New artificial neural networks for true triaxial stress state analysis and demonstration of intermediate principal stress effects on intact rock strength

Simulations are conducted using five new artificial neural networks developed herein to demonstrate and investigate the behavior of rock material under polyaxial loading. The effects of the intermediate principal stress on the intact rock strength are investigated and compared with laboratory results from the literature. To normalize differences in laboratory testing conditions, the stress state is used as the objective parameter in the artificial neural network model predictions. The variations of major principal stress of rock material with intermediate principal stress, minor principal stress and stress state are investigated. The artificial neural network simulations show that for the rock types examined, none were independent of intermediate principal stress effects. In addition, the results of the artificial neural network models, in general agreement with observations made by others, show （a） a general trend of strength increasing and reaching a peak at some intermediate stress state factor, followed by a decline in strength for most rock types; （b） a post-peak strength behavior dependent on the minor principal stress, with respect to rock type; （c） sensitivity to the stress state, and to the interaction between the stress state and uniaxial compressive strength of the test data by the artificial neural networks models （two-way analysis of variance; 95% confidence interval）. Artificial neural network modeling, a self-learning approach to polyaxial stress simulation, can thus complement the commonly observed difficult task of conducting true triaxial laboratory tests, and/or other methods that attempt to improve two-dimensional （2D） failure criteria by incorporating intermediate principal stress effects.     

中主应力对砾石料变形和强度的影响

对砾石料进行了σ3不变,σ1和σ2等比例同时加载的等b试验,分别研究了中主应力对大、中、小主应变及强度的影响规律。将Mohr-Coulomb准则、Lade-Duncan准则、Matsuoka-Nakai准则和方开泽准则与砾石料的真三轴试验结果进行比较,发现Matsuoka-Nakai准则和方开泽准则反映的内摩擦角与b的关系与试验得到的规律差别较大,Lade-Duncan准则反映的规律与试验结果最接近,但数值上高估了b对内摩擦角的影响。因此,建议了一个破坏准则,推导了该准则的内摩擦角与b的关系式,并用几组真三轴试验结果进行验证,表明本文建议的准则比Lade-Duncan准则、Matsuoka-Nakai准则更准确地反映砾石料的内摩擦角与b的关系。     

Interaction of shotcrete with rock and rock bolts—A numerical study

The shotcrete–rock interaction is very complex and is influenced by a number of factors. The influence of the following factors was investigated by a series of numerical analyses: the surface roughness of the opening, the rock strength and Young's modulus, the discontinuities, the extent and properties of the excavated disturbed zone, the mechanical properties of the interface between shotcrete and rock, and the thickness of the shotcrete lining and the rock bolts. The study was carried out as a sensitivity analysis. The results showed that the rock strength and the surface roughness had significant impact on the number of failures at the rock–shotcrete interface and in the shotcrete lining. Furthermore, the behaviour of the lining is sensitive to small amplitudes of the surface roughness. In all the cases investigated, a high interface strength was favourable. The results indicate that if a thick shotcrete lining is dependent on the bond strength. The benefit of using a thicker lining can be doubtful. The analyses showed that for an uneven surface the extent of the EDZ had a minor effect on the behaviour of the shotcrete lining. Furthermore, if rock bolts were installed at the apex of the protrusion instead of at the depression, the number of failures decreased both at the interface and in the lining.     

考虑中间主应力影响的压力隧洞围岩抗力系数通用计算式

采用双剪统一强度理论,考虑中间主应力影响,建立了压力隧洞围岩抗力系数K的计算方法,给出了其相应解析计算式,并退化到莫尔–库仑屈服模型、特雷斯卡屈服模型,验证了所获成果的正确性与通用性。     

考虑中间主应力的横观各向同性深埋圆隧弹塑性解

平面应变条件下的深埋圆形交通隧道问题一般忽略中间主应力影响,但塑性区围岩的变形与实际情况会产生较大差异。岩土与地下工程中多遇到层状岩体,常将其处理为横观各向同性固体材料。充分考虑中间主应力对深埋圆形隧道的影响,基于平面应变假设得出了与横观各向同性材料相适应的Drucker-Prager准则并将其与Mohr-Coulomb准则精确匹配,在此基础上推导了考虑剪胀特性的横观各向同性理想弹塑性材料在塑性阶段的中间主应力表达式;根据所得的中间主应力表达式,推导出横观各向同性深埋圆形隧道围岩塑性区应力位移解析式;结合实际算例,分析了横观各向同性参数与围岩剪胀角对横观各向同性深埋圆形公路隧道围岩塑性区位移的影响规律。为深埋圆形交通隧道的计算和设计提供更为合理的理论基础。     

A statistical evaluation of intact rock failure criteria constrained by polyaxial test data for five different rocks

In this study we examine seven different failure criteria by comparing them to published polyaxial test data (σ₁>σ₂>σ₃) for five different rock types at a variety of stress states. We employed a grid search algorithm to find the best set of parameters that describe failure for each criterion and the associated misfits. Overall, we found that the polyaxial criteria Modified Wiebols and Cook and Modified Lade achieved a good fit to most of the test data. This is especially true for rocks with a highly σ₂-dependent failure behavior (e.g. Dunham dolomite, Solenhofen limestone). However, for some rock types (e.g. Shirahama Sandstone, Yuubari shale), the intermediate stress hardly affects failure and the Mohr–Coulomb and Hoek and Brown criteria fit these test data equally well, or even better, than the more complicated polyaxial criteria. The values of C₀ yielded by the Inscribed and the Circumscribed Drucker–Prager criteria bounded the C₀ value obtained using the Mohr–Coulomb criterion as expected. In general, the Drucker–Prager failure criterion did not accurately indicate the value of σ₁ at failure. The value of the misfits achieved with the empirical 1967 and 1971 Mogi criteria were generally in between those obtained using the triaxial and the polyaxial criteria. The disadvantage of these failure criteria is that they cannot be related to strength parameters such as C₀. We also found that if only data from triaxial tests are available, it is possible to incorporate the influence of σ₂ on failure by using a polyaxial failure criterion. The results for two out of three rocks that could be analyzed in this way were encouraging.     

Influence of stress path on tunnel excavation response – Numerical tool selection and modeling strategy

The actual stress path in a rock mass during tunnel excavation is complex. To capture the correct tunnel excavation response, it is important to correctly resemble the stress path in situ in the numerical tools.FLAC and Phase² are two powerful two-dimensional continuum codes for modeling soil, rock, and structural behavior, in the fields of geotechnical, geomechanics and in civil and mining engineering. FLAC is based on explicit finite difference formulation while Phase² is based on implicit finite element formulation. When the two codes are applied to the analysis of tunnel excavation problems, difference in results might occur simply due to the different formulation methodologies used in these codes. It is shown that for linear elastic tunnel excavation problems, both codes provide the same result because stress path is unimportant. For tunnel excavation in elasto-plastic materials using long-round drill and blast method, there is significant difference in terms of yielding zone distribution by the two codes if conventional modeling approach is used, especially when the rock strength is low relative to the in situ stress magnitude. The mechanism of the difference is investigated and recommendation provided for choosing appropriate tools and modeling strategies for tunnel excavation problems. The importance of honoring the true stress path in tunnel excavation response simulation is illustrated using a few examples.     

结构强度试验中平面应力区测点相当应力的计算

本文从应力分量叠加的角度出发，提出了工程机械结度试验中在自重和负载联合作用下，平面应力区测点的相当应力的计算方法，并导出了其计算公式。     

Polyaxial strength criterion and closed-form solution for squeezing rock conditions

In this paper,a nonlinear strength criterion is proposed using the average of intermediate(σ_2) and minor(σ_3) principal stresses in place of σ_3 in Ramamurthy(1994)'s strength criterion.The proposed criterion has the main advantages of negligible variation of strength parameters with confining stress and ability to link with conventional strength parameters.Additionally,a new closed-form solution based on the proposed criterion is derived and validated for Chhibro Khodri tunnel.Further,analytical solutions including Singh's elastoplastic theory,Scussel's approach,and closed-form solutions based on conventional and modified Ramamurthy(2007) criteria are compared with the results of proposed approach.It is shown that the in situ squeezing pressure predictions made by the proposed approach are more accurate.Also,a parametric study of the present analytical solution is carried out,which displays explicit dependency of tunnel stability on internal support pressure and tunnel depth.The influence of tunnel geometry is observed to be dependent on the applied support pressure.     

The effect of principal stress orientation on tunnel stability

In order to investigate the effect of principal stress orientation on the stability of regular tunnels and cracked tunnels, experiments by using square specimens with a centralized small tunnel were conducted, and the corresponding numerical study as well as photoelastic study were implemented. Two kinds of materials, cement mortar and sandstone, were used to make tunnel models, and three types of tunnel models were studied, i.e. (1) regular tunnel models loaded by different orientation’s principal stresses, (2) tunnel models with various orientation’s radial cracks in the spandrel under compression, and (3) tunnel models with a fixed radial crack loaded by various orientation’s principal stresses. In the numerical study, the stress intensity factors of the radial cracks were calculated, and the results agree well with the test results. For regular tunnels, when the angle θ between the major principal stress and the tunnel symmetrical axis is 45°, the corresponding tunnel is the most unfavorable; for tunnels with a radial crack in the spandrel, when the angle β between the crack and the tunnel wall is 135°, the corresponding tunnel is the most unfavorable; for tunnels with a β = 130° radial crack, when θ = 0° or θ = 70°, the compressive strengths of the tunnel models are comparatively low, whereas when θ = 90°, it is the highest.     

考虑主应力方向变化的原状黏土强度及超静孔压特性研究

针对许多实际岩土工程问题中,土体所受应力路径主应力方向会旋转变化的特点,采用空心圆柱仪(HCA)对主应力轴方向突变和连续旋转条件下杭州典型原状黏土的强度和孔压特征进行研究。试验表明:土体强度主要受原生各向异性影响,试样在破坏时的主应力作用方向以及中主应力参数是影响土体强度的主要因素,而主应力轴旋转对于强度则无显著影响;试样无论是否经历主应力轴旋转,在破坏时都会有显著的剪切带产生,同时剪切带平面与大主应力作用方向的夹角基本保持一个常数;主应力轴旋转会引起土中孔压积累,积累程度受主应力轴转幅及旋转时剪应力幅值、剪应力水平支配。这部分孔压增量较之主应力方向固定不变剪切产生的极限孔压而言不能忽略。     

中主应力系数对应力主轴循环旋转条件下砂土变形特性的影响

采用香港科技大学的空心圆柱扭剪仪对日本标准丰浦砂进行了四个系列、每个系列包含中主应力系数b=0.1,0.5和1.0三种不同情况的纯应力主轴循环旋转排水试验,即试验过程中控制作用在砂样上的有效主应力的幅值不变,仅应力主轴在0°～180°循环旋转。试验发现中主应力系数b对应力主轴循环旋转条件下砂土的变形特性有显著影响,着重分析了这一参数对纯应力主轴循环旋转条件下砂土的应变分量和体应变的发展、剪应力剪应变关系曲线及流动规律等变形特性的影响。     

砂土中主应力与内摩擦角统一关系研究

提出了一种适用于砂土的各向异性破坏准则,该准则能够反映不同砂土各向异性破坏特性,其参数可以根据某些特定应力区的三轴压缩和三轴拉伸试验结果获得,即根据强度比值确定。为了考虑不同应力区内的中主应力对内摩擦角的影响,提出了广义中主应力系数和广义内摩擦角的概念和表达式,并且建立了基于一种各项异性破坏准则的内摩擦角和中主应力系数的统一显示表达式。通过对一些真三轴试验结果预测,结果表明所提出的摩擦表达式能够整体上描述各向异性砂土的中主应力系数对内摩擦角的影响。     

Precursors for rock fracturing and failure—Part I: IRR image abnormalities

There are many precursors, including the abnormality of infrared radiation (IRR), for rock fracturing and failure. As the comprehensive effect of rock thermoelasticity and rock friction, the study of the IRR abnormality of loaded rock, as one of the important issues of remote sensing rock mechanics (RSRM), is facilitated by the fast development of IR remote sensing imaging technology. In view of energy input and consumption by the loading system, comprised of loader, rock and air, the mechanism of surface IRR from loaded rock is studied. The concepts that surface IRR is the comprehensive effect of a series of physical–mechanical processes inside loaded rock and that the thermoelastic effect and the frictional–thermal effect are two of the main mechanisms are presented here. Based on retrospective investigation of the fundamental experiments on RSRM during the past decade, it is concluded that there are two kinds of IRR abnormality as precursors of rock fracturing and failure: IRR image abnormality and IRR temperature curve abnormality. The spatial–temporal evolution of abnormal surface IRR images of loaded rock in a condition of uniaxial stress, compressive shear, biaxial stress, frictional slide and impact is systematically analyzed. The fact that large IRR can occur in the fracturing center of compressively loaded and shearing fractured strong and brittle rock is also revealed. Finally, the relation between rock stress and IRR temperature are studied based on thermomechanical coupling theory for solid materials. It is concluded that IRR image abnormalities are important precursors for rock fracturing and meaningful for the forecast of rockbursts and tectonic earthquakes.     

Measurements of induced stress and strength in the near-field around a tunnel and associated estimation of the Mohr–Coulomb parameters for rock mass strength

The state of induced stress measured by the compact conical-ended borehole overcoring technique in the immediate roof of an approach tunnel excavated under high rock stress is described. During the measurements, core disking was observed. An X-ray Computed Tomography (CT) scanner was used to select strain data uninfluenced by the core disking; then the induced rock stress was estimated from selected strain data. From these results, it is shown that the non-destructive investigation using X-ray CT is effective for visualization of the fracturing within cores and the selection of strains measured during overcoring. Furthermore, the Mohr–Coulomb failure criterion parameters for the rock mass were estimated by comparing the measured stresses with the shear strength of in situ rock and the uniaxial compressive strength determined in laboratory tests.     

Influence of grain size on strength of polymineralic crystalline rock: New insights from DEM grain-based modeling

Grain size effect on rock strength is a topic of great interest in geotechnical engineering.A consensus obtained from earlier laboratory tests is that rock strength generally decreases with the increase of grain size for both silicate and carbonate rocks;however,some recent numerical results conflict with such laboratory test results.To address this intriguing issue,the effect of grain size on strength of polymineralic crystalline rock with low porosity is investigated numerically using the grain-based modeling(GBM) approach in discrete element method(DEM) by interpreting micro-cracking process in response to loading.In agreement with some previous DEM simulation results,the simulated rock strength is found to increase with increasing grain size for both homogeneous and heterogeneous models,even when the number of assembled disks in one mineral grain changes.The mechanism of strength increase with increasing grain size is mainly associated with the number of assembled smooth-joint contacts along grain interfaces and the generation of grain boundary cracks in response to loading.The grain interfaces significantly weaken the integrity of the rock model,which is similar to effects of inherent defects in real rock.As the grain size increases,fewer grain interfaces are built in the model and the rock strength becomes much higher.Hence,by solely changing the mineral grain size in a model,the mechanism of grain size effect as observed in laboratory tests cannot be replicated.To address this issue,a method of degradation of grain boundary strength parameters is used to mimic the possible mechanism of grain size effect.The simulated strength using the method becomes comparable with those obtained from laboratory tests when the heterogeneity in the rock is considered.Degradation of grain boundary parameters with increasing grain size provides a plausible explanation for the grain size effect on rock strength.     

An overview of particle-based numerical manifold method and its application to dynamic rock fracturing

This review summarizes the development of particle-based numerical manifold method (PNMM) and its applications to rock dynamics. The fundamental principle of numerical manifold method (NMM) is first briefly introduced. Then, the history of the newly developed PNMM is given. Basic idea of PNMM and its simulation procedure are presented. Considering that PNMM could be regarded as an NMM-based model, a comparison of PNMM and NMM is discussed from several points of view in this paper. Besides, accomplished applications of PNMM to the dynamic rock fracturing are also reviewed. Finally, some recommendations are provided for the future work of PNMM.     

Precursors for rock fracturing and failure—Part II: IRR T-Curve abnormalities

There are many precursors including the abnormality of infrared radiation (IRR) for rock fracturing. The temporal evolution of surface IRR from loaded rock is the combined effect of rock thermoelasticity, pore gas desorbing–escaping, fracture propagation and extension, rock friction, heat transfer and environmental radiation. Being the integral indicator of the surface IRR energy, the mean IRR temperature (AIRT) is selected as the quantitative index to study the temporal evolution of IRR from loaded rock and to identify the precursors for rock fracturing and failure. This paper introduces some typical AIRT curves of uniaxially loaded, compressively sheared and biaxially loaded rock samples. The temporal evolution features of the AIRT curves and three precursor messages, which are short dropping, fast rising and dropping-to-rising, for rock fracturing are analyzed. For theoretical interpretation, the mechanism of AIRT abnormality is studied by taking the actuator, the rock sample and the environment as an independent system in an energy balance state. The heat transfer, as well as the thermoelastic effect based on the sum of principal stresses, has a positive or negative effect on AIRT; the desorbing and escaping of pore gas, as well as the production of new fractures and the expansion of initial fissures, joints and new produced fractures, have a negative effect on AIRT, while the friction action between fractures and between grains has a positive effect on AIRT. It is concluded that the occurrence of precursors is at 77–94% rock strength, i.e., stress peak, and the compressively loaded rock and biaxially loaded rock have clear AIRT precursors for rock fracturing and failure.     

Overhanging rock slope by design: An integrated approach using rock mass strength characterisation,large-scale numerical modelling and limit equilibrium methods

Overhanging rock slopes(steeper than 90°) are typically avoided in rock engineering design, particularly where the scale of the slope exceeds the scale of fracturing present in the rock mass. This paper highlights an integrated approach of designing overhanging rock slopes where the relative dimensions of the slope exceed the scale of fracturing and the rock mass failure needs to be considered rather than kinematic release of individual blocks. The key to the method is a simplified limit equilibrium(LE) tool that was used for the support design and analysis of a multi-faceted overhanging rock slope. The overhanging slopes required complex geometries with constantly changing orientations. The overhanging rock varied in height from 30 m to 66 m. Geomechanical modelling combined with discrete fracture network(DFN)representation of the rock mass was used to validate the rock mass strength assumptions and the failure mechanism assumed in the LE model. The advantage of the simplified LE method is that buttress and support design iterations(along with sensitivity analysis of design parameters) can be completed for various cross-sections along the proposed overhanging rock sections in an efficient manner, compared to the more time-intensive, sophisticated methods that were used for the initial validation. The method described presents the development of this design tool and assumptions made for a specific overhanging rock slope design. Other locations will have different geological conditions that can control the potential behaviour of rock slopes, however, the approach presented can be applied as a general guiding design principle for overhanging rock cut slope.     

岩土类摩擦材料空间Mohr应力圆与强度准则

 分析传统空间Mohr应力圆理论,并指出该理论不能完全反映双向受力下(即考虑中间主应力时)岩土类摩擦材料的应力状态。试验表明岩土类摩擦材料包括混凝土、岩石和土体在双向受压下(以压为正,此时?3 = 0)抗压强度大于单向受压(此时?2 = ?3 = 0)抗压强度,由此提出双向受力状态下2个主剪切平面上承载能力比单向受力状态下剪切平面上的承载能力大,其原因在于双向受力状态下的法向应力大于单向受力下的法向应力,从而使摩擦力和黏聚力增大。这表明空间应力状态下最大压应力?1随?2增大而增大,此时Mohr圆也随之增大。当?2从?2 = ?3 = 0增大至?2 =?1时,不仅2个小极限应力圆在变动,而且3个极限应力圆都在不断增大,由此建立适应双向受力下岩土类摩擦材料的空间Mohr应力圆理论。考虑上述特性,将基于传统空间Mohr应力圆理论的等强度能量强度准则发展为变强度能量强度准则,这一准则能很好地反映岩土类摩擦材料在双向受力条件下的强度特性。