Stress field determination from local stress measurements by numerical modelling

A back analysis using a three-dimensional (3D) boundary element method (BEM) is used to calculate the far-field stress state from local stresses measured in situ. The far-field stresses are decomposed into tectonic and gravitational components and account for the influence of localized faulting and topography. Therefore, the far-field stresses are taken to consist of a constant term, a term that varies linearly with depth, and a hyperbolic term, with one of the principal stresses being vertical. A BEM for inhomogeneous bodies is introduced to calculate elastic gravitational stresses, which is necessary for determination of the far-field stresses.An application to the stress field determination for the Mizunami underground research laboratory (MIU) is carried out. Based upon the local stresses generally measured by conventional hydraulic fracturing (HF), the unknown stress state at MIU is estimated and compared with the measurements carried out recently by the improved HF method with flow rate measurements at the position of straddle packer. After calculating the far-field stress state by BEM back analysis, 3D-finite difference methods (FDM) forward analysis was carried to calculate the in situ stresses at certain locations. The 3D FDM results roughly coincide with the measured results.     

瀑布沟工程地下厂房区地应力场的二次计算研究

首先，采用遗传算法与有限单元法相结合的联合反演方法，对瀑布沟工程地下厂房区地应力场进行大范围的反演分析；然后，考虑主要断层，基于复合单元法，采用位移边界条件，对地下厂房区地应力场进行二次计算，其计算范围与洞室开挖稳定性分析的范围一致。研究结果表明：考虑主要断层的二次计算，不仅可以得到主要断层准确的初始应力，而且可改善一次反演所得的初始地应力场，减小计算相对误差；同时，在计算水平提高的条件下，进行第一次大范围反演时，应尽量考虑主要断层等不连续结构面。     

高拱坝坝址区初始地应力场的二次计算

 建立小湾水电站坝址区大范围有限元模型,考虑工程附近较大区域内的地形、地势和河流大转弯等因素,采用遗传算法与有限单元法相结合的联合反演方法,对坝址区初始地应力场进行一次反演;然后,考虑坝址区附近主要地质构造,建立坝基开挖松弛效应分析的小范围有限元模型,基于子模型方法,通过在一次反演模型中插值获得小范围模型的位移边界条件,对初始地应力场进行二次计算。研究结果表明：软弱地质构造对初始地应力场的反演有一定影响,一次反演中不连续结构面附近应力计算值与实测值相差较大;考虑软弱地质构造后的二次计算改善了一次反演所得的初始地应力场精度,大部分测点应力计算值更接近实测值,相对误差也逐渐减小,可将其应用于后续坝基开挖松弛效应分析中;反演结果同时也表明所采用的研究方法是可行的,对类似工程具有参考意义。     

Quality control of overcoring stress measurement data

The in situ state of stress is one of the key rock mechanics factors related to the safety and stability of underground excavations for civil and mining engineering purposes. However, measurement and interpretation of stress have their difficulties. In particular, practical and objective tools have not been developed to judge transient strain behaviour during overcoring. The work described in this paper was set up by the nuclear waste management companies Posiva Oy (Finland) and Svensk Kärnbränslehantering AB (Sweden) to improve the quality of interpretation of overcoring stress measurement results. Thus, the primary product of the project is a quality control capability for overcoring stress measurement data. For this purpose, a computer program was developed which can simulate the transient strains and stresses during the overcoring process for any in situ stress and coring load conditions. The solution is based on superposition of elastic stresses and the basic idea can be applied for different overcoring probes with minor modifications and recalculation of stress tensors. The measured strains can be compared to the calculated ones to check whether the measured transient behaviour accords with the interpreted in situ state of stress. If not, the in situ state of stress can be calculated based on any transient or final strain values. The transient stresses can also be compared to a strength envelope of intact rock and thereby the core damage potential can be estimated.     

基于声弹理论的地应力超声测量方法

首先描述岩石的声弹理论,给出岩石的应力与弹性波波速之间的理论关系;其次利用岩石应力与弹性波波速之间的理论关系提出地应力超声测量方法,即通过测量套孔应力解除前后的孔壁超声波波速的变化,利用声弹理论反演出地应力。通过数值算例讨论地应力对孔壁超声波速的影响,其结果表明,该方法可以有效地确定地应力的大小和方向。     

Determination of three dimensional in situ stress from core discing based on analysis of principal tensile stress

To determine all of the components of in situ stress from core discing, both the directions and magnitudes of the principal in situ stresses must be determined for a disc of a given thickness. In this study, we analyzed the direction and magnitude of tensile stress below an HQ core stub for 11 core lengths using stress conditions under which core discing is likely to occur. First, based on an analysis of the direction of tensile stress below the core stub, we propose a method for determining directions of in situ stress from the height distribution at the periphery of the end surface of a disc. This method can be used with a disc of any thickness. Next, based on an analysis of the magnitude of tensile stress in the central part of a core, we propose a linear criterion for core discing, which can be applied to a core of any length. This criterion was in good agreement with an empirical formula obtained previously in laboratory experiments. By combining information on the direction of in situ stress and the linear criterion for core discing, we propose a method for determining all of the components of in situ stress from core discing under the assumption that vertical stress is given by the overburden stress. Finally, these methods were applied to discs obtained from a field where hydraulic fracturing was performed to measure horizontal stresses. The results showed that the azimuths of the principal stresses estimated from core discing were consistent with those of the principal horizontal stresses determined by hydraulic fracturing and that while the magnitudes of the principal horizontal stresses estimated from core discing showed a large scatter, they were similar to those determined by hydraulic fracturing.     

Measurement of local stress and estimation of regional stress associated with stability assessment of an open-pit rock slope

This paper discusses the concept of a new methodology for rock slope stability assessment. Then, results on rock stress measurement using the compact conical-ended borehole overcoring (CCBO) technique at Torigata limestone mine in Japan are presented. A procedure for back analysis of the regional strain and stress field with the 3-D finite element method, using the measured local stress, is suggested and demonstrated successfully in relation to Torigata limestone mine. Finally, to estimate the state of stress at the mine excavation level, 3-D finite element analyses were performed using boundary conditions from the analyzed regional strain and stress field. It is shown that the horizontal stress at the present excavation level is not reduced, and that the horizontal stress component cannot be disregarded in estimating the stability of rock slopes at this location, even though the mine is located near the top of a mountain.     

巷道围岩应力及力学性质的套筒致裂试验研究

本文介绍了用套筒致裂量测岩体应力及力学性质的方法及量测结果。研究结果表明,岩体的基本参数——主应力的大小和方向、岩体的弹性和刚性,可以用成本低廉的钻孔套筒致裂装置进行量测。用套筒致裂法不仅能测出岩体在弹性阶段的变形特性,而且能测出非弹性阶段的特性,从而可为矿山应力监控方法提供可靠的数据基础。     

Analysis of stress measurements using a numerical model methodology

A method is described that enables the boundary conditions of numerical models to be calibrated to individual or groups of stress measurements. The method was developed to interpret stress measurements made in mines where it is not possible to locate the measurement points far enough away from excavations to obtain a direct measurement of the pre-mining stress field. It can also be used to analyze measurements that are influenced by surface topography. The stress field at any point is assumed to be comprised of gravitational and tectonic components. The tectonic component is assumed to act entirely in the horizontal plane in the far-field and at the model boundary. Unit normal and shear tractions are applied to the model boundaries and the response is computed at the location of the measurement points in the model. An optimization procedure is used to compute the proportions of each unit response tensor that is required, in addition to the gravitational stress, to reproduce the measured stress at the measurement point in the model. Scaling of the measured stress tensor can be included in the optimization to account for incorrect rock modulus scaling of the measured strains. The method is demonstrated using a synthetic set of stresses from a numerical model in which the measurements are influenced by a nearby excavation and topography.     

超声波钻孔电视在地应力测量研究中的应用

通过一个300m和一个800m典型钻孔的实际测试结果,揭示超声波钻孔电视在地应力测量研究领域中的几个应用实例,如:岩层裂缝的检测、地应力测试段的选定、岩芯定向,特别是对水压致裂法形成的诱发裂缝和孔壁崩落的测定及分析,在地应力测量研究中将可显示出较强的优势,尤其是最大水平主应力方向的获取,更优于其它方法。并将在两个钻孔中所得结果与常用的定向印模测试结果进行了对比,取得了较为一致的成果。关于超声波钻孔电视对水压致裂法诱发裂缝的测试还未曾见过报道。最后简述了地应力数值大小的推估研究与展望。     

非圆形洞室应力监测反馈分析的复变函数方法

在地下工程设计中，横截面上二维初始应力场是地下洞室稳定性分析的重要依据，必须首先需要解决的问题之一。初始应力场一般通过现场试验来测定，但费工费时而且往往很难得到理想效果。在洞室开挖时，利用现场监测资料进行反馈计算能得到较理想的初始应力场。20世纪80年代后提出了多种位移反分析方法，用少数的实测数据分析洞室稳定性，获得较为满意的结果，已得到广泛应用。但应力监测的反馈分析仍鲜为人知。采用穆斯海里什维里弹性平面问题的复变函数解法的基本原理，对非圆形地下洞室应力反馈分析进行了探讨，相应地推导了一系列公式。对映射函数的推求采用实际边界上几个控制点的限定方法，简捷又方便。     

A stress calculation model for the 3D borehole slotter

A stress calculation model is proposed for a new stress measurement device called the 3D borehole slotter. This instrument allows the calculation of the 3D in situ stress tensor in a single borehole without the need for a drill on the site at the time of the measurement and without bonding strain gauges at the borehole wall. The 3D borehole slotter requires cutting half moon shaped slots with different orientations at a borehole wall using a small diamond impregnated blade and monitoring the strains which are relieved normal to the slot. This paper shows that combining six slots cut on the borehole wall with one to three slots cut parallel to the borehole axis and five to three cut with a 45° angle, allows the calculation of the in situ stress tensor. The optimal slot combination is determined and 3D finite element analyses are used to evaluate the degree of stress relief normal to the slot at the strain sensor location and also to estimate the strains induced parallel to the slot by this local stress relief. The results obtained from these analyses are then used directly in the stress calculation model.     

某拱坝右岸拱肩槽开挖边坡锚固仿真与优化研究

首先基于一次宏观反演的初始应力场进行二次精细模拟得到了某拱坝坝区局部模型的初始地应力场。接着基于加锚节理岩体流变模型,应用自主开发的三维弹粘塑性有限单元程序模拟了该初始地应力场作用下该拱坝右岸拱肩槽岩石高边坡开挖过程预应力锚索、系统锚杆等锚固件的支护作用。分析了现行锚固方案与锚固进度下边坡岩体的位移、应力和点安全系数等分布规律,最后在此基础上对该锚固方案和锚固进度进行了优化,确保了该边坡的稳定与安全。     

Measurements of induced stress and strength in the near-field around a tunnel and associated estimation of the Mohr–Coulomb parameters for rock mass strength

The state of induced stress measured by the compact conical-ended borehole overcoring technique in the immediate roof of an approach tunnel excavated under high rock stress is described. During the measurements, core disking was observed. An X-ray Computed Tomography (CT) scanner was used to select strain data uninfluenced by the core disking; then the induced rock stress was estimated from selected strain data. From these results, it is shown that the non-destructive investigation using X-ray CT is effective for visualization of the fracturing within cores and the selection of strains measured during overcoring. Furthermore, the Mohr–Coulomb failure criterion parameters for the rock mass were estimated by comparing the measured stresses with the shear strength of in situ rock and the uniaxial compressive strength determined in laboratory tests.     

岩层剪切错位及其对地基边坡稳定的影响

 　地基边坡大规模的开挖造成地应力在一定程度上的复活, 从而形成岩层或岩体的剪切 错位, 外观表现为地基边坡炮孔和大口径钻孔的剪切错位。由此建立了地应力动态平衡论。 以此错位量, 可以反演该区的地应力数值。地应力可以集中, 也可以传递和扩散, “边坡作用 地应力”对边坡稳定有一定的影响。     

Numerical modelling of three-dimension stress rotation ahead of an advancing tunnel face

As underground excavations and construction works progress into deeper and more complex geological environments, understanding the three-dimensional redistribution of excavation-induced stresses becomes essential given the adverse consequences such stresses will have on the host rock strength and the subsequent excavation stability. This paper presents the results from a detailed three-dimensional finite-element study, which explores near-field stress paths during the progressive advancement of a tunnel face. These results demonstrate that as the tunnel face approaches and passes through a unit volume of rock, the spatial and temporal evolution of the three-dimensional stress field encompasses a series of deviatoric stress increases and/or decreases as well as several rotations of the principal stress axes. Particular emphasis is placed on the rotation of the principal stress axes as being a controlling factor in the direction of fracture propagation. If this orientation changes in time, i.e. during the progressive advancement of the tunnel face, the type of damage induced in the rock mass and the resulting failure mechanisms may also vary depending on the type and degree of stress rotation. The significance of these effects is discussed in terms of microfracture initiation and propagation, brittle fracture damage and rock strength degradation. Further analysis is also presented for varying tunnelling conditions including the effects of tunnel alignment with respect to the initial in situ stress field, excavation sequencing and elasto-plastic material yielding. Implications with respect to the new Gotthard base tunnel, currently under construction in Switzerland, are presented using examples from the nearby Furka tunnel.     

An overview of rock stress measurement methods

This paper presents an overview of methods that have been used to estimate the state of stress in rock masses, with the emphasis on methods applicable to hard rocks and Scandinavia. Rock stress is a difficult quantity to estimate because the rock stress measuring techniques consist of perturbing the rock, measuring displacements or hydraulic parameters, and converting the measured quantities into rock stresses. There are two main types of method: those that disturb the in situ rock conditions, i.e. by inducing strains, deformations or crack opening pressures; and those that are based on observation of rock behaviour without any major influence from the measuring method. The most common methods are briefly described including their application areas and limiting factors.     

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.     

Damage in a rock core caused by induced tensile stress and its relation to differential strain curve analysis

A finite element analysis was carried out to analyze the distribution of tensile stress within and below a long HQ core stub for 77 in situ stress conditions. The maximum tensile stress experienced by the core along the axis during boring under in situ stress was accumulated in an equal-area stereonet for a central part of the cross-section. The maximum tensile stress accumulated for a central area of less than about 60% of the total cross-sectional area was concentrated in a certain direction, which was nearly the same direction as the minimum principal stress for all of the stress conditions, except those in which the minimum principal stress (σ₃) was equal to the intermediate principal stress (σ₂). When σ₂=σ₃, the direction of the cumulative maximum tensile stress lay approximately in the plane of σ₂=σ₃, which is perpendicular to the maximum principal stress. Based on the assumption that a penny-shaped crack is produced normal to the maximum tensile stress in proportion to the magnitude of such stress, the crack density in the core was analyzed by calculating strain under hydrostatic pressure as in differential strain curve analysis (DSCA). The maximum principal crack density in the central part of the core was much greater than the intermediate and minimum principal crack densities, excluding special cases in which σ₂=σ₃. The direction of the maximum crack density was similar to that of the accumulated maximum tensile stress. Thus, the direction of the maximum crack density obtained by DSCA predicts the direction of the minimum principal stress rather than that of the maximum principal stress, if the distribution of pre-existing microcracks before stress relief is isotropic and if additional microcracks are produced only by tensile stress during boring under in situ stress. To verify this, crack parameters were measured by DSCA for two cores of quartz-diorite, which were taken by overcoring when the hemispherical-ended borehole technique was used to measure in situ stress. The directions of the maximum crack parameters measured by DSCA were nearly the same as that of the minimum principal stress for one of the cores. For the other core, for which the magnitudes of the intermediate and minimum principal stresses were close to each other and, accordingly, the direction of the minimum principal stress was uncertain, the direction of the maximum crack density estimated by damage analysis under the assumption that σ₂=σ₃ coincided with the directions of the maximum crack parameters measured by DSCA.     

地层三维粘弹性反演分析

本文在假设围岩服从三元件粘弹性模型和初始地应力场分量按线性规律分布的基础上,采用直接边界单元法,依据边界、域内位移量测信息和域内扰动应力量测信息,建立了可以同时反演确定三维初始地应力和弹性常数E₁,E₂,v以及粘性常数η₂的计算法。文中采用插值函数,考虑了在边界上量测点的任意设置问题。最后,给出了算例验证及工程应用实例。