Numerical modelling of in situ stress calculation using borehole slotter test

Accurate determination of in situ stress magnitude and orientation is an essential element of the design process of all underground openings. A stress calculation method was proposed for the new stress measurement technique using the borehole slotter device. Two major objectives were the focus of this research work. The first goal was to simulate the slotter test process numerically and delve into the mechanisms involved in this test. A precise 3D numerical model of a typical slotter test condition was constructed using the FLAC3D code. The effects of variations in rock mass deformation modulus on the strain/stress relieve, and thus borehole slotter test results, were investigated numerically. The second objective of the work was to employ 3D modelling in the interpretation of slotter field tests conducted at Bakhtiari dam site. These tests were aimed at determining the stress magnitude and orientation to be used in the design of underground chambers and tunnels associated with Bakhtiari dam. The stress regimes measured in field were applied as boundary condition on the constructed 3D model and a backward analysis was conducted. For each case the actual strain field measured was compared against strain field calculated numerically. Accordingly, the boundary condition (stress magnitude and orientation) associated with the model results that provided the best fit to the measured data was determined as the governing stress regime. A good agreement was achieved between numerical and field test results. The obtained numerical results provided valuable insights in selecting the governing in situ stress condition from a set of recorded field data.     

Numerical methods in rock mechanics

The purpose of this CivilZone review paper is to present the techniques, advances, problems and likely future development directions in numerical modelling for rock mechanics and rock engineering. Such modelling is essential for studying the fundamental processes occurring in rock, for assessing the anticipated and actual performance of structures built on and in rock masses, and hence for supporting rock engineering design. We begin by providing the rock engineering design backdrop to the review in Section 1. The states-of-the-art of different types of numerical methods are outlined in Section 2, with focus on representations of fractures in the rock mass. In Section 3, the numerical methods for incorporating couplings between the thermal, hydraulic and mechanical processes are described. In Section 4, inverse solution techniques are summarized. Finally, in Section 5, we list the issues of special difficulty and importance in the subject. In the reference list, ‘significant’ references are asterisked and ‘very significant’ references are doubly asterisked.     

Influence of faulting on a mine shaft—a case study: part II—Numerical modelling

The X41 shaft is the man and supply shaft at Copper Mine, Mount Isa, Australia. There has been observed evidence of degradation manifested by the development of cracks in the shaft concrete lining since the early nineties. In addition, the shaft steel structure is being deformed and needs regular and meticulous maintenance. The shaft degradation has been attributed to the presence of two major geological structures, the W41 and W42 faults, which intersect the shaft in two distinct locations.Since the X41 shaft gives a direct access to the Copper Mine, it has to remain operational for the mine life. An objective of this study was to gain a better understanding of the mechanisms inducing damage to the shaft. In order to assess the long-term integrity of the shaft, it was essential to evaluate the impact of its deformation, related to the late mining status of the Copper Mine and the presence of the two major faults. It was important to determine an estimate of the future rate of displacement, as well as the total displacement, for the rest of the mine life.This paper presents a case study whereby the causes of shaft degradation were examined. The influence of faulting and mining sequence on the stability of the main mine shaft were investigated by means of field investigations and numerical modelling. This paper concentrates on the numerical modelling performed as part II of this project. It presents exhaustively the methodology used to build the numerical model and presents the outcomes.     

Numerical modelling of ore dilution in blasthole stoping

The paper presents the results of a study of the factors causing stope wall overbreak or ore dilution in a blasthole stoping environment. A series of three-dimensional numerical models are developed and analyzed to examine the effect of mining depth, in situ stress as well as stope geometry and orientation on stope wall overbreak. A characteristic orebody and mine design configuration is adopted and used as a basis to carry out comprehensive model parametric study, from which a simple, graphical design tool is derived for the prediction of stope overbreak. It is shown that stope overbreak is significantly affected by the stope aspect ratio and the orientation of major principal in situ stresses with respect to the stope. The methodology presented in this paper can be adopted to develop mine-specific design tools for the estimation of ore dilution associated with a proposed mine design. This can be extremely helpful in the process of underground mine planning and optimization.     

A review of techniques, advances and outstanding issues in numerical modelling for rock mechanics and rock engineering

The purpose of this review paper is to present the techniques, advances, problems and likely future developments in numerical modelling for rock mechanics. Such modelling is essential for studying the fundamental processes occurring in rocks and for rock engineering design. The review begins by explaining the special nature of rock masses and the consequential difficulties when attempting to model their inherent characteristics of discontinuousness, anisotropy, inhomogeneity and inelasticity. The rock engineering design backdrop to the review is also presented. The different types of numerical models are outlined in Section 2, together with a discussion on how to obtain the necessary parameters for the models. There is also discussion on the value that is obtained from the modelling, especially the enhanced understanding of those mechanisms initiated by engineering perturbations. In Section 3, the largest section, states-of-the-art and advances associated with the main methods are presented in detail. In many cases, for the model to adequately represent the rock reality, it is necessary to incorporate couplings between the thermal, hydraulic and mechanical processes. The physical processes and the equations characterizing the coupled behaviour are included in Section 4, with an illustrative example and discussion on the likely future development of coupled models. Finally, in Section 5, the advances and outstanding issues in the subject are listed and in Section 6 there are specific recommendations concerning quality control, enhancing confidence in the models, and the potential future developments.     

Numerical analysis of stresses and displacements for the Tafjord slide, Norway

Numerical modelling has been used for analyzing stresses and displacements for the very steep and more than 1,000 m high Heggura rock slope near Tafjord, Norway where a disastrous 3 million m³ rock slide occurred in 1934. It is shown that very anisotropic stresses exist near the slope surface and displacements of the remaining slope as result of the 1934 slide have been calculated to up to 210 mm. Such considerable displacements are believed to have a significant impact on the present and future stability of the Heggura slope.     

Limit analysis solutions for the bearing capacity of rock masses using the generalised Hoek–Brown criterion

This paper applies numerical limit analyses to evaluate the ultimate bearing capacity of a surface footing resting on a rock mass whose strength can be described by the generalised Hoek–Brown failure criterion [Hoek E, Carranza-Torres C, Corkum B. Hoek–Brown failure criterion—2002 edition. In: Proceedings of the North American rock mechanics society meeting in Toronto, 2002]. This criterion is applicable to intact rock or heavily jointed rock masses that can be considered homogeneous and isotropic. Rigorous bounds on the ultimate bearing capacity are obtained by employing finite elements in conjunction with the upper and lower bound limit theorems of classical plasticity. Results from the limit theorems are found to bracket the true collapse load to within approximately 2%, and have been presented in the form of bearing capacity factors for a range of material properties. Where possible, a comparison is made between existing numerical analyses, empirical and semi-empirical solutions.     

Shear strength criteria for rock,rock joints,rockfill and rock masses: Problems and some solutions

Although many intact rock types can be very strong, a critical confining pressure can eventually be reached in triaxial testing, such that the Mohr shear strength envelope becomes horizontal. This critical state has recently been better defined, and correct curvature or correct deviation from linear Mohr–Coulomb (M-C) has finally been found. Standard shear testing procedures for rock joints, using multiple testing of the same sample, in case of insufficient samples, can be shown to exaggerate apparent cohesion. Even rough joints do not have any cohesion, but instead have very high friction angles at low stress, due to strong dilation. Rock masses, implying problems of large-scale interaction with engineering structures, may have both cohesive and frictional strength components. However, it is not correct to add these, following linear M-C or nonlinear Hoek–Brown (H-B) standard routines. Cohesion is broken at small strain, while friction is mobilized at larger strain and remains to the end of the shear deformation. The criterion ‘c then σ_n tan φ’ should replace ‘c plus σ_ntan φ’ for improved fit to reality. Transformation of principal stresses to a shear plane seems to ignore mobilized dilation, and caused great experimental difficulties until understood. There seems to be plenty of room for continued research, so that errors of judgement of the last 50 years can be corrected.     

Influence of geometry and material properties on the axial vibration of a rock bolt

A continuous dynamic model for the axial vibration of a rock bolt system is presented. The model comprises three sections: the fixed length, bonded into the rock, the free length, which is not coupled to the rock, and the protruding length, which extends beyond the rock. The head assembly is modelled as a discrete mass and a spring, and a further discrete mass is included, representing a testing device that can be attached to the protruding end. Each section is modelled as a continuous elastic rod governed by the wave equation, with suitable compatibility conditions applied between the sections and boundary conditions, which also account for the effect of the discrete components, applied at the ends. Solutions in non-dimensional form are substituted into the boundary conditions to allow the natural frequencies to be calculated, and it is shown that two possible solutions for the mode shapes can be used for the fixed length—an exponential solution or the classical sinusoidal solution—depending on the stiffness of the grout relative to that of the bar. The conditions for which the two solutions are valid are developed, and changes in the frequency ratio with changes in length ratio, and the stiffness ratios of the grout and the anchor head relative to the stiffness of the fixed length of the anchorage are examined. Generally, the state of a bolt after installation is unknown and this does not provide proper assurance of the safety of the structure for which the bolts are used. The model provides a viable tool for helping to assess the condition of the bolt by using the natural frequencies associated with areas of the bolt of particular interest, e.g. the free length. The results show how the changes in the stiffness and/or length ratios affect the dynamics associated with fixed length of the bolt and the quality of the bonding installation. A case study is presented showing how the model can be used effectively to interpret real data.     

Numerical simulation of compaction-induced stress for the analysis of RS walls under working conditions

This paper aimed to verify numerical modelling of compaction-induced stress (CIS) for the analysis of geosynthetic-reinforced soil (GRS) walls under working stress conditions. Data from a full-scale well-instrumented GRS wall was used for a numerical analysis. The results from the wall used in this study have already been used for validation in several other numerical modelling studies. Nevertheless, in none of these studies was the real value of CIS specified for the vibrating plate compactor used in the wall employed. In the present study, the real value of CIS is employed. The CIS is modelled using a new procedure presented in this paper in addition to two other procedures found in the literature. The results indicate that when the real value of CIS was simulated using a strip load applied to the top of each backfill layer, the numerical model accurately represented the measurements. The accuracy of the results, however, depends on the width of the strip load used to model the CIS. Nevertheless, as this type of compaction modelling procedure is time consuming, modelling of CIS by applying a distribution load at the top and bottom of each soil layer is suggested as an alternative procedure.     

Numerical modelling and mechanical behaviour analysis of ancient tunnel masonry structures

As with all older construction, ancient tunnels feature particular characteristics, especially as regards past construction methods, geometrical design considerations and the set of construction materials used. Old tunnels usually display a unique vaulted section shape built with masonry. The present paper proposes two numerical models of an old tunnel supported by masonry; these models were developed by the well-known Universal Distinct Element Code (UDEC). A masonry mechanical behaviour analysis and numerical simulation of the masonry ageing phenomenon will also be addressed by means of an experimental design to study the influence of masonry block physical properties on the mechanical behaviour of masonry structures in old tunnels.     

Numerical analysis of concrete block masonry beams under three point bending

A parametrical study of masonry beams through numerical modelling has been performed in order to better understand the mechanical behaviour of these elements. Boundary conditions, geometry and reinforcement ratios are the main parameters analysed in this study. The numerical simulation is performed with DIANA^® software, based on the Finite Element Method. A comparison between numerical and experimental results is presented in order to validate the simulation. In conclusion, it was verified that the behaviour of masonry beams is greatly affected by the boundary conditions and geometry, as expected. With regard to reinforcement, it was noted that horizontal reinforcement increases the flexural strength of beams. On the other hand, variation in horizontal reinforcement had no influence on the shear resistance of masonry beams. Finally, the combination of horizontal and vertical reinforcements is shown to enhance the flexural and shear behaviour of masonry beams.     

龙潭隧道页岩段施工优化数值模拟

选取龙潭隧道右线页岩地段为研究对象,用有限差分程序研究了该段施工过程中,不同开挖方法条件下围岩的受力和变形特征,通过对比分析,确定了该段施工的优化方案,方案安全有效,对类似工程具有一定的借鉴意义。     

Numerical modelling of strength and energy release characteristics of pillar-scale coal mass

Coal burst is a manifestation of rapid energy release,which is considered as one of the most critical operational hazards in underground coal mines.This study numerically investigates the effects of discontinuities on the strength and energy release characteristics of coal mass samples under uniaxial compression.The universal distinct element code(UDEC) was used to model pillar-scale coal mass samples that were represented by an assembly of triangular deformable blocks,and pre-existing discontinuities such as bedding planes and cleats were also included in the models.It shows that cleat spacing can have a significant impact on compressive strength and energy release,with both strength and energy release(magnitude and rate) reducing as the number of cleats was increased.This work is one of the first attempts to numerically model and quantify the energy release which occurs during the failure of pillar-scale coal mass samples with varying cleat densities.The insights from the numerical modelling can help to understand the possible energy release mechanisms and associated coal burst potential in changing coal cleat conditions.     

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.     

Numerical modelling of high strength steel beams at elevated temperature

High strength steels are increasingly common in structural engineering applications owing to their favourable strength to weight ratio, excellent sustainability credentials and attractive physical and mechanical properties. However, these grades are under-used in structures owing to a lack of reliable information relating to their structural performance, particularly at elevated temperature. This paper presents a review of high strength steels in structural applications including the key design considerations. Particular focus is given to the lateral torsional buckling response of laterally unrestrained beams. A finite element model is developed to investigate this behaviour at ambient and elevated temperature. A series of beams between 500 and 4500 mm in length are studied in order to develop buckling curves which are comparable with current design provisions. At ambient temperature, it is shown that all of the buckling curves currently included in Eurocode 3 Part 1-1 give unsatisfactory and potentially unsafe predictions. In elevated temperature conditions, the buckling curves presented in Eurocode 3 Part 1–2 depict the behaviour reasonably well but, at relatively high slenderness values, the standard does not always provide a safe prediction. Revised bucking curves are proposed for high strength steel beams for laterally unrestrained beams made from high strength steel.     

Nonlinear simulation of lattice girder segment tests

Lattice girders often replace conventional steel rib arches as a means of temporary support in tunnels and often have a comparative advantage over the latter mainly due to their lighter weight. Their use is directly related to the application of a shotcrete layer, in which they are encased, forming thus a composite structure that has been proved successful over numerous projects worldwide. However, any loads from the surrounding rock before shotcrete placement or hardening, have to be carried out by the lattice girder itself. Such loads may be concentrated in parts of the girder, due to sliding or falling blocks, detaching strata, reacting ground, etc. Their effects on it, which are nonlinear, necessitate analysis with detailed models; their adequacy should be experimentally validated. Therefore, a series of loading tests is conducted on simply supported arched lattice girder segments, in which the load is induced horizontally at the roller support. These tests are then simulated numerically with various 3D models. The appropriateness of the latter is thus checked by comparing the ultimate loads and deflections, which were found to be limited by buckling.     

The elastic deformability and strength of a high porosity, anisotropic chalk

The submission explores the mechanical behavior of a very porous chalk formation, in which a system of ancient caverns was excavated. Incidents of general and localized failure of these ancient caverns initiated a comprehensive laboratory testing program aimed at investigating the anisotropic nature of the stress–strain response and strength of the material. It was felt that these aspects could be of profound importance in the stability of the cavern systems. The effect of water content over a broad range from 1.5% to saturation, on the compressive and tensile strength was also studied. Testing was based on the hollow cylinder methodology and was supplemented with uniaxial compression of solid cylinders and diametric compression of Brazilian disks. Use of the hollow cylinder methodology was extended to failure conditions.Test results illustrate the anisotropic nature of the stress–strain response of the chalk. The material clearly displays transverse isotropy, with horizontal bedding planes corresponding to the plane of material symmetry. The modulus of deformation within the plane of material symmetry is significantly higher than that perpendicular to bedding planes. Torsional shear of hollow cylinder specimens was employed to measure the shear modulus of the chalk.The testing carried out up to failure illustrated the anisotropy of the chalk strength. The compressive strength was found to be 50% higher in compression parallel to bedding than perpendicular to bedding. Increasing water content was found to have a consistent detrimental effect on compressive strength, tensile strength and material stiffness. The most drastic effect was found due to relatively small increases in water content, at initial water contents of less than 5%. Anisotropy of the chalk strength was found to persist over the entire range of water contents considered.     

Numerical simulation and sensitivity analyses of full-scale test embankment with reinforced lightweight geomaterials on soft Bangkok clay

A full-scale test embankment was constructed on soft Bangkok clay using rubber tire chip–sand mixture as a lightweight geomaterial reinforced with geogrid under working stress conditions. The facing of the embankment was made of segmental concrete blocks with rock filled gabion boxes as the facing to the sloping sides. This paper attempts to simulate the behavior of the full-scale test embankment using PLAXIS finite element 2D program by means of undrained analysis in the construction stage and thereafter consolidation analysis was performed during the service stage. The settlement predictions of the soft clay foundation mostly depended on the assumed thickness of the weathered crust and the OCR values of the soft clay layer. The predicted excess pore water pressures were sensitive to the OCR values of the soft clay layer. The lateral wall movements were overpredicted by the analysis due to the partially drained consolidation process at the early stage of the construction. The FEM computed geogrid movements were smaller than the observed field data due to the use of lightweight tire chips-sand backfill. The maximum tension line agreed reasonably well with the coherent gravity bilinear failure plane. The sensitivity analyses of settlements, excess pore water pressures, lateral wall movements, geogrid movements and tensions in geogrid were performed by varying the weathered crust thickness, the OCR values of soft clay, the permeability values of the soft clay and the interface coefficient of the geogrid. The settlements and the excess pore water pressures changed significantly when the OCR and the permeability values of soft clay were varied. The interface coefficient of the geogrid reinforcements affected the lateral wall movements, geogrid movements and tensions in the geogrids. The higher interface coefficient yielded less wall/geogrid movement and resulted in higher tensions in geogrids as expected. The results of analyses show that the FEM analysis using 2D plane strain conditions provided satisfactory predictions for the field performance.