Design of tabular excavations in foliated rock: an integrated numerical modelling approach

Summary This paper presents a rock mechanics design methodology applicable to steeply dipping orebodies typical of many underground hardrock mines. The first stage in the design process is the characterization of the rock mass using bothin situ and laboratory data. The effects of anisotropy on rock mass behaviour are discussed with reference to laboratory and field observations. The second stage involves the use of a number of selected numerical modelling techniques to investigate ground response in the near-field rock mass surrounding the mining excavations. This study shows that the use of several numerical methods in conjunction, allowing for the advantages of each method to be maximized, provides a more comprehensive analysis of the different facets of stope design. This approach differs from those in the literature which seek to compare the different numerical methods in order to select just one method best suited for a problem. The design methodology employed emphasizes the importance of developing an understanding of ground deformation mechanisms as opposed to predicting absolute behaviour.     

A new versatile constitutive law for modelling the monotonic response of soft rocks and structured fine-grained soils

This paper deals with a new critical state–based constitutive model for soft rocks and fine-grained soils. The model, formulated in the single-surface plasticity framework, is characterised by the following main features: (i) a generalised three-invariant yield surface capable of reproducing a wide set of well-known criteria, (ii) the dependency of the elastic stiffness on the current stress state by means of a hyperelastic formulation, (iii) the ability of simulating the plastic strain–driven structure degradation processes by a set of appropriate isotropic hardening laws, and (iv) a nonassociate flow rule in the meridian plane. The adopted formulation is hierarchical, such that the various features of the model can be activated or excluded depending on the specific kind of geomaterial to be modelled and on the quality and quantity of the related available experimental results. The constitutive model was implemented in a commercial finite element code by means of an explicit modified Euler scheme with automatic substepping and error control. The procedure does not require any form of stress correction to prevent drift from the yield surface. The performance of the model is first analysed by means of a wide set of parametric analyses, in order to highlight the main features and to evaluate the sensitivity of the formulation with reference to the input parameters. The model is then adopted to simulate the experimental response observed on three different geomaterials, ranging from soft clays to soft rocks.     

Development of a technique for modelling clay liner desiccation

This paper presents a model for the analysis of clay liner desiccation in a landfill barrier system due to temperature effects. The model incorporates consideration of fully coupled heat‐moisture‐air flow, a non‐linear constitutive relationship, the dependence of void ratio and volumetric water content on stress, capillary pressure and temperature, and the effect of mechanical deformation on all governing equations. Mass conservative numerical schemes are proposed to improve the accuracy of the finite element solution to the governing equations. The application of the model is then demonstrated by examining three test problems, including isothermal infiltration, heat conduction and non‐isothermal water and heat transport. Comparisons are made with results from literature, and good agreement is observed. Copyright © 2003 John Wiley & Sons, Ltd.     

基于环形扫面测量的三维直流电阻率法任意各向异性模型响应特征

高精度地下任意各向异性介质电性分布特征识别是当前的热门研究课题。本文以国内外前人工作为基础,基于非结构化网格,利用基于梯度恢复的后验误差估计指导网格自适应细化过程,实现了直流电阻率法三维有限元数值模拟。通过与一维模型半解析解的对比,验证了本文算法的有效性。考虑到电各向异性介质在观测中存在视电阻率反常现象,本文采用了环形扫面测量方法。通过对几种典型各向异性模型的模拟分析,得到了相应的各向异性影响规律和识别特征,各向异性主轴电阻率之间的比值大小决定了椭圆型视电阻率极性曲线长轴与短轴的比值大小,主轴电阻率的旋转方向会改变视电阻率极性曲线的形状。本文的算法研究及数值模拟技术可为直流电法数据精细处理和解释提供技术支撑。     

Mechanical behaviour of geo-encased sand columns: small scale experimental tests and numerical modelling

This paper presents experimental monotonic and cyclic test results on small scale sand columns reinforced by means of geosynthetics. The influence of the stiffness of the georeinforcement on the system mechanical response is discussed as well as that of the previous loading history. The experimental test results have also been numerically simulated by employing a 3D finite difference commercial code. A parametric study concerning the georeinforcement stiffness and the soil-column interface friction angle is presented. The results prove the influence of the encasing geosynthetic on the overall stiffness of the system, as well as of the stiffening effect induced by a possible preload applied on the column. The effect of shear stresses at column-soil interface is also observed to play a non negligible role, which is expected to become even more evident for real scale geo-encased columns. Numerical approaches based on standard constitutive models are able to capture the behaviour of the system under virgin load, but they totally fail in reproducing the unload-reloading response.     

On the mechanics of basin formation in the Pannonian basin: Inferences from analogue and numerical modelling

We present the results of a thrust fault reactivation study that has been carried out using analogue (sandbox) and numerical modelling techniques. The basement of the Pannonian basin is built up of Cretaceous nappe piles. Reactivation of these compressional structures and connected weakness zones is one of the prime agents governing Miocene formation and Quaternary deformation of the basin system. However, reactivation on thrust fault planes (average dip of ca. 30°) in normal or transtensional stress regimes is a problematic process in terms of rock mechanics. The aim of the investigation was to analyse how the different stress regimes (extension or strike-slip), and the geometrical as well as the mechanical parameters (dip and strike of the faults, frictional coefficients) effect the reactivation potential of pre-existing faults.

Results of analogue modelling predict that thrust fault reactivation under pure extension is possible for fault dip angle larger than 45° with normal friction value (sand on sand) of the fault plane. By making the fault plane weaker, reactivation is possible down to 35° dip angle. These values are confirmed by the results of numerical modelling. Reactivation in transtensional manner can occur in a broad range of fault dip angle (from 35° to 20°) and strike angle (from 30° to 5° with respect to the direction of compression) when keeping the maximum horizontal stress magnitude approximately three times bigger than the vertical or the minimum horizontal stress values.

Our research focussed on two selected study areas in the Pannonian basin system: the Danube basin and the Derecske trough in its western and eastern part, respectively. Their Miocene tectonic evolution and their fault reactivation pattern show considerable differences. The dominance of pure extension in the Danube basin vs. strike-slip faulting (transtension) in the Derecske trough is interpreted as a consequence of their different geodynamic position in the evolving Pannonian basin system. In addition, orientation of the pre-existing thrust fault systems with respect to the Early to Middle Miocene paleostress fields had a major influence on reactivation kinematics.

As part of the collapsing east Alpine orogen, the area of the Danube basin was characterised by elevated topography and increased crustal thickness during the onset of rifting in the Pannonian basin. Consequently, an excess of gravitational potential energy resulted in extension (σ_v > σ_H) during Early Miocene basin formation. By the time topography and related crustal thickness variation relaxed (Middle Miocene), the stress field had rotated and the minimum horizontal stress axes (σ_h) became perpendicular to the main strike of the thrusts. The high topography and the rotation of σ_h could induce nearly pure extension (dip-slip faulting) along the pre-existing low-angle thrusts. On the contrary, the Derecske trough was situated near the Carpathian subduction belt, with lower crustal thickness and no pronounced topography. This resulted in much lower σ_v value than in the Danube basin. Moreover, the proximity of the retreating subduction slab provided low values of σ_h and the oblique orientation of the paleostress fields with respect to the master faults of the trough. This led to the dominance of strike-slip faulting in combination with extension and basin subsidence (transtension).     

Anisotropic damage of rock joints during cyclic loading: constitutive framework and numerical integration

This work describes a constitutive framework for modeling the behavior of rough joints under cyclic loading. Particular attention is paid to the intrinsic links between dilatancy, surface degradation, and mobilized shear strength. The framework also accounts for the important effect of shear‐induced anisotropy. The resulting approach is fully three‐dimensional and is not restricted to plane‐displacement kinematics. Both the governing formulation and an algorithm for implicit numerical integration are presented. While the proposed methods are general, we also postulate a specific model that is compared with experimental data. It employs relatively few free parameters but shows good agreement with laboratory tests. Copyright © 2013 John Wiley & Sons, Ltd.     

Fibre reinforced sands: from experiments to modelling and beyond

Based on hypotheses derived directly from experimental observations of the triaxial behaviour, a constitutive model for fibre reinforced sands is built in this paper. Both the sand matrix and the fibres obey their own constitutive law, whereas their contributions are superimposed using a volumetric homogenization procedure. The Severn‐Trent sand model, which combines well‐known concepts such as critical state theory, Mohr‐Coulomb like strength criterion, bounding surface plasticity and kinematic hardening, is adopted for the sand matrix. Although the fibres are treated as discrete forces with defined orientation, an equivalent continuum stress for the fibre phase is derived to allow the superposition of effects of sand and fibres. The fibres are considered as purely tensile elements following a linear elastic constitutive rule. The strain in the fibres is expressed as a fraction of the strain in the reinforced sample so that imperfect bonding is assumed at the sand‐fibre interface. Only those fibres oriented within the tensile strain domain of the sample can mobilize tensile stress—the orientation of fibres is one of the key ingredients to capture the anisotropic behaviour of fibre reinforced soil that is observed for triaxial compression and extension loading. A further mechanism of partition of the volume of voids between the fibres and the sand matrix is introduced and shown to be fundamental for the simulation of the volumetric behaviour of fibre‐reinforced soils. Copyright © 2012 John Wiley & Sons, Ltd.     

Appraise the structural mitigation of landslide risk via numerical modelling: a case study from the northern Apennines (Italy)

The Ca’ Lita landslide is a large and deep-seated mass movement located in the northern Apennines, about 70 km west of Bologna (Northern Italy). It consists of a composite landslide that affects Cretaceous to Eocene flysch rock masses and chaotic complexes. Many of the sectors making up the landslide have resumed activity between 2002 and 2006, threatening some villages and an important road connecting several key industrial facilities located in the upper watershed. This paper presents the management of the emergency, dealing with the investigation campaigns (geological, geomorphological and LiDAR surveys, borehole drillings, seismic surveys), with the monitoring (in situ instrumentation) and with the design and construction of mitigation measures. The whole process, from landslide reactivation to date, has been modelled on a numerical basis with the finite difference code FLAC 2D, to assess the efficiency of the mitigation system and to propose further countermeasure works in different scenarios.     

Rheological and physical characteristics of crustal-scaled materials for centrifuge analogue modelling

We characterize a set of analogue materials used for centrifuge analogue modelling simulating deformation at different levels in the crust simultaneously. Specifically, we improve the rheological characterization in the linear viscoelastic region of materials for the lower and middle crust, and cohesive synthetic sands without petroleum-binding agents for the upper crust. Viscoelastic materials used in centrifuge analogue modelling demonstrate complex dynamic behaviour, so viscosity alone is insufficient to determine if a material will be an effective analogue. Two series of experiments were conducted using an oscillating bi-conical plate rheometer to measure the storage and loss moduli and complex viscosities of several modelling clays and silicone putties. Tested materials exhibited viscoelastic and shear-thinning behaviour. The silicone putties and some modelling clays demonstrated viscous-dominant behaviour and reached Newtonian plateaus at strain rates < 0.5 × 10⁻² s⁻¹, while other modelling clays demonstrated elastic-dominant power-law relationships. Based on these results, the elastic-dominant modelling clay is recommended as an analogue for basement cratons. Inherently cohesive synthetic sands produce fine-detailed fault and fracture patterns, and developed thrust, strike-slip, and extensional faults in simple centrifuge test models. These synthetic sands are recommended as analogues for the brittle upper crust. These new results increase the accuracy of scaling analogue models to prototype. Additionally, with the characterization of three new materials, we propose a complete lithospheric profile of analogue materials for centrifuge modelling, allowing future studies to replicate a broader range of crustal deformation behaviours.     

拉应力条件下岩石细观力学本构模型和渗透系数张量研究(I):各向异性损伤本构模型

在拉应力作用下的考虑渗流的岩石本构模型研究尚且很少。采用细观力学研究了岩石损伤变形过程,考虑了渗流过程。由于选用了新的微裂纹扩展准则,提高了解方程效率;采用细观力学成果建立了考虑渗流的微裂纹面不连续变形对岩石变形影响规律,并采用断裂力学成果建立了考虑渗流的微裂纹应力强度因子;建立了同时考虑微裂纹扩展过程和渗流过程的岩石各向异性损伤本构模型,该模型也适用于岩体。     

月表撞击坑形成过程数值模拟理论与方法

数值模拟是研究撞击坑形成过程的一种主要方法,尤其是认识撞击坑形成机制的重要手段。撞击坑形成过程数值模拟的基本原理是用离散方法描述物质在高速撞击作用下的运动及状态,在模拟中首先将物质与空间划分成离散的网格,在每一次迭代计算中逐步求解各个网格的形变、运动与状态改变的规律。牛顿运动定律、物质的连续体模型与热力学方程是撞击坑形成过程数值模拟的理论基础,牛顿运动定律以偏微分方程的形式贯穿在离散化的网格空间中,物质的连续体模型将物质的屈服强度与破裂、温度、孔隙、振动等联系起来,而热力学方程则通过其他热力学参数计算网格单元内物质的压强与物质所处的状态。     

Constitutive and numerical framework for modeling joints and faults in rock

A three‐dimensional constitutive model for joints is described that incorporates nonlinear elasticity based on volumetric elastic strain, and plasticity for both compaction and shear with emphasis on compaction. The formulation is general in the sense that alternative specific functional forms and evolution equations can be easily incorporated. A corresponding numerical structure based on finite elements is provided so that a joint width can vary from a fraction of an element size to a width that occupies several elements. The latter case is particularly appropriate for modeling a fault, which is considered simply to be a joint with large width. For small joint widths, the requisite equilibrium and kinematic requirements within an element are satisfied numerically. The result is that if the constitutive equation for either the joint or the rock is changed, the numerical framework remains unchanged. A unique aspect of the general formulation is the capability to handle either pre‐existing gaps or the formation of gaps. Representative stress–strain plots are given to illustrate both the features of the model and the effects of changes in values of material parameters. Copyright © 2015 John Wiley & Sons, Ltd.     

Strike-slip fault bridge fluid pumping mechanism: insights from field-based palaeostress analysis and numerical modelling

We present a finite-element study of stress perturbation in evolving compressive and extensional strike-slip fault bridges. The results are compared with a fracture study of a compressive bridge at St Donats, UK. Horizontally interbedded calcareous mudstone and bioclastic calcilutite at St Donats have a distinct vertical permeability anisotropy. This sedimentary sequence behaves as a set of horizontal aquifers. The fluid flow in these aquifers is sensitive to mean stress gradients. Paleostress analysis of field fracture data, verified by finite-element modelling, indicates a rotation of σ₁ towards parallelism with boundary faults inside the growing compressive bridge. Boundary faults and bridge faults recorded numerous fluid flow events. The modelled mean stress pattern shows a regional maximum within the bridge and local maxima/minima pairs at boundary fault tips.Finite-element modelling of an extensional bridge indicates that σ₃ rotates towards parallelism with boundary faults. The mean stress pattern is similar to the pattern in compressive bridge but with maxima and minima locations interchanged. The stress patterns are reestablished by each stress build-up preceding the rupturation of the boundary faults throughout the development stages of strike-slip fault bridges. Mean stress gradients developed pre-failure control the fluid flow in fractures of the strike-slip fault system at and after the end of each stress build-up and the fluid flow in boundary faults post-failure. Fracture reactivation and new fracture generation within an evolving bridge is a process consisting of multiple successive events that retain the storage capacity of the bridge. Rupture and sealing of the main bounding-faults is a step-wise process that opens and closes fluid conduits between areas with different pressures.     

Effective stress concept in unsaturated soils: Clarification and validation of a unified framework

The effective stress principle, conventionally applied in saturated soils, is reviewed for constitutive modelling purposes. The assumptions for the applicability of Terzaghi's single effective stress are recalled and its advantages are inventoried. The possible stress frameworks applicable to unsaturated soil modelling are reassessed in a comparative manner, specifically the Bishop's single effective stress, the independent stress variables approach and the generalized stress framework. The latter considerations lead to the definition of a unified stress context, suitable for modelling soils under different saturation states. In order to qualify the implications brought by the proposed stress framework, several experimental data sets are re‐examined in the light of the generalized effective stress. The critical state lines (CSLs) at different saturation states tend to converge remarkably towards a unique saturated line in the deviatoric stress versus mean effective stress plane. The effective stress interpretation is also applied to isotropic paths and compared with conventional net stress conception. The accent is finally laid on a second key feature for constitutive frameworks based on a unified stress, namely the sufficiency of a unique mechanical yield surface besides the unique CSL. Copyright © 2007 John Wiley & Sons, Ltd.     

A visco‐damage model for brittle materials under monotonic and sustained stresses

A theoretical model is proposed to describe the evolution of damage in brittle materials, such as concrete and masonry, subjected to increasing or sustained stresses of relatively high intensity. The model is based on the introduction of suitable damage variables in a rheological model. In this way, it is possible to describe the material behaviour under stresses either increasing or constant in time. The capabilities of the model in describing the mechanical response of material elements subjected to different stress histories are illustrated. Some correlations with experimental data from tests performed on masonry and concrete specimens are presented, to assess the reliability of the theoretical predictions. The results of some numerical applications to non‐proportional stress paths are also illustrated. Finally, the limitations of the proposal are discussed and possible further improvements are envisaged. Copyright © 2005 John Wiley & Sons, Ltd.     

Three dimensional steady-state locus for dry monodisperse granular materials: DEM numerical results and theoretical modelling

In this paper, steady-state conditions for ideal monodisperse dry granular materials are both theoretically and numerically analysed. A series of discrete element (DEM) numerical simulations have been performed on a periodic cell by imposing stress paths characterized by different Lode angles, pressures, and deviatoric strain rates. The dependence of the material response on both inertial number and loading path has been discussed in terms of void ratio, fabric, and granular temperature. DEM numerical results have been finally compared with the prediction of an already conceived model based on both kinetic and critical state theories, here suitably modified to account for three-dimensional conditions.     

Integration and calibration of a plasticity model for granular materials

A new macroscopic constitutive model for non‐cohesive granular materials, with the focus on coarse‐sized materials (railway ballast), is presented. The model is based on the concepts of rate‐independent isotropic plasticity. The Backward Euler rule is used for integrating the pertinent evolution equations. The resulting incremental relations are solved in the strain space that is extended with the internal (hardening) variables. The model is calibrated using data from Conventional Triaxial Compression (CTC) tests, carried out at the University of Colorado at Boulder. A function evaluation method is used for the optimization, whereby a ‘multi‐vector’ strategy for choosing the appropriate start vector is proposed. Copyright © 2002 John Wiley & Sons, Ltd.     

Relay ramps as pathways for turbidity currents: a study combining analogue sandbox experiments and numerical flow simulations

Unlike for subaerial settings, the impact of subaqueous relay ramps on sediment dispersal is still poorly understood. A combination of analogue laboratory experiments in a sandbox with numerical flow calculations is used to simulate relay ramp topographies on rifting continental margins and to analyse the resulting turbidity current pathways and their deposits. Various scenarios are investigated, including inflow perpendicular and oblique to the relay ramp axis as well as flow constrained by an incised channel on the ramp and by a landward‐directed tilt of the ramp. Without channelling, most sedimentation takes place on the basin floor because the bulk of the flow follows the steepest gradient down the fault and into the rift basin. With a channel along the relay ramp, significant flow occurs initially down the ramp axis, but channel spillover and basinward ramp tilting combine to redirect much of the sediment down the fault slope into the basin. When the relay ramp has a landward‐oriented tilt, most of the current flows down the ramp and deposits its sediment load there and at the foot of the ramp. However, also here a considerable amount of the flow is shed over the hanging wall fault and into the basin, forming a secondary depocentre, while ponding redistributes thin deposits over a wider area of the basin. The quantitative dependence of these results on the specific ramp geometries remains to be investigated further but may bear great importance for refined sedimentary models in subaqueous rifted settings as well as for hydrocarbon exploration therein.     

Mechanical behaviour of Lixhe chalk partly saturated by oil and water: experiment and modelling

Two or more different fluids generally saturate chalk in oil reservoir, and therefore its behaviour can be very complicated. In this paper, a constitutive law is proposed for modelling the mechanical behaviour of a chalk saturated by two non‐miscible fluids, water and oil. The effects of the capillary pressure or suction are taken into account. They are considered as an independent variable, as in the Barcelona's basic model developed for unsaturated soils. On the other hand, internal friction and pore collapse are modelled as independent mechanisms. The determination of the parameters is based on triaxial and oedometer tests. Finally, in order to validate the model, predictions are compared with experimental results of water‐flooding test. Copyright © 2002 John Wiley & Sons, Ltd.