Optimized back analysis method for stress determination based on identification of local stress measurements and its application

This paper presents an optimization method, including the identification of local stress measurements and a two-stage back analysis, to determine in situ stress under complex conditions. Firstly, the macro-regional distribution characteristics of in situ stress can be interpreted by analyzing regional geological conditions, topography, as well as rock mass failure phenomena. Then, a stereographic projection method (SPM) is used to determine the distribution features of stress tensor on an arbitrary plane. On this basis, some representative measured data, which can reflect the distribution characteristics of in situ stress in the study area can be identified. After that, a first-stage back analysis by finite difference method (FDM) is used to calculate the field stresses from the selected in situ measured data. The obtained boundary stresses are taken to consist of a constant term, a term that varies linearly with depth, and a hyperbolic term. Further, a second-stage back analysis by discrete element method (DEM) is carried out to determine the local field stresses which are significantly affected by discontinuities and excavations. The FDM back analysis results can serve as the initial input stress conditions for DEM analysis, and the optimum stress conditions for DEM analysis will be reasonably obtained by using the uniform design method through the second-stage back analysis. To show the feasibility of the optimized method, it is applied to the Wudongde Hydropower Station to determine in situ stress. Based on local stress measurements by borehole stress relief method using hollow inclusion strain gauges, some representative measured data are selected by SPM. The unknown state of stress in the station is estimated through the first-stage back analysis by FDM. For some local key areas, encountered discontinuities or excavations in the vicinity, the local field stresses are calculated through the second-stage back analysis by DEM. Finally, the results are compared with those elicited from the borehole stress relief method. It is shown that the calculated results by the first-stage back analysis agree well with the measured ones on the whole, but the discrepancy is large in the vicinity of discontinuities as well as excavation disturbance. However, the calculated results by the second-stage back analysis roughly coincide with the measured data with lower allowable error.

     

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。     

Influences of changes in mechanical properties of an overcored sample on the far-field stress calculation

The concentration factors for the determination of far-field stresses have been calculated based on three-dimensional FLAC^3D simulated results. FLAC^3D is an explicit finite difference computer program. Three-dimensional numerical simulations have been conducted using FLAC^3D to determine the influence of altered overcored sample parameters on the far-field stress calculation. Both Young's modulus and Poisson's ratio are known to change during overcoring in highly stressed rock as a result of stress-relief damage. Modification factors have been proposed to take into account the influence of the reduction in Young's modulus on the far-field stress calculation. The influence of change in Poisson's ratio has also been analyzed. A method of determining a Young's modulus value suitable for use in the far-field stress calculation is described and the influence of reduction in Young's modulus of an overcored sample on the determination of the stress ratio (SR) in the RPR method is analyzed. Using the proposed modification, the in situ stresses for the Atomic Energy of Canada Limited's Underground Research Laboratory are re-calculated based on 21 deep doorstopper measurements. The re-calculation shows an increase in the trend of stress magnitudes versus depth in the URL.     

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.     

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.     

二滩水电站地下厂房三维边界元分析及稳定性评价

我们用三维边界元法计算了二滩水电站地下厂房围岩的应力重分布和变形。不仅分析了厂房稳定性的应力条件,还考察了开挖引起的围岩能量变化对厂房稳定性的影响。 该厂房处于高应力区,由三个大洞室和许多与它们相连接的管道组成,所以厂房围岩的应力重分布和变形是一个典型而又复杂的空间问题。为此采用了特别适于处理空间问题的边界元法。在计算中又采用了笔者提出的“数值积分的非均匀精度法”有效地节省了计算机时。 分析结果表明,在主厂房与管道的连接处附近应力集中相当严重。同时也证实,就大型岩石工程的空间课题研究而言,无论在输入数据准备量、计算机时和结果的精确度方面,边界元法都显著优于有限元法。 我们认为,这分析结果对类似的水电站地下厂房的稳定性研究也有一定的参考价值。     

Stress measurements from oriented core

A low-cost methodology that allows the estimation of in situ and induced stress using oriented rock core specimens has been investigated. The technique can be used to determine the stresses either during the early stages of a project, even in undeveloped areas of a mine, or to measure in situ and induced stress within active mine workings, such as stopes and pillars. The research aim was to compare the experimental results estimated by the Acoustic Emission and Deformation Rate Analysis methods with those estimated by conventional HI cell measurements. Data was collected from a number of sites with different geological environments and in most cases the core was obtained from the same hole in which a conventional stress measurement had been carried out. The studies have focused on the determination of the full stress tensor from a single oriented cored rock. In all cases, the rock core specimens recollected similar in situ stress values to those estimated using conventional overcoring methods.     

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.     

A test of different stress measurement methods in two orthogonal bore holes in Äspö Hard Rock Laboratory (HRL), Sweden

Within the scope of works to provide the necessary rock mechanics support for site investigations for a radioactive waste repository, the Swedish Nuclear Fuel and Waste Management Co (SKB) has studied some of the available equipment for in situ stress measurements in deep boreholes. A project with the objective of comparing three different types of equipment for in situ stress measurement under similar conditions has been carried out. The tests were performed in orthogonal boreholes at the Äspö Hard Rock Laboratory (HRL), Oskarshamn, Sweden. The two most common methods to measure in situ stress are the overcoring and hydraulic fracturing methods. Among the three tests, two are carried out using the overcoring method, the third uses the hydraulic fracturing method. The overcoring equipment's are the AECL's Deep Doorstopper Gauge System (DDGS) and SwedPower's Triaxial Strain Cell (Borre Probe). The measured results could be verified against known conditions at the Äspö HRL. The results from the three in situ stress measurement methods illustrate the complexity of determining the in situ stresses in a rock mass. To understand the difference in results and answer the associated questions, it was necessary to undertake deeper investigations involving laboratory tests and theoretical calculations.     

Stresses in anisotropic rock masses: an engineering perspective building on geological knowledge

Rock stress measurement is cast in the more general context of the determination of boundary conditions for rock engineering. A study on the effect of elastic anisotropy on underground excavations reveals that this effect is actually controlled by the imposed boundary conditions. Applications to tunneling and to the Underground Research Laboratory (URL), Canada, exemplify a procedure for boundary condition estimation formerly developed by the authors. In this procedure, previous information is accounted for, so that boundary conditions can be updated at the various stages of a project, as soon as new information becomes available; strain, stress, or displacement measurement can be used as input data. The procedure displayed fast convergence despite the complex geometry, and the high degree of non-linearity of the models. The application to the two-dimensional (2-D) plane strain synthetic model of a tunnel in a yielding rock mass shows the need to use absolute displacements (rather than relative displacements) in order for the boundary condition identification problem to be well-posed. As for the URL application, the 3-D model was able to completely reproduce the complex measured stress pattern, and the 90° rotation of the principal in situ stresses with depth. In order to reliably estimate the boundary conditions reproducing the current in situ state of stress, response measurements of the rock mass to current disturbances are necessary as input data.     

Determination of stress fields in the elastic lithosphere by methods based on stress orientations

Theoretical reconstruction of the stress fields in tectonic plates or particular tectonic regions is an important geophysical problem. Conventional approaches for solving this vital issue are based on classical formulations of boundary value problems of elasticity. In these approaches, stress fields are calculated for diverse boundary conditions defined on the margins of the region in order to fit the experimentally observed orientations of principal stresses inside the region.The present article identifies the major flaw in the conventional approach, which is the impossibility of obtaining a unique and reliable stress field, and suggests alternative methods based on the analysis of orientations of principal stresses. Three methods for determining the elastic state of stress in relatively stable blocks of the lithosphere are described and applied to particular tectonic domains. All of the methods are based on the direct use of experimental data on the stress orientations as input information. The first method exploits direct integration of the equations of elasticity when the field of principal stress trajectories is prescribed within a region. The second one utilizes the non-classical boundary value problem of elasticity, which uses experimentally obtained stress orientations at the region margins as boundary conditions. The third method is aimed at the numerical determination of the stress field from a given set of spatially discrete principal stress orientations.In contrast to the conventional approach, the methods suggested here do not require knowledge of the boundary stress magnitudes. As a consequence, the general solution of the problem becomes non-unique. However, in the case of an elastic medium, only a certain (finite) number of arbitrary parameters control the general solutions. These parameters can be determined from in situ stress measurements within the region under study. Therefore, for the selected spatial scale, the unique stress field can be singled out. In the second method, the number of parameters (and, thus, the minimum number of field measurements) is determined from an analysis of boundary stress orientations alone. In other methods, this number depends upon the harmonicity or non-harmonicity of inclination of the prescribed stress trajectories (for the second method) and the calculated stress trajectories (for the third method).To illustrate the essence of the proposed methods, they are applied to the determination of first-order stress fields in the West European and Australian platforms. These platforms represent two basically different types of stress domains. The stress field for the West European platform reflects nearly homogeneous stress orientations throughout the extent of the region, whereas the Australian platform is characterized by rotation of the principal stress axes while traversing the region margins. In the case of Australia, an important result is the existence (at the chosen spatial scale) of a singular point inside the Australian continent at which the curvature of the stress trajectories is infinite. The local state of stress near such a point has important geophysical and engineering implications.The proposed approaches can be applied not only for the determination of regional stress fields but also at other spatial scales, depending on the scale at which the stress indicators have been characterized.     

Evaluation of earthquake impact on magnitude of the minimum principal stress along a shotcrete lined pressure tunnel in Nepal

In situ stress condition in rock mass is influenced by both tectonic activity and geological environment such as faulting and shearing in the rock mass.This influence is of significance in the Himalayan region,where the tectonic movement is active,resulting in periodic dynamic earthquakes.Each large-scale earthquake causes both accumulation and sudden release of strain energy,instigating changes in the in situ stress environment in the rock mass.This paper first highlights the importance of the magnitude of the minimum principal stress in the design of unlined or shotcrete lined pressure tunnel as water conveyance system used for hydropower schemes.Then we evaluated the influence of local shear faults on the magnitude of the minimum principal stress along the shotcrete lined high pressure tunnel of Upper Tamakoshi Hydroelectric Project(UTHP) in Nepal.A detailed assessment of the in situ stress state is carried out using both measured data and three-dimensional(3 D) numerical analyses with FLAC~(3 D).Finally,analysis is carried out on the possible changes in the magnitude of the minimum principal stress in the rock mass caused by seismic movement(dynamic loading).A permanent change in the stress state at and nearby the area of shear zones along the tunnel alignment is found to be an eminent process.     

帽子模型在强夯动应力计算中的应用

采用帽子模型对强夯时非饱和湿陷性黄土中的动应力分布进行了计算 ,计算结果与现场测试结果一致 ,证明帽子模型可作为非饱和黄土强夯动应力计算模型。通过对计算结果与实测资料的分析对比 ,对强夯法的加固机理作了进一步的探讨 ,最后得到了一些有益的结论。     

Modelling natural stresses in the arc syncline and comparison with in situ measurements

In the Provence coal basin, the HBCM company mines lignite at great depths. Several measurements of the natural stresses were carried out using flat jack and hydraulic fracturing. A strong stress anisotropy and high stresses were observed. To interpret these measurements, large scale numerical modelling is used. This study presents a comparison between the predicted natural stresses and those measured during field investigations. Three models are successively developed and loaded on the basis of assumptions about current tectonics and historical tectonics. Calculations lead to a better explanation of the orientations and magnitudes of the principal stresses which are not in contradiction with the observation of a NE-SW stress deviation in the vicinity of the area where the measurements were carried out. It appears that the natural stresses in the Arc depend mostly on the major geological structures in comparison to the loading type. The results indicate that there is a relatively good match between predicted and measured stress magnitudes, and orientations. Finally, on the basis of a good estimation of the tectonic loading stages, it is possible to explain the distribution of the natural stresses in theArc syncline, even though the magnitudes of the tectonic stresses were unknown.     

Long term stability assessment of Siah Bisheh powerhouse cavern based on displacement back analysis method

Siah Bisheh pumped storage powerhouse cavern with complex geometry, changeable geological formations and diverse geotechnical properties of rocks, is under construction on the Chalus River at the north of Iran. Powerhouse cavern is located near the lower dam reservoir and its crown is more than 30 m down the lower dam maximum lake level. After impounding of lower dam, powerhouse region will be located under saturated condition. Therefore long term stability assessment of the powerhouse cavern under saturated condition is unavoidable. In this study, displacement based direct back analysis using univariate optimization algorithm were applied and geomechanical properties of rocks, stress ratio and joints parameters were identified. Numerical modeling results are in good agreement with measured displacements using extensometers which confirm the numerical modeling accuracy and back analysis results. Then ordinary analysis of powerhouse cavern under natural condition using back analysis results were carried out. Results of analysis shows that powerhouse cavern is stable under natural condition and existing support system has suitable efficiency and could effectively control displacements. Finally, powerhouse cavern long term stability under saturated condition was analyzed. Results of analysis shows that after lower dam impounding, pore water pressure and uplift pressure in discontinuities around powerhouse cavern will arose and tend to local failure of powerhouse cavern in region 2nd and 3rd instrumentation arrays. To obtain powerhouse long term stability, it is recommended to construct a cutoff curtain around powerhouse cavern.     

Numerical back analysis for estimation of soil parameters in the Resalat Tunnel project

Determination of in situ soil or rock geotechnical properties is a difficult task for a design engineer. Back analysis is a helpful technique for evaluation of soil properties by considering and measuring the convergence of an underground opening. In this article, the results of numerical back analysis, performed for Resalat tunnel in Tehran, Iran, are reported. The main purpose of this study was to estimate the soil cohesion and the in situ horizontal stress. Back analysis was performed by matching numerical modeling results with the measured tunnel convergence. In addition, the results of in situ direct shear, plate load and pressure meter tests are reported and compared with those from back analysis. It is shown that the back analysis presented is capable of determining the horizontal in situ stress and soil cohesion with good accuracy.     

天荒坪抽水蓄能电站试验洞的位移反分析研究

为查明天荒坪抽水蓄能电站地下厂房所在位置围岩初始地应力场的情况,沿厂房的拟设轴线开挖了模型试验洞,量测了围岩位移与洞周收敛位移,并据以进行了反分析计算。文中所用的数值计算法为边界单元性,包括弹性问题和粘弹性问题的反演计算,所得初始地应力的方向及量值与以其它方法测得的结果符合较好。     

Investigation into in situ stress fields in the asymmetric V-shaped river valley at the Wudongde dam site,southwest China

The Wudongde Reservoir, now being constructed on the lower reaches of the Jinsha River, will be the forth largest hydropower plant in terms of capacity in China. This project includes a concrete arch dam and two large-span underground caverns in both abutments. For their design and construction, in situ stress measurements and geological survey were conducted. In this study, following an introduction of the geological conditions and topography, an interpretation on the test results of in situ stresses is presented for clarifying the distribution features of natural stresses in the engineering area. It is interesting to find that the vertical stress is predominant in the project area and that the horizontal stress reduces largely in the relaxation zone near the bank slopes, while concentrates at the valley bottom and becomes normal in the depth of both abutments. Also analyzed are the effects of valley topography, geological conditions in the project area as well as the macro-regional tectonics on the distribution of in situ stresses at the dam site. A noteworthy finding is that topography and thickness of overburden are the main factors for the intermediate–low stress levels, that regional tectonics governs the stress orientation at the regional scale, and that river erosion, caprock structure and karstic processes have also contributed to the evolution of the valley and in situ stress state.     

Bayesian estimation of rock mass boundary conditions with applications to the AECL underground research laboratory

In this paper, the estimation of boundary conditions for rock mass models is addressed by means of Bayesian identification procedures. Basic information can consist of stress, strain, or displacement measurements. Previous information is accounted for, so that boundary conditions can be updated at the various stages of a project, as soon as new information becomes available. For linearly elastic rock masses, the boundary conditions are computed in a one-step solution. For rock masses with non-linear behavior, an iterative procedure must be followed. Potential advantages and shortcomings are also discussed, together with comparisons with other methods available in the literature. The proposed procedure is applied to two(2)- and three-dimensional (3-D) non-linear models of the Underground Research Laboratory (URL) of the Atomic Energy of Canada Limited (AECL), Canada. The procedure displayed fast convergence despite the complex geometry of the site, and the high degree of non-linearity of the models. The 3-D model was able to completely reproduce the complex measured stress pattern, and the 90° rotation of the principal in situ stresses with depth. In order to reliably estimate the boundary conditions reproducing the current in situ state of stress, response measurements of the rock mass to current disturbances are necessary as input data.     

三维地应力场BP反分析的改进

从回归分析出发,对地应力场的神经网络反分析进行了改进:采用线弹性有限元计算进行线性回归分析,获得优化参数的大致范围;应用均匀设计来确定计算参数不同水平的组合,进行弹塑性有限元计算获得训练的样本;采用Levenberg-Marquardt算法来训练BP神经网络,以提高效率;使用及早停止和正规化方法来避免神经网络的过拟合问题;得到离散化的应力值后,用神经网络拟合出了以坐标为参量的全场应力函数。