P‐wave transmission across fractures with nonlinear deformational behaviour

Stress wave attenuation across fractured rock masses is a great concern of underground structure safety. When the wave amplitude is large, fractures experience nonlinear deformation during the wave propagation. This paper presents a study on normal transmission of P‐wave across parallel fractures with nonlinear deformational behaviour (static Barton–Bandis model). The results show that the magnitude of transmission coefficient is a function of incident wave amplitude, nondimensional fracture spacing and number of fractures. Two important indices of nondimensional fracture spacing are identified, and they divide the area of nondimensional fracture spacing into three parts (individual fracture area, transition area and small spacing area). In the different areas, the magnitude of transmission coefficient has different trends with nondimensional fracture spacing and number of fractures. In addition, the study reveals that under some circumstances, the magnitude of transmission coefficient increases with increasing number of fractures, and is larger than 1. Copyright © 2006 John Wiley & Sons, Ltd.     

Considerations of the discontinuous deformation analysis on wave propagation problems

In rock engineering, the damage criteria of the rock mass under dynamic loads are generally governed by the threshold values of wave amplitudes, such as the peak particle velocity and the peak particle acceleration. Therefore, the prediction of wave attenuation across fractured rock mass is important on assessing the stability and damage of rock mass under dynamic loads. This paper aims to investigate the applications of the discontinuous deformation analysis (DDA) for modeling wave propagation problems in rock mass. Parametric studies are carried out to obtain an insight into the influencing factors on the accuracy of wave propagations, in terms of the block size, the boundary condition and the incident wave frequency. The reflected and transmitted waves from the interface between two materials are also numerically simulated. To study the tensile failure induced by the reflected wave, the spalling phenomena are modeled under various loading frequencies. The numerical results show that the DDA is capable of modeling the wave propagation in jointed rock mass with a good accuracy. Copyright © 2009 John Wiley & Sons, Ltd.     

Transmission of Elastic P-waves across Single Fractures with a Nonlinear Normal Deformational Behavior

Summary This paper presents a theoretical study on normally incident elastic P-wave transmission across single dry fractures with a nonlinear normal deformational behavior. The effects of nonlinear fracture normal behavior on P-wave transmission are examined without the mixture of fracture shear behavior. The linear displacement discontinuity model for wave propagation across fractures is extended to a nonlinear model – the hyperbolic elastic model (BB model). Numeric solutions of magnitudes of transmission (|T _non|) and reflection (|R _non|) coefficients, for normally incident P-wave transmission across the nonlinear deformable fractures, are obtained and related to the closure behavior of fractures. Parametric studies are conducted to acquire an insight into the effects of the nonlinear fracture normal deformation on P-wave transmission, in terms of initial normal stiffness and the ratio of current maximum closure to maximum allowable closure of the fractures, as well as the incident wave amplitude and frequency. Comparisons between the linear and nonlinear models are presented. It is shown that, |T _lin| and |R _lin| for the linear model are special solutions of |T _non| and |R _non| for the nonlinear model, when the incident wave amplitude is so low that the current maximum closure of fracture incurred during the wave transmission is much smaller, relative to the maximum allowable closure. In addition, the nonlinear fracture behavior gives rise to a phenomenon of higher harmonics during the wave transmission across the fracture. The higher harmonics contribute to the increase of |T _non| from |T _lin|.     

节理对爆炸波传播影响的数值研究

采用加入无反射边界条件的DDA程序,研究了节理面对应力波传播的影响。结果表明,节理面能阻碍波的传播,有利于波的衰减,节理面越多,波的反射越强,而波的透射越弱。模拟了一个现场爆炸试验,研究爆炸产生的应力波在节理岩体中传播、衰减的规律,模拟结果与现场试验结果比较吻合。研究表明,DDA方法可以模拟节理面对应力波传播的阻碍作用,用它来模拟爆炸波在节理岩体中的传播是适用的。     

基于DDA方法一种流-固耦合模型的建立及裂隙体渗流场分析和应用

以非连续变形分析方法（DDA）为基础并采用稳态流体计算方法将二者结合进行裂隙岩体流-固耦合分析。利用DDA方法生成裂隙岩体模型,在此基础上采用矩阵搜索等方法形成新的裂隙水通网络模型。采用稳态迭代算法和立方定律求得裂隙水压力,并把裂隙水压力作为线载荷施加到块体边界,在DDA算法中每个迭代步完成后更新裂隙开度和水压值,与DDA算法结合研究裂隙水与块体之间相互作用关系。利用以上裂隙岩体流-固耦合计算方法研究了某水封油库开挖和运行过程洞室围岩流量和密封性,为该工程预测水封效果提供了有益的主要依据,也是国内首次采用DDA方法做大型工程的流-固耦合模型分析。     

基于离散颗粒模型的岩体结构面动-静态刚度系数对比的数值模拟研究

岩体工程计算分析中结构面刚度系数是至关重要的力学参数,计算分析的精度和可靠程度与这个参数密不可分,结构面刚度系数取值仍然是一个难点.岩体中应力波传播至结构面处将会发生反射和透射现象,利用应力波透射系数可反演结构面动态刚度系数.本文从细观力学角度运用颗粒离散元方法,开发分段线性接触模型及应力波吸收边界模型,开展宏观岩体中...     

Analysis of Blast Wave Interaction with a Rock Joint

The interaction between rock joints and blast waves is crucial in rock engineering when rock mass is suffered from artificial or accidental explosions, bursts or weapon attacks. Based on the conservation of momentum at the wave fronts and the displacement discontinuity method, quantitative analysis for the interaction between obliquely incident P- or S-blast wave and a linear elastic rock joint is carried out in the present study, so as to deduce a wave propagation equation. For some special cases, such as normal or tangential incidence, rigid or weak joint, the analytical solution of the stress wave interaction with a rock joint is obtained by simplifying the wave propagation equation. By verification, it is found that the transmission and reflection coefficients from the wave propagation equation agree very well with the existing results. Parametric studies are then conducted to evaluate the effects of the joint stiffness and incident waves on wave transmission and reflection. The wave propagation equation derived in the present study can be straightforwardly extended for different incident waveforms and nonlinear rock joints to calculate the transmitted and reflected waves without mathematical methods such as the Fourier and inverse Fourier transforms.     

Experimental studies on the effects of fracture on the P and S wave velocity propagation in sedimentary rock (“Calcarenite del Salento”)

Experimental studies were carried out in laboratory in order to investigate the effects of fracture on compressional (P) wave and shear (S) wave velocity propagation and therefore the relations between seismic properties and rock mass parameters. The discontinuity index, I_d, fracture density parameter C, linear fracture parameter Γ and the rock quality designation (RQD) were used to describe the rock mass parameters. These parameters are analyzed and then related to the seismic properties. Four vertical aligned fractures were created on an intact calcarenite block, 0.6 m long, 0.4 m thick and 0.4 m width, by sawing. The measures were carried out in four different blocks of cacarenite, having the same physical properties, and in four different phases: in first block the fractures were filled with air; in the second block the fractures were filled with “terra rossa”; in third block the fractures were filled with wet “terra rossa” and in the fourth block the fractures were filled with clay. The test results were statistically analysed using the method of least squares regression and polynomial relationships with high correlation coefficient were found between the fractured rock parameters and P-wave, S-wave velocities and V_p/V_s ratio. The investigations suggest that the P-wave and S-wave velocities decrease with increasing the fracture parameters, while the V_p/V_s ratio increases with decreasing the fracture parameters.

Furthermore the results of the experimental studies were applied on the seismic refraction tomography data acquired in a great measurements campaign undertaken in the Adriatic salentina coast (south Italy) in order to monitor the coastal erosion.

The geophysical results, using the polynomial relationships between the fractured rock parameters and P-wave velocity, are in good agreement with the geomorphological and geological results.     

Manuel Rocha Medal Recipient Wave interaction with underground openings in fractured rock

Summary The objective of this work is to lead to improved models of seismic wave propagation around underground openings by studying the interaction of the waves with the fractured rock surrounding these openings. It demonstrates that seismic models can help in stability problems such as rockbursting in deep-level mining, or in the interpretation of micro-fracturing at waste storage sites. A significant emphasis is placed on comparing the models with observations from controlled experiments. These comparisons demonstrate that the wave propagation can be reliably and accurately modelled, and in so doing it motivates their application to the larger rock engineering problems. Seismic wave models are first applied to laboratory experiments on multiple fractures. Simulation through multiple displacement discontinuities yields strikingly similar waveforms to the experiments, while also identifying the need to build stress dependence into the fracture models, such as stress dependent fracture stiffness. The wave-fracture modelling is extended to in situ fractures in rock at the surface of a deep tunnel, using data collected during an acoustic emission experiment at the URL Mine-by tunnel. Waveforms from the velocity scans are compared against those from elastic models and various models of fracture, such as random assemblies of small open fractures (cracks) and larger fractures with fracture stiffness. Results indicate that it is possible to account for the wave-speeds and amplitudes using models with fractures. A generic method is then proposed for calculating the frequency variation of wave-speed and amplitude for any collection of cracks. The models of fracture are then applied to the rockburst problem, to investigate how the excavation affects the amplitude and the distribution of ground motion. The results provide important insights into the causes of the apparent amplification observed by researchers in this field. The thesis also covers the theory of the models used, including novel numerical work on dispersion and new grid schemes. The full detail of the work cannot be covered in this paper which instead seeks to summarize the main achievements.     

A New Viscous Boundary Condition in the Two-Dimensional Discontinuous Deformation Analysis Method for Wave Propagation Problems

Viscous boundaries are widely used in numerical simulations of wave propagation problems in rock mechanics and rock engineering. By using such boundaries, reflected waves from artificial boundaries can be eliminated; therefore, an infinite domain can be modeled as a finite domain more effectively and with a much greater accuracy. Little progress has been made, thus far, with the implementation and verification of a viscous boundary in the numerical, discrete element, discontinuous deformation analysis (DDA) method. We present in this paper a new viscous boundary condition for DDA with a higher absorbing efficiency in comparison to previously published solutions. The theoretical derivation of the new viscous boundary condition for DDA is presented in detail, starting from first principles. The accuracy of the new boundary condition is verified using a series of numerical benchmark tests. We show that the new viscous boundary condition works well with both P waves as well as S waves.     

Stress‐dependent elastic wave velocity of microfractured sandstone

A model for the stress‐dependent elastic wave velocity response of fractured rock mass is proposed based on experimental evidence of stress‐dependent fracture normal and shear stiffness. Previously proposed models and previous experimental studies on stress‐dependent fracture stiffness have been reviewed to provide a basis for the new model. Most of the existing stress‐dependent elastic wave velocity models are empirical, with model parameters that do not have clear physical meanings. To propose the new model, the rock mass is assumed to have randomly oriented microscopic fractures. In addition, the characteristic length of microfractures is assumed to be sufficiently short compared to the rock mass dimensions. The macroscopic stress‐dependent elastic wave velocity response is assumed to be attributed to the stress dependency of fracture stiffness. The stress‐dependent fracture normal stiffness is defined as a generalized power law function of effective normal stress, which is a modification of the Goodman's model. On the other hand, the stress dependency of fracture shear stiffness is modeled as a linear function of normal stress based on experimental data. Ultrasonic wave velocity responses of a dry core sample of Berea sandstone were tested at effective stresses ranging from 2 to 55 MPa. Visual observation of thin sections obtained from the Berea sandstone confirms that the assumptions made for microstructure of rock mass model are appropriate. It is shown that the model can describe the stress‐dependent ultrasonic wave velocity responses of dry Berea sandstone with a set of reasonable material parameter values. Published 2013. This article is a U.S. Government work and is in the public domain in the USA.     

应力波斜入射对岩体节理端部的影响

岩体节理在受到应力波扰动时端部受力会发生不同程度的连续性变化,为具体分析这种动态变化与应力波入射角度之间的关系,引用岩石非线性法向本构关系与线性切向本构关系的组合模型以及相应的在P波斜入射节理的应力波传播方程,结合岩石断裂力学中Ⅰ、Ⅱ型裂纹尖端应力和位移场的相关理论,得出组合形式下的节理端部应力场和位移场随质点振速变化的计算公式。通过不同入射角的模拟脉冲信号作用对端部应力位移的变化分析：应力波斜入射节理导致节理端部上、下两侧应力与位移场非对称分布,随着入射波质点振速的增减变化,应力集中位置会出现变化;计算并整理模型中节理端部上、下两侧0.005 m位置的数据,节理法向刚度由入射波质点振速带来的变化直接影响到应力波的透射与反射,进而会导致端部的应力与位移出现滞后效应;节理端部横向位移值与入射角度并非单调变化,而竖向位移会随着入射角的增大呈现下降趋势。     

爆破开挖对岩体含水裂纹扩展的扰动机制

岩体裂纹的水力劈裂是岩体开裂渗漏甚至施工涌水的重要影响因素之一,也是岩土工程界的研究热点。从断裂力学角度分析了爆破开挖对岩体含水裂纹扩展的扰动作用,结果表明,爆破开挖扰动下,岩体含水裂纹的扩展,与爆炸应力波强度及其入射角、地应力的大小与方向、孔隙水压大小、裂纹的倾角及断裂韧度等因素相关;爆炸应力波的作用,相当于增大了岩体裂纹中的孔隙水压力,每1 cm/s的峰值振动速度相当于增大100 kPa的孔隙水压力,爆破振动速度越大,所产生的爆破扰动荷载越大;岩体开挖引起的岩体裂纹近区地应力及其孔隙水压力的变化,对裂纹的失稳与扩展具有较复杂的影响,可改变裂纹的失稳扩展模式。     

Boundary setting method for the seismic dynamic response analysis of engineering rock mass structures using the discontinuous deformation analysis method

Large deformations and discontinuous problems can be calculated using the discontinuous deformation analysis (DDA) method by solving time steps, and this method is suitable for simulating the seismic dynamic response of engineering rock mass structures. However, the boundary setting must be carefully analyzed. In this paper, four boundary settings for the DDA method are investigated. First, the contributions to the DDA equations for nonreflecting boundaries (including the viscous boundary and the viscoelastic boundary) are deduced based on the Newmark method. Second, a free‐field boundary is introduced in the DDA method with boundary grid generation and coupling calculation algorithms to accurately simulate external source wave motion, such as earthquakes. Third, seismic input boundary treatments are intensively examined, and the force input method is introduced based on nonreflecting boundaries. Finally, the static‐dynamic unified boundary is implemented to ensure consistent boundary transformation. The boundary setting method in the DDA method is discussed, and the suggested treatments are used to analyze the seismic dynamic response of underground caverns. Copyright © 2015 John Wiley & Sons, Ltd.     

Analysis of Stochastic Seismic Wave Interaction with a Slippery Rock Fault

Stochastic seismic wave interaction with a slippery rock fault is studied, based on the principle of conservation of momentum at the wave fronts along the fault. By using the displacement discontinuity method, the wave propagation equations are derived for incident longitudinal-(P-) and shear-(S-) waves, respectively. This is an extension of the study by Li and Ma (2010) for blast-induced wave propagation across a linear rock joint. Stochastic seismic waves are generated from a frequency spectrum and used to analyze the seismic wave interaction with a rock fault having a Coulomb-slip behavior. Parametric studies are carried out to investigate the effect of the intensity and impinging angle of the incident seismic waves on wave propagation across a slippery rock fault. Results show that the transmission of the incident P-wave is almost not affected by the fault, on the contrary, this is not the case for an incident S-wave, due to the occurrence of a relative slip which is related to the impinging angle of the incident S-wave. A quantitative study is presented which is of help in understanding the propagation and attenuation laws of seismic waves in discontinuous rock masses.     

岩体裂隙模拟的扩展有限元法应用研究

岩体中普遍存在着断层﹑节理和裂隙等结构面,这些结构面的存在和发展对岩体的整体强度﹑变形及稳定性有极大的影响。因此,研究岩体中原生结构面的萌生﹑发展以及贯通演化过程对评估岩体工程安全性和可靠性具有非常重要的理论与现实意义。扩展有限元法（XFEM）作为一种求解不连续问题的有效数值方法,模拟裂隙时独立于网格,因此,在模拟岩体裂隙扩展﹑水力劈裂等方面具有独特优势。针对扩展有限元法的基本理论及其在岩体裂隙扩展模拟中的应用展开了研究,建立了扩展有限元法求解岩体裂隙摩擦接触、岩体裂隙破坏等问题的数值模型,并将计算模型应用于岩质边坡稳定性分析和重力坝坝基断裂破坏等工程问题。     

Capturing the two‐way hydromechanical coupling effect on fluid‐driven fracture in a dual‐graph lattice beam model

Fluid‐driven fractures of brittle rock is simulated via a dual‐graph lattice model. The new discrete hydromechanical model incorporates a two‐way coupling mechanism between the discrete element model and the flow network. By adopting an operator‐split algorithm, the coupling model is able to replicate the transient poroelasticity coupling mechanism and the resultant Mandel‐Cryer hydromechanical coupling effect in a discrete mechanics framework. As crack propagation, coalescence and branching are all path‐dependent and irreversible processes, capturing this transient coupling effect is important for capturing the essence of the fluid‐driven fracture in simulations. Injection simulations indicate that the onset and propagation of fractures is highly sensitive to the ratio between the injection rate and the effective permeability. Furthermore, we show that in a permeable rock, the borehole breakdown pressure, the pressure at which fractures start to grow from the borehole, depends on both the given ratio between injection rate and permeability and the Biot coefficient.     

An explicitly coupled hydro‐geomechanical model for simulating hydraulic fracturing in arbitrary discrete fracture networks

Modeling hydraulic fracturing in the presence of a natural fracture network is a challenging task, owing to the complex interactions between fluid, rock matrix, and rock interfaces, as well as the interactions between propagating fractures and existing natural interfaces. Understanding these complex interactions through numerical modeling is critical to the design of optimum stimulation strategies. In this paper, we present an explicitly integrated, fully coupled discrete‐finite element approach for the simulation of hydraulic fracturing in arbitrary fracture networks. The individual physical processes involved in hydraulic fracturing are identified and addressed as separate modules: a finite element approach for geomechanics in the rock matrix, a finite volume approach for resolving hydrodynamics, a geomechanical joint model for interfacial resolution, and an adaptive remeshing module. The model is verified against the Khristianovich–Geertsma–DeKlerk closed‐form solution for the propagation of a single hydraulic fracture and validated against laboratory testing results on the interaction between a propagating hydraulic fracture and an existing fracture. Preliminary results of simulating hydraulic fracturing in a natural fracture system consisting of multiple fractures are also presented. Copyright © 2012 John Wiley & Sons, Ltd.     

Modeling 3D thermal fracture propagation by transient cooling using virtual multidimensional internal bonds

Thermal fracturing can play an important role in development of unconventional petroleum and geothermal resources. Thermal fractures can result from the nonlinear deformation of the rock in response to thermal stress related to cold water injection as well as heating. Before the rock reaches the final failure stage, material softening and bulk modulus degradation can cause changes in the thermo‐mechanical properties of the solid. In order to capture this aspect of the rock fracture, a virtual multidimensional internal bond‐based thermo‐mechanical model is derived to track elastic, softening, and the failure stages of the rock in response to the temporal changes of its temperature field. The variations in thermo‐mechanical properties of the rock are derived from a nonlinear constitutive model. To represent the thermo‐mechanical behavior of pre‐existing fractures, the element partition method is employed. Using the model, numerical simulation of 3D thermal fracture propagation in brittle rock is carried out. Results of numerical simulations provide evidence of model verification and illustrate nonlinear thermal response and fracture development in rock under uniform cooling. In addition, fracture coalescence in a cluster of fractures under thermal stress is illustrated, and the process of thermal fracturing from a wellbore is captured. Results underscore the importance of thermal stress in reservoir stimulation and show the effectiveness of the model to predict 3D thermal fracturing. Copyright © 2016 John Wiley & Sons, Ltd.     

岩体夹层应力波能量演化及应力响应特征分析

夹层是常见的地质结构,在地震或爆破荷载作用下,夹层对应力波的传播以及对岩体的响应具有重要的影响。以往对应力波在夹层介质中传播的研究多集中于夹层对应力波的隔振或透射性能,而对应力波在夹层中的多次折、反射过程中能量的演化规律缺乏讨论,对夹层介质的应力响应与破坏没有开展较好地分析。通过理论方法对应力波在夹层内部传播过程中的能量系数的变化规律进行了研究,分析了岩体介质波阻抗和应力波入射角对夹层内外介质中累积波动能量系数的影响规律,以及平面型边坡中软弱夹层的应力响应特征和动态稳定性。研究发现,应力波在夹层内部往复反射过程中,夹层内剩余应力波能量随折、反射发生次数呈指数曲线下降,第4次折、反射后产生的应力波能量可以忽略;夹层内外介质中应力波的累积能量系数的差异随着夹层内外介质波阻抗的相对差异的增大而增大。在平面谐波入射下,边坡内部的夹层中的剪应力和抗剪强度呈波动变化;相对P波,SV波入射会产生较高水平的剪应力,对边坡稳定性影响最大。且SV波入射时,边坡的安全系数对夹层的倾角变化更为敏感,随倾角增大而迅速降低。