值形式强度准则能够提高岩石强度的预测精度1.2~2.0倍;相较于其他真三轴强度准则,修正强度准则对不同硬脆性岩石的真三轴试验结果均具有良好的强度预测精度,体现了修正强度准则的适用性和可靠性。

不同控制方式和卸荷应力路径下类岩石节理剪切强度特征研究

为研究不同控制方式和卸荷应力路径下岩石节理失稳剪切强度特征,借助RDS-200型岩石节理剪切试验系统开展了2种控制方式和3种卸荷应力路径下的类岩石节理直剪试验。结果表明:(1)采用应力控制方式进行切向加卸载时,各剪切加卸载路径下,节理剪切应力-时间曲线多存在失稳跌落现象,剪切应力-位移曲线失稳后多表现为折线形式。(2)与采用应力控制方式进行切向加载的试样结果相比,采用位移控制方式进行切向加载、采用应力控制方式进行法向卸载并保持剪切应力恒定、采用应力控制方式进行法向卸载和切向加载、采用应力控制方式同时进行法向和切向卸载的试样失稳剪切强度均有所降低;节理黏聚力减小百分比平均值为36.07%,而内摩擦角变化范围仅在4.12%以内,所以黏聚力降低是节理失稳剪切强度降低的主要原因。(3)以采用应力控制方式进行切向加载试样的拟合摩尔-库仑公式为基准,位移控制方式或其他采用应力控制方式的加卸载应力路径下试样失稳剪切强度的相对误差平均值最大可达55.78%。经引入黏聚力修正系数k对摩尔-库仑准则进行修正后,相对误差平均值的最大值减小到5.23%,说明对经受位移控制方式或采用应力控制方式的其他加卸载应力路径的工程节理来说,进行黏聚力的折减修正是必要和可行的。研究结果对不同控制方式及卸荷应力路径下岩体节理剪切承载能力的准确估计具有一定参考价值。

卸载状态下非均质圆形寒区隧道围岩弹塑性统一解

以统一强度理论作为卸载状态下寒区隧道冻结围岩屈服准则,综合考虑围岩非均质特性和中间主应力效应对冻结围岩强度影响,建立寒区隧道应力位移弹塑性力学模型,联合各区域边界条件,计算获得冻结围岩均质与非均质状态下,弹性解、塑性统一解以及塑性区半径的隐式方程,分别对其应力位移场讨论分析。研究表明:考虑冻结围岩的非均质特性,塑性区环向应力峰值增大40%,塑性区范围相对减少40.4%,内壁位移减少9.3%,弹性极限承载力提高41%,塑性极限承载力提高14%,影响显著。中间主应力效应能充分发挥非均质冻结围岩承载潜能,计算得到的承载力明显增大,塑性半径明显减小。所得结果可为寒区隧道开挖支护设计以及数值模拟,提供理论指导。

岩石卸荷的Mogi-Coulomb强度准则适用性研究

大量工程实践表明:岩石在卸荷条件下的强度特性与加载条件下相比,存在本质上的不同。结合岩石卸荷的破坏特征和强度特性,建立了岩桥贯通力计算模型,并基于应力强度因子叠加减原理,推导了岩石卸荷条件下的岩桥贯通力计算公式,从而探究Mogi-Coulomb强度准则对于岩石卸荷强度的适用性。将岩桥贯通力作为表征岩石卸荷破坏的强度参数,并与Mogi-Coulomb强度准则的核心参数——八面体剪应力进行对比,发现二者的量值具有极高相似性,这一发现可以间接证明Mogi-Coulomb强度准则适用于岩石卸荷强度方面的相关研究。本文揭示了岩石卸荷破坏时其岩桥贯通与八面体剪应力之间存在的紧密联系,可为岩石卸荷破坏的研究提供借鉴与参考。

陡倾片麻岩滑坡演化过程研究——以兰陵溪滑坡为例

弯曲-倾倒破坏是陡倾顺层岩质斜坡的一种变形模式,当其折断面贯通形成滑移面时,斜坡演化为滑坡。以三峡库区兰陵溪滑坡为例,引入反转应力法、梁板强度理论对滑坡变形模式与演化过程进行了研究。结果表明:①该岩质斜坡具有典型的陡倾顺层、岩体结构软硬相间的特点,为其发生弯曲-倾倒破坏提供了先天性条件。②差异性风化是兰陵溪滑坡发生弯曲-倾倒变形的主要原因,片状片麻岩抗弯强度变弱,促使片麻岩逐渐发生弯曲,最后产生弯曲折断-倾倒变形破坏。③兰陵溪滑坡演化过程历经差异性风化、岩层弯曲变形、岩层倾倒破坏、折断面贯通等4个阶段,所有折断面贯通形成潜在滑移面时,斜坡演化为滑坡。研究成果可为该滑坡工程治理提供理论依据,也可为同类型岩质斜坡治理提供思路。