数值解及解析解在岩体工程中的应用

本文是在第三届全国岩土力学数值分析和解析方法讨论会上所作的专题综述报告,是据提交给会议的部分论文,着重从数值方法在岩体工程的应用方面进行概括。它包括以下若干方面的课题,如岩体本构方程的模拟、锚喷支护的分析、岩体工程的反分析计算、洞室及竖井的围岩稳定与支护以及高边坡的稳定分析。从所提交的会议论文来看,在研究上述课题时,所采用的方法种类繁多,并具有独特的见解,它们在工程上的应用也已经取得了可喜的成效。     

Application of Numerical and Analytical Methods to Geotechnical Engineering

This is a summing-up report of the topic on application of numerical and analytical methods to geotechnical engineering, presented in the Third National Symposium on Numerical and Analytical Methods in Geomechanics. The application to rock mass and engineering is emphasized in this paper, based on the papers submitted to this symposium.     

Numerical study of boundary conditions for solute transport through a porous medium

A transition region may be defined as a region of rapid change in medium properties about the interface between two porous media or at the interface between a porous medium and a reservoir. Modelling the transition region between different porous media can assist in the selection of the most appropriate boundary conditions for the standard advection–dispersion equation (ADE). An advantage of modelling the transition region is that it removes the need for explicitly defining boundary conditions, though boundary conditions may be recovered as limiting cases. As the width of a transition region is reduced, the solution of the transition region model (TR model) becomes equivalent to the solution of the standard ADE model with correct boundary conditions. In this paper numerical simulations using the TR model are employed to select the most appropriate boundary conditions for the standard ADE under a variety of configurations and conditions. It is shown that at the inlet boundary between a reservoir and porous medium, continuity of solute mass flux should be used as the boundary condition. At the boundary interface between two porous media both continuity of solute concentration and solute mass flux should be used. Finally, in a finite porous medium where the solute is allowed to advect freely from the exit point, both continuity of solute concentration and solute mass flux should be used as the outlet boundary condition. The findings made here are discussed with reference to a detailed review of previous relevant theoretical and experimental observations. Copyright © 2001 John Wiley & Sons, Ltd.     

Numerical modelling of multistage caving processes: insights from multi‐seam longwall mining‐induced subsidence

Evaluating the induced subsidence is a critical step in multi‐seam longwall mining. Numerical modelling can be a cost‐effective approach to this problem. Numerical evaluation of longwall mining‐induced subsidence is much more complicated when more than one seam is to be extracted. Only a few research works have dealt with this problem. This paper discusses the essential requirements of a robust numerical modelling approach to simulation of multi‐seam longwall mining‐induced subsidence. In light of these requirements, the previous works on this topic are critically reviewed. A simple yet robust FEM‐based modelling approach is also proposed that is capable of simulating caving process, rock mass deterioration and subsidence around multi‐seam excavations. The effectiveness of this approach in comparison with two other conventional FEM approaches is demonstrated through numerical examples of two different multi‐seam mining configurations. Results show that the proposed numerical modelling approach is the only robust method, which is capable of simulating multi‐seam subsidence in both demonstrated cases. Copyright © 2016 John Wiley & Sons, Ltd.     

Numerical simulation of liquefaction in porous media using nonlinear fluid flow law

It is well known that for a sufficiently high seepage velocity, the governing flow law of porous media is nonlinear (J. Computers & Fluids 2010; 39 : 2069–2077). However, this fact has not been considered in the studies of soil‐pore fluid interaction and in conventional soil mechanics. In the present paper, a fully explicit dynamic finite element method is developed for nonlinear Darcy law. The governing equations are expressed for saturated porous media based on the extension of the Biot (J. Appl. Phys. 1941; 12 : 155–164) formulation. The elastoplastic behavior of soil under earthquake loading is simulated using a generalized plasticity theory that is composed of a yield surface along with non‐associated flow rule. Numerical simulations of porous media subjected to horizontal and vertical components of ground motion excitations with different permeability coefficients are carried out; while computed maximum pore water pressure is specially taken into consideration to make the difference between Darcy and non‐Darcy flow regimes tangible. Finally, the effect of non‐Darcy flow on the evaluated liquefaction potential of sand in comparison to conventional Darcy law is examined. Copyright © 2014 John Wiley & Sons, Ltd.     

爆炸荷载作用下土中爆坑形成的数值模拟

利用爆破产生能量可进行软基处理,但不同药量、不同药包埋设深度下爆坑形态和土体属性变化会存在差异。采用基于欧拉法的爆炸流体动力学数值模拟技术对土中爆破问题进行了分析,结果表明,最终爆坑形态与已有试验成果具有较好一致性;爆坑直径与药量和埋药深度存在一定的非线性关系;爆炸荷载在近域传播与冲击波类似,随着远离药包中心,则表现为应力波特征;随埋药深度增加,爆破挤密效果明显,但浅层爆破对土体挤密效果有限     

Numerical manifold method for dynamic nonlinear analysis of saturated porous media

It is well known that the Babuska–Brezzi stability criterion or the Zienkiewicz–Taylor patch test precludes the use of the finite elements with the same low order of interpolation for displacement and pore pressure in the nearly incompressible and undrained cases, unless some stabilization techniques are introduced for dynamic analysis of saturated porous medium where coupling occurs between the displacement of solid skeleton and pore pressure. The numerical manifold method (NMM), where the interpolation of displacement and pressure can be determined independently in an element for the solution of u–p formulation, is derived based on triangular mesh for the requirement of high accurate calculations from practical applications in the dynamic analysis of saturated porous materials. The matrices of equilibrium equations for the second‐order displacement and the first‐order pressure manifold method are given in detail for program coding. By close comparison with widely used finite element method, the NMM presents good stability for the coupling problems, particularly in the nearly incompressible and undrained cases. Numerical examples are given to illustrate the validity and stability of the manifold element developed. Copyright © 2006 John Wiley & Sons, Ltd.     

Semi-empirical method for calculation of maximum subsidence in coal mines

Summary Most empirical methods of subsidence prediction are based on the prior knowledge of the maximum possible subsidence, S_max, for a particular coalfield. The subsidence profile and other associated parameters along a desired line may be derived, in most cases, as a function of S _max. These methods are site specific and are not based upon the rational concepts of mechanics. Purely mechanistic methods, on the other hand, could not find wide application because of their limitations in representing the complex behaviour of a rockmass.Therefore a semi-empirical method of calculation of S _max or S, which is an improvement over the empirical method reported elsewhere (Bahuguna et al., 1991a), has been derived from combining the mechanistic and empirical approach. The effects of various parameters are studied by numerical modelling. These qualitative results are then used to influence the development of a more general semiempirical method. The method has been tested for 125 coal mine workings in India and 22 mines of the North Appalachian basin. The method is easily adaptable to other countries.     

接触摩擦问题的数值模拟

无网格伽辽金法(EFGM)可脱离单元的概念,特别适合岩体裂纹面的接触摩擦分析。基于EFGM,在裂纹面引入罚参数,通过迭代计算,得到裂纹面真实的应力状态,从而模拟闭合裂纹的粘接、滑移和张开行为,数值结果表明该方法是合理可行的。     

Proof of multiplicity of solutions for groundwater seepage in recharged heterogeneous unconfined aquifers

A new analytical proof is presented for steady‐state seepage in recharged heterogeneous unconfined aquifers. The paper also presents a detailed procedure and important rules for performing correctly numerical studies of unsaturated seepage. Once a numerical solution is calibrated with field data, using a set of spatially distributed values for hydraulic conductivity K and effective infiltration EI, any new numerical analysis with a set of αK and αEI values, where α is a constant, yields an equally good calibration. However, if the effective porosities of each layer are unchanged, the groundwater velocities are multiplied by α, whereas the travel times are divided by α, which may help to select α in order to match known travel time data. This is a clear example of multiple solutions to an inverse problem. The paper underlines the role and the need to finely mesh unsaturated zones and also contacts between layers to reach the asymptotic convergence range, as it was carried out to verify the proof and as it should be completed to study any seepage problem. A few consequences of the new analytical proof and the rigorous procedure are shown with examples. Copyright © 2016 John Wiley & Sons, Ltd.     

Porphyroblast crystallization kinetics: the role of the nutrient production rate

The mechanisms that govern porphyroblast crystallization are investigated by comparing quantitative textural data with predictions from different crystallization models. Such numerical models use kinetic formulations of the main crystallization mechanism to predict textural characteristics, such as grain size distributions. In turn, data on porphyroblast textures for natural samples are used to infer which mechanism dominated during their formation. Whereas previous models assume that the rate‐limiting step for a porphyroblast producing reaction is either transport or growth, the model advanced in this study considers the production of nutrients for porphyroblasts as a potentially rate‐limiting factor. This production reflects the breakdown of (metastable) reactants, which at a specific pressure (P) and temperature (T) depends on the bulk composition of the sample. The production of nutrients that potentially contribute to the formation of porphyroblasts is computed based on thermodynamic models. The conceptual model assumes that these nutrients feed into some intergranular medium, and products form by nutrient consumption from that medium, with rates depending on reaction affinity. For any sequence of P–T conditions along a P–T–t path, the numerical model first computes an effective supersaturation (σ_eff) of the product phase(s), then an effective nucleation rate (J), and finally the amount of (porphyroblast) growth. As a result, the model is useful in investigating how the textural characteristics of a sample (of given bulk composition) depend on the P–T–t path followed during porphyroblast crystallization. The numerical model is tested and validated by comparing simulation results with quantitative textural data for garnet porphyroblasts measured in samples from the Swiss Central Alps.     

Numerical modelling of staged stope extraction in a tabular steeply dipping deposit

Stope stability is a key factor for the success of a mining operation. To optimise ore productivity while maintaining stope stability, the mining block/stope must be extracted in stages. Ore dilution will occur if the stope is not properly excavated/blasted. This study examines stope stability during mining in three stages, where the height of each stage stope is 10 m. The paper also presents simulation analysis of a typical steeply dipping tabular orebody at 1200 m depth below the surface, which is common in many Canadian underground hard rock mines. Numerical modelling analysis was conducted using the finite element program, RS^2D, where the non-linear elasto-plastic Mohr-Coulomb failure criterion was adopted. The rock reinforcement system (i.e. cable bolts) was modelled/installed in the stope footwall after each mining stage to strengthen access drifts and stabilise the rock mass around the stope that was disturbed by mining activity. Results are discussed in terms of depth of failure zones, total deformation and axial forces in cable bolts with respect to mining stage.     

A numerical simulation of gas flow during coal/gas outbursts

Summary A model of the gas flow in airways during an instantaneous outburst of coal and gas is formulated and solved numerically using MacCormack's explicit finite-difference scheme. This model is based on the assumption that geological structures, in-situ stresses and high-gas-pressure gradients play important roles in initiating an outburst, with the gas content and gas-pressure gradients being the most dominant factors. The fluid-dynamic processes that occur after an outburst are computed by the numerical integration of the complete time-dependent Navier-Stokes equations. The mixture velocity, the density and the gas-concentration profiles in both time and space domains (immediately after an outburst) are presented. The global results are useful in gaining an improved understanding of gas-flow patterns during coal/gas outbursts and in determining the range of the disturbance so that effective methods of control can be developed.Nomenclature a speed of sound - C gas concentration (mass) - C _v specific heat at constant volume - C _p specific heat at constant pressure - CFL Courant-Friedrichs-Lewy number - E total energy of the mixture - F the vector defined in Equation 27 - G the vector defined in Equation 28 - h entropy - h _i entropy at inlet - J _xi diffusion flux in the i-direction - k thermal conductivity of a gas - M Mach number - P pressure of a mixture (the partial pressure of gas) - P gas pressure - P _a atmospheric pressure     

岩土力学数值方法的应用及发展

本文为在第三届全国岩土力学数值分析与解析方法讨论会上的专题综述报告。文中就提交本届会议有关数值方法在岩土力学中的应用的论文以及数值方法的应用及发展的若干问题作一综合报导与述评。     

岩土力学数值分析方法研究

随着岩土工程领域的不断扩展与延伸,岩土力学数值分析方法得到了迅速发展,出现了各种各样的数值分析方法。将岩土力学常用的数值分析方法分为连续变形分析方法与非连续变形分析方法两大类,对各种方法的研究现状和最新进展进行了评述,着重介绍了各种方法的优缺点,并提出了解决问题的思路、方法和建议。     

Numerical computations of rock dissolution and geomechanical effects for CO2 geological storage

The paper is motivated by the long‐term safety analysis of the CO₂ geological storage. We present a methodology for the assessment of the geomechanical impact of progressive rock dissolution. The method is based on the use of X‐ray tomography and the numerical dissolution technique. The influence of evolution of the microstructure on the macroscopic properties of the rock is analysed by using periodic homogenization method. The numerical computations show progressive degradation of all components of the stiffness (orthotropic) tensor. Moreover, the evolution of associated mass transfer properties (as tortuosity and conductivity tensors), by using the periodic homogenization method, is also calculated. The correlation between the mechanical parameters and the transfer properties during the dissolution process is presented. The results show that the highest increase of the hydraulic conductivity (in direction Y) is not associated with the highest decrease of Young modulus in this direction. Moreover, the highest decrease of Young modulus (in the direction X) is not associated with percolation in this direction. Finally, an incremental law to calculate settlement, in case of a rock with evolving microstructure, is proposed. The solution of the macroscopic settlement problem under constant stress and drained conditions showed that the geomechanical effects of the rock dissolution are rather limited. Copyright © 2014 John Wiley & Sons, Ltd.     

Analysis of A Braced Excavation In Soft Soils Considering The Consolidation Effect

The studies of excavations in soft clayey soils are normally based on undrained total stress analyses. A better approach consists of taking into account the effects of consolidation during the excavation-bracing process and after the completion of the construction by means of coupled finite element analyses in effective stresses. In this paper, the geotechnical behaviour of a braced excavation in the soft soils of San Francisco (USA) is analysed, both during and after the construction period. Numerical analyses are performed with a finite element program, which incorporates the Biot consolidation theory (coupled formulation of the water flow and equilibrium equations) and soil constitutive relations simulated by the p-q-θ critical state model. Numerical results are compared with field results.     

Multi‐slicing strategy for the three‐dimensional discontinuity layout optimization (3D DLO)

Discontinuity layout optimization (DLO) is a recently presented topology optimization method for determining the critical layout of discontinuities and the associated upper bound limit load for plane two‐dimensional and three‐dimensional (3D) problems. The modelling process (pre‐processing) for DLO includes defining the discontinuities inside a specified domain and building the target function and the global constraint matrix for the optimization solver, which has great influence on the the efficiency of the computation processes and the reliability of the final results. This paper focuses on efficient and reliable pre‐processing of the discontinuities within the 3D DLO and presents a multi‐slicing strategy, which naturally avoids the overlapping and crossing of different discontinuities. Furthermore, the formulation of the 3D discontinuity considering a shape of an arbitrary convex polygon is introduced, permitting the efficient assembly of the global constraint matrix. The proposed method eliminates unnecessary discontinuities in 3D DLO, making it possible to apply 3D DLO for solving large‐scale engineering problems such as those involving landslides. Numerical examples including a footing test, a 3D landslide and a punch indentation are considered, illustrating the effectiveness of the presented method. © 2016 The Authors. International Journal for Numerical and Analytical Methods in Geomechanics published by John Wiley & Sons Ltd.     

Quantification of stability improvement of a dump through biological reclamation

An integrated study on biological stabilisation of a dump slope has indicated that biological reclamation with grass and tree species should be considered for long term stability of this coal mine dump in India. The grasses have greater soil binding capacity and help to control soil erosion and improve dump stability. Native grasses such as Bamboo (Dendrocalmus strictus) and Kashi (Saccharum spontaneum) are the important constituents of grass species which can stabilise the dump slopes. Field observation of growth performance of grasses have indicated that mean grass height, root depth and below-ground root biomass are 185 cm (±68), 45 cm (±5) and 467 g m^–2 (±170), respectively after three years of grass growth on Mudidih overburden dump slope in India. The growth performance of tree species, namely Sisum (Dalbergia sisoo) and Subabool (Leucena lecocephala), in terms of height, diameter increment, below-ground biomass and root depth have shown mean values of 219 cm (±94), 48 mm (±6), 4.0 kg m^–2 (±1.5) and 1 m (±0.1), respectively. This acts as biological fertility which helps in root proliferation and enhancement of dump stability. From the numerical modelling it is suggested that roots of these grass and tree species have significantly enhanced the factor of safety of dump from 1.4 to 1.8 and therefore have a positive role in maintaining long term stability.