Analysis of the in situ Hydromechanical Behavior of a Fractured Calcareous Rock Mass

Summary. Hydromechanical experiments have been carried out since 1997 within a small fractured calcareous rock mass in southeastern France, at a site called Coaraze. Simultaneous measurements of fluid pressure and joint displacement were performed during these experiments. The interpretation generated has led to characterizing various types of hydromechanical behavior of the jointed rock mass and has provided several lessons. An original analytical interpretation, coupled with a modeling approach, has allowed one to derive the in situ normal joint stiffness, which proves to be highly non-linear. It has been shown that a coefficient able to take into account stiffness contribution from the surrounding rock mass must be included in order to fully interpret the pressure-displacement curves. This analytical interpretation also yields an estimate of the normal stress across the fracture. A comparison between in situ data and laboratory tests is also presented.     

Applying bi-directional evolutionary structural optimisation method for tunnel reinforcement design considering nonlinear material behaviour

In the empirical methods for reinforcement design of underground excavations, an even distribution of rock bolts is generally recommended. This work proves that this design is not necessarily optimal and shows how the state-of-the-art reinforcement design could be improved through topology optimisation techniques. The Bidirectional Evolutionary Structural Optimisation (BESO) method has been extended to consider nonlinear material behaviour. An elastic perfectly-plastic Mohr–Coulomb model is utilised for both original rock and reinforced rock. External work along the tunnel wall is considered as the objective function. Various in situ stress conditions with different horizontal stress ratios and different geostatic stress magnitudes are investigated through several examples. The outcomes show that the proposed approach is capable of improving tunnel reinforcement design. Also, significant difference in optimal reinforcement distribution for the cases of linear and nonlinear analysis results proves the importance of the influence of realistic nonlinear material properties on the final outcome.     

Instantaneous Friction Angle and Cohesion of 2-D and 3-D Hoek–Brown Rock Failure Criteria in Terms of Stress Invariants

The Mohr–Coulomb (M–C) failure criterion is one of the most widely used failure criteria in rock mechanics, although it has a number of shortcomings such as neglecting the nonlinear strength observed in rock or the effect of the intermediate principal stress σ ₂. Other failure criteria have been proposed to effectively include in the predictions of failure the non-linear response of rock to confinement or the effects of the intermediate principal stress. The M–C criterion is still widely used, and it is arguably the criterion most used in practice. For example, stability evaluations of shallow rock structures such as slopes and foundations are routinely carried out by estimating a friction angle and a cohesion of the rock mass. To include the dependency of cohesion and friction angle on stresses, efforts are being made to estimate equivalent values of the M–C parameters for the range of stresses applicable to a particular design. The paper suggests a new and convenient approach to find the equivalent friction angle and cohesion from any failure criterion that can be expressed in terms of the Nayak and Zienkiewicz’s stress invariants. To demonstrate the capabilities and application of the methodology, the new approach is applied to two failure criteria: the Hoek–Brown (H–B) criterion and the Hoek–Brown and Willam–Warnke (HB–WW) criterion, 2-D and 3-D failure criteria, respectively. Results from the new method, in terms of equivalent friction and cohesion for the H–B criterion, are exactly the same as the results obtained from Balmer’s theory, which confirms the validity of the new method. The predicted equivalent friction and cohesion for the HB–WW criterion show a dependency on σ ₂, which does not occur for a 2-D failure criterion.     

An examination of in situ rock stress estimation using the Kaiser effect

When rock cores are loaded in uniaxial compression, acoustic emission occurs when the stress reaches a level greater than that which the rock has previously experienced. This phenomenon, known as the Kaiser Effect, has been used as an indirect method of estimating the in situ stress field in rock masses. If the procedure is valid, then the Kaiser Effect method has the advantage that the stress field can be estimated through laboratory tests on rock cores, rather than the field drillhole methods of overcoring and hydraulic fracturing. However, the Kaiser Effect method is an enigma: on the one hand, there are good reasons why the method cannot be valid; on the other hand, there are reports in the literature of it being successfully applied. In this paper, we explore the variety of geological and mechanical factors involved and report on a case example for the Olkiluoto crystalline rock site in western Finland. We conclude that the Kaiser Effect method for stress measurement is only likely to be successful if it is supported by key geological and other stress measurement information and if certain procedures are followed as explained in the paper.     

Demonstration of spatial anisotropic deformation properties for jointed rock mass by an analytical deformation tensor

This paper develops a joint deformation tensor (JD), which considers all of the joint's mechanical and geometrical parameters that affect the deformability of the rock mass. The method based on JD (JD method) and an elastic deformation anisotropy index (EDAI) are deduced for estimating the spatial anisotropy deformation of a jointed rock mass. The numerical modeling and in situ true triaxial compressive experiments well verified the effectiveness of the EDAI and JD method for the rock mass containing one joint set, orthogonal joint sets or the rock mass containing any types of joint network with unity stiffness ratio.     

In-situ rock stress measurement from rock cores using the acoustic emission method and deformation rate analysis

In this study the possibilities of the acoustic emission (AE) technique and deformation rate analysis (DRA) were investigated to measure in situ rock stress. The rock cores were obtained from three vertically drilled exploratory boreholes from the surface and one borehole drilled from within an underground coal mine. The AE method was found to determine in situ rock stress with reasonable accuracy using AE signatures in repeated loadings of a rock core specimen. Based on the results of in situ stress estimation from the AE method, the time interval, up to seven years, did not strongly influence the previous stress determination using the AE method. Cored rock recollected the in situ stress condition reasonably well (within ±10%), when compared to the results from over coring and hydraulic fracturing technique. Also, there was significant correlation between overburden pressure and estimated vertical stress from the AE method.     

Rock mass characterization by fractal dimension

Fractal theory is used in the present study to develop a more reliable method for rock mass characterization. Field studies have been carried out in opencast mines of dolomite, limestone, fluorite; sandstone and shale in coalmines. Fractal dimension of blasted fragments (D_frag) and in situ rock blocks (D_{in situ}) is calculated using size distribution curves according to Schumann's model. Based on the co-relation between Uniaxial Compressive Strength (UCS) and D_frag, it is observed that change in fractal dimension is nominal beyond the UCS value of 20. From the co-relation between Bieniawaski's Rock Mass Rating (RMR) and D_{in situ}, it is found that there is a sharp increase in fractal dimension for RMR greater than 40. Co-relation between RMR and D_frag/D_{in situ} shows that as RMR increases, D_frag/D_{in situ} ratio decreases. Rock mass classification based on fractal geometry is suggested.     

基于Hoek建议的非线性关系求取岩体抗剪强度的算法及工程应用

阐述了Hoek建议的非线性关系原理,以此提出了求取岩体抗剪强度的算法：考虑了岩体抗剪破坏时总体或平均水平,通过计算出不同正应力 下对应的剪应力 ,线性回归确定一定应力范围内线性化后的 、 值,解决了Hoek-Brown准则拟合算法不能求解一定正应力 条件下岩土的抗剪强度的问题。在对中缅油气管道（国内段）澜沧江跨域工程边坡岩体应用以及进一步对比研究,结果表明：采用文中算法给出的第1种确定正应力 的方法所得的 、 值与Hoek-Brown准则拟合算法所得的结果相差不大,究其原因是两种算法考虑的因素不太一样,导致围压 或正应力 大小有所差别;在实际工程正应力 较低的情况下,应采用文中算法给出的第2种确定正应力 的方法来获取的 、 值,这样所得的结果才与实际情况比较接近,克服了Hoek-Brown准则拟合算法对围压 依赖的问题。     

Estimation of the Specific Energy of TBM Using the Strain Energy of Rock Mass,Case Study: Amir-Kabir Water Transferring Tunnel of Iran

The specific energy (SE) is the most important parameter to estimate the energy consumption in tunnel boring machines (TBMs). It is defined as the amount of required energy to excavate a unit volume of rock mass which used to predict the performance of TBMs. Several models are used to estimate the SE based on different parameters such as the rock mass properties, disc cutter dimensions and cutting geometry. The aim of this work is to propose new relations between the SE and the strain energy of rock mass (W) using the geological mappings of rock mass and TBM operational parameters from Amir-Kabir Water Transferring Tunnel of Iran. W is an appropriate criterion to estimate SE because it is a function of different parameters such as rock mass behavior, pre and post failure properties and peak and residual strains. In this study, to increase the correlation coefficient of relation between the mentioned parameters, the rock mass is classified in two methods, in the first method according to the geological strength index (GSI) all data is classified in three classes such as weak, fair and good and in the second method using the drop to deformation modulus ratio (η) the classification of data is performed in three classes such as η < 0.05, 0.05 ≤ η < 10 and η ≥ 10. The results show that there are direct relations between both parameters. It is suggested to estimate SE in all rock mass classes using the proposed relations based on GSI classification.     

Critical review on shear strength models for soil-infilled joints

An infilled rock joint is likely to be the weakest plane in a rock mass. The presence of infill material within the joint significantly reduces the friction of the discontinuity boundaries (i.e. rock to rock contact of the joint walls). The thicker the infill, the smaller the shear strength of the rock joint. Once the infill reaches a critical thickness, the infill material governs the overall shear strength, and the joint walls (rock) play no significant role. Several models have been proposed to predict the peak shear strength of soil-infilled joints under both constant normal load (CNL) and constant normal stiffness (CNS) boundary conditions, taking into account the ratio of infill thickness (t) to the height of the joint wall asperity (a). CNS models provide a more realistic picture of the soil-infilled joint behaviour in the field. This paper presents a critical review on the existing mathematical models for predicting the shear strength of soil-infilled rock joint and verifies the normalised peak shear stress model with further laboratory investigations carried out on idealised saw-tooth rock joints at the University of Wollongong. Based on the prediction of the experimental data, the normalised peak shear stress model is slightly modified by the authors. A simplified approach for using this model in practice is presented and a new expression for prediction of dilatation at peak shear stress is suggested.     

A simplified conceptual model for estimating roof bolting requirements

Summary The selection of rock bolting lengths and spacings for a mine roof or back is relatively straightforward when wedges of rock bound by discrete discontinuities require support, or when the immediate roof can be anchored into a recognizably stable layer or rock mass. When neither of these situations is present the choice of bolt lengths and spacings is more difficult.In this paper a simplified conceptual model is presented which invokes the concept of an ellipticallyshaped zone of loosening above the opening, all, or a portion of which, may require support. The analysis includes the influence of opening span, height,in situ stress state, and rock mass quality as measured by the CSIR Rock Mass Classification.Validation of the model was sought by analysing a number of case histories in the literature.     

An approach to large-scale field stress determination

The construction of stable structures in rock masses requires knowledge of the in situ stresses at the scale of excavations. However, the measurements obtained by the conventional overcoring technique are related to a small scale (centimetres). To extrapolate them to the scales of interest to rock mechanics (from meters to kilometres) requires a large number of individual stress measurements, followed by statistical analysis to avoid a considerable scatter of the measured values. In this paper, a method is proposed based on (a) large-scale surface stress and modulus measurements using the cylindrical jack method complemented by a special measuring scheme and then (b) back analysis for a given excavation shape. The method allows the simultaneous reconstruction of the stress components at the scale of excavation. A numerical simulation for a cylindrical excavation in an isotropic rock mass demonstrates the high accuracy and robustness of the method. The presence of a fractured zone surrounding the excavation can hamper the stress reconstruction, hence special measures should be taken to conduct the measurements in competent rock.     

基于改进遗传算法的粘弹性岩体力学参数反演

把模式搜索嵌入目前广为应用的遗传算法中,使之和神经网络有机结合,提出了搜索—遗传—神经网络算法。该方法用经过最佳预测学习算法训练的神经网络来表达粘弹性岩体力学参数和位移之间的映射关系,除具有一般遗传算法的优点外,还提高了参数反演的精度,节省了参数反演的计算时间。结合某工程实例,验证了该方法在粘弹性岩体力学参数反演中的优越性。      

Effect of rock discontinuities on certain rock strength and fracture energy parameters under uniaxial compression

Summary Five series of test blocks of Pendeli marble with artificially created discontinuities of different crack densities (simulating three mutually orthogonal joint sets) were tested in uniaxial compression in order to study the effect of discontinuities on: (a) the compressive strength and the modulus of elasticity, and (b) certain fracture energy parameters expressed by the ratio W _A/W _V, where W _A is the surface energy and W _V the volume elastic strain energy. Mathematical relationships are derived similar to those suggested by other authors relating strength parameters to crack densities. Such relationships clearly show a reduction in strength with increased crack density. The experimental results obtained permit the extension of Persson's relation (which refers to ideal intact rock) to the more realistic case of discontinuous rock mass by introducing the appropriate term that takes into consideration the effect of rock mass discontinuities on the energy ratio W _A/W _V. A comparison between laboratory results and field observations was subsequently carried out assuming the rock mass to behave as a linearly elastic material, obeying the Hoek and Brown failure criterion. This comparison showed that laboratory results can be extended to larger scale. Furthermore, in order to predict the in situ strength and stability of a rock mass in uniaxial compression (which is of major importance in underground excavations) certain concepts are proposed based on laboratory tests, in situ investigations and first principles of linear elastic fracture mechanics.     

Calculation of pH and mineral equilibria in hydrothermal waters with application to geothermometry and studies of boiling and dilution

Using chemical analyses and 25° pH measurements of quenched high-temperature waters, we calculate in situ pH and distribution of aqueous species at high temperature. This is accomplished by solving simultaneous mass action equations for complexes and redox equilibria and mass balance equations, on all components, including a H⁺ equation with as many as 60 terms (depending on water composition). This calculation provides accurate values for the activities of aqueous ions in a given water at high temperature, which are used to calculate an ion activity product (Q) for each of more than 100 minerals. The value of log(Q/K) for each mineral, where K is the equilibrium constant, provides a measure of proximity of the aqueous solution to equilibrium with the mineral. By plotting log Q/Kvs. T for natural waters, it is possible to determine: a) whether the water was in equilibrium with a host rock mineral assemblage, b) probable minerals in the equilibrium assemblage and c) the temperature of equilibrium. In cases where the fluid departs from equilibrium with a host rock assemblage, it is possible to determine whether this may result from boiling or dilution, and an estimate of amount of lost gas or diluting water can be determined.The calculation is illustrated by application to geothermal waters from Iceland, Broadlands, and Sulphur Bank, hot spring waters from Jemez, Yellowstone and Blackfoot Reservoir (Idaho) and fluid inclusions from the Sunnyside Mine, Colorado. It is shown that most geothermal waters approach equilibrium with a subsurface mineral assemblage at a temperature close to measured temperatures and that some hot springs also approach equilibrium with the host rock at temperatures above outlet temperatures but commonly below the Na-K-Ca temperatures. The log Q/K plots show that some discrepancies between Na-K-Ca temperatures on spring waters and actual temperatures result from a failure of alkali feldspars to equilibrate with the fluid and with each other.Calculations on Sulphur Bank fluids show that boiling probably caused cinnabar precipitation near 150°C and that the boiled fluids equilibrated with secondary minerals near 150° even though temperatures up to 185° have been measured at depth. For the fluid inclusions, the measured bubble temperatures are close to those calculated for equilibration of the fluid with the observed sulfide mineral assemblage.New estimates of stability constants for aluminum hydroxide complexes are included at the end of the paper.     

Application of the strain energy to estimate the rock load in squeezing ground condition of Eamzade Hashem tunnel in Iran

Estimation of rock load is a very important issue because the selection of a support system is highly related to this parameter. Several methods are used to estimate this parameter such as experimental, empirical, and numerical methods. This study propose a new empirical method to estimate the rock load in squeezing ground condition using actual collapses data of Emamzade Hashem tunnel of Iran based on the ration of the post-failure residual strain energy to the pre-failure stored strain energy. Prediction of squeezing ground condition in this study is performed based on Jethwa, Singh, and Hoek criterions. Results show that some sections in shale and sandstone of the Shemshak formation are prone to squeezing. Finally, the relation between the rock load and the ratio of the post-failure residual strain energy to the pre-failure stored strain energy, Ψ, in squeezing ground condition is estimated. Based on the statistical analysis, the maximum correlation between both parameters is achieved when Alejano’s equations are used to estimate the drop modulus. As the rock mass behavior changes from elastic–plastic to elastic–brittle, the drop modulus changes from 0 to infinite. The reason is that by increasing the quality of rock mass and reducing the minimum principal stresses, the ratio of post-failure residual strain energy to pre-failure stored strain energy and rock load height (H _p) reduce. So, regression analysis is used to investigate the relation between the rock load height and the ratio of post-failure residual strain energy to pre-failure stored strain energy, and finally, a formulation is presented to determine rock load height based on power function.     

Hoek-Brown强度参数取值及水电工程应用方法对比研究

岩体强度和地应力之间的矛盾导致的应力型破坏在我国西部水电开发过程中比较普遍地出现,岩体强度参数取值因此成为西部水电工程实践中重要的环节之一,直接影响着工程问题的解决方案。针对我国水电行业岩体取值方法所考察因素与Hoek-Brown方法的差异,本文在论述岩性、围压条件、岩块破损对岩体强度参数取值影响的基础上,重点讨论了水电经验取值方法与Hoek-Brown经验取值方法的差异及其在西部复杂条件下的适用性。结论如下:（1）岩性、围压水平和破损特性对强度参数的影响不容忽视;（2）水电经验取值方法适用于低围压条件,在西部水电工程中适用性相对较差;（3）Hoek-Brown经验取值方法同时考虑了岩石材质、围压效应和破损效应的影响,既能实现中东部地区水电工程岩体力学参数取值经验的延续,也适用于西部水电工程的高应力环境和复杂地质环境。     

An Integrated Numerical Modelling–Discrete Fracture Network Approach Applied to the Characterisation of Rock Mass Strength of Naturally Fractured Pillars

Naturally fractured mine pillars provide an excellent example of the importance of accurately determining rock mass strength. Failure in slender pillars is predominantly controlled by naturally occurring discontinuities, their influence diminishing with increasing pillar width, with wider pillars failing through a combination of brittle and shearing processes. To accurately simulate this behaviour by numerical modelling, the current analysis incorporates a more realistic representation of the mechanical behaviour of discrete fracture systems. This involves realistic simulation and representation of fracture networks, either as individual entities or as a collective system of fracture sets, or a combination of both. By using an integrated finite element/discrete element–discrete fracture network approach it is possible to study the failure of rock masses in tension and compression, along both existing pre-existing fractures and through intact rock bridges, and incorporating complex kinematic mechanisms. The proposed modelling approach fully captures the anisotropic and inhomogeneous effects of natural jointing and is considered to be more realistic than methods relying solely on continuum or discontinuum representation. The paper concludes with a discussion on the development of synthetic rock mass properties, with the intention of providing a more robust link between rock mass strength and rock mass classification systems.     

A hybridized numerical and regression method for estimating the minimum rock pillar width of twin circular tunnels

Twin tunnels can be used for many applications. Interaction between two tunnels is an important problem in tunnel engineering that should be studied specially. Numerical investigations are well adapted to field data and numerical methods can be used in design of rock pillar of twin circular tunnels. So far, no relationship has been provided to estimate the minimum stable rock pillar width. In this paper, the interaction between twin circular tunnels has been studied using 2D finite element analysis. To do this, a great number of twin tunnels were modeled in Phase2 software with different conditions of rock mass (RMR value) and depth of tunnel. Models were analyzed and minimum stable rock pillar width was determined. This process was repeated for three different ratios of K (ratio of horizontal stress to vertical stress, 0.5, 1, and 1.5). Finally, according to the linear and nonlinear regression methods, the best merit function was fitted to result of numerical analysis. Then, new approximate formula was proposed to estimate the minimum rock pillar width according to RMR value and depth of twin circular tunnels with different K values. The formulae are very accurate (coefficient of correlation equals to minimum 0.96) that can be used for estimating the minimum rock pillar width of twin circular tunnels.