Pillar Stability Experiment Research Articles

Numerical manifold method for thermo-mechanical coupling simulation of fractured rock mass

As a calculation method based on the Galerkin variation, the numerical manifold method (NMM) adopts a double covering system, which can easily deal with discontinuous deformation problems and has a high calculation accuracy. Aiming at the thermo-mechanical (TM) coupling problem of fractured rock masses, this study uses the NMM to simulate the processes of crack initiation and propagation in a rock mass under the influence of temperature field, deduces related system equations, and proposes a penalty function method to deal with boundary conditions. Numerical examples are employed to confirm the effectiveness and high accuracy of this method. By the thermal stress analysis of a thick-walled cylinder (TWC), the simulation of cracking in the TWC under heating and cooling conditions, and the simulation of thermal cracking of the Swedish Äspö Pillar Stability Experiment (APSE) rock column, the thermal stress, and TM coupling are obtained. The numerical simulation results are in good agreement with the test data and other numerical results, thus verifying the effectiveness of the NMM in dealing with thermal stress and crack propagation problems of fractured rock masses.

Numerical study on coupled thermo-mechanical processes in Äspö Pillar Stability Experiment

This paper presents a study of the full three-dimensional thermo-mechanical (TM) behavior of rock pillar in Äspö Pillar Stability Experiment (APSE) using a self-developed numerical code TM-EPCA3D. The transient thermal conduction function was descritized on space and time scales, and was solved by using cellular automaton (CA) method on space scale and finite difference method on time scale, respectively. The advantage of this approach is that no global, but local matrix is used so that it avoids the need to develop and solve large-scale linear equations and the complexity therein. A thermal conductivity versus stress function was proposed to reflect the effect of stress on thermal field. The temperature evolution and induced thermal stress in the pillar part during the heating and cooling processes were well simulated by the developed code. The factors that affect the modeling results were discussed. It is concluded that, the complex TM behavior of Äspö rock pillar is significantly influenced by the complex boundary and initial conditions.

Analysis of Äspö Pillar Stability Experiment: Continuous thermo-mechanical model development and calibration

The paper describes an analysis of thermo-mechanical (TM) processes appearing during the Äspö Pillar Stability Experiment (APSE). This analysis is based on finite elements with elasticity, plasticity and damage mechanics models of rock behaviour and some least squares calibration techniques. The main aim is to examine the capability of continuous mechanics models to predict brittle damage behaviour of granite rocks. The performed simulations use an in-house finite element software GEM and self-developed experimental continuum damage MATLAB code. The main contributions are twofold. First, it is an inverse analysis, which is used for (1) verification of an initial stress measurement by back analysis of convergence measurement during construction of the access tunnel and (2) identification of heat transfer rock mass properties by an inverse method based on the known heat sources and temperature measurements. Second, three different hierarchically built models are used to estimate the pillar damage zones, i.e. elastic model with Drucker–Prager strength criterion, elasto-plastic model with the same yield limit and a combination of elasto-plasticity with continuum damage mechanics. The damage mechanics model is also used to simulate uniaxial and triaxial compressive strength tests on the Äspö granite.

Numerical modeling for the coupled thermo-mechanical processes and spalling phenomena in Äspö Pillar Stability Experiment (APSE)

In this paper, the coupled thermo-mechanical (TM) processes in the Äspö Pillar Stability Experiment (APSE) carried out by the Swedish Nuclear Fuel and Waste Management Company (SKB) were simulated using both continuum and discontinuum based numerical methods. Two-dimensional (2D) and three-dimensional (3D) finite element method (FEM) and 2D distinct element method (DEM) with particles were used. The main objective for the large scale in situ experiment is to investigate the yielding strength of crystalline rock and the formation of the excavation disturbed/damaged zone (EDZ) during excavation of two boreholes, pressurizing of one of the boreholes and heating. For the DEM simulations, the heat flow algorithm was newly introduced into the original code. The calculated stress, displacement and temperature distributions were compared with the ones obtained from in situ measurements and FEM simulations. A parametric study for initial microcracks was also performed to reproduce the spalling phenomena observed in the APSE.

Thermo-mechanical coupling analysis of APSE using submodels and neural networks

The Äspö Pillar Stability Experiment (APSE) is an in situ experiment for investigating the spalling mechanism under mechanical and thermal loading conditions in a crystalline rock. In this study, the thermo-mechanical behaviors in the APSE were investigated with three models: (1) a Full model with rough meshes for calculating the influence of tunnel excavation; (2) a Submodel with fine meshes for predicting the thermo-mechanical behavior in the pillar during the borehole drilling, heating, and cooling phases; and (3) a Thin model for modeling the effect of slot cutting for de-stressing around the pillar. In order to import the stresses calculated from the Full model to the Submodel and to define the complex thermal boundary conditions, artificial neural networks (NNs) were utilized. From this study, it was possible to conclude that the stepwise approach with the application of NNs was useful for predicting the complex response of the pillar under severe thermo-mechanical loading conditions.

Modelling fracture propagation and failure in a rock pillar under mechanical and thermal loadings

The Äspö Pillar Stability Experiment (APSE) was conducted to study the rock mass response in a heated rock pillar between two large boreholes. This paper summarizes the back calculations of the APSE using a two-dimensional (2D) fracture propagation code FRACOD. To be able to model all the loading phases of the APSE, including the thermal loading, the code was improved in several ways. A sequential excavation function was developed to model promptly the stepwise changing loading geometry. Prior to the modelling, short-term compressive strength test models were set up aiming to reproduce the stress–strain behaviour observed for the Äspö diorite in laboratory. These models simulate both the axial and lateral strains of radial-controlled laboratory tests. The volumetric strain was calculated from the simulations and compared with the laboratory results. The pillar models include vertical and horizontal 2D models from where the stress in the pillar wall was investigated. The vertical model assesses the stability of the experimental rock volume and suggests the resultant stress below the tunnel floor in the pillar area. The horizontal model considers cross-sections of the pillar between the two large boreholes. The horizontal model is used to simulate the evolution of the stress in the rock mass during the excavation of the boreholes and during and the heating phase to give an estimation of the spalling strength. The modelling results suggest that the excavation-induced stresses will cause slight fracturing in the pillar walls, if the strength of the APSE pillar is set to about 123MPa. Fracture propagation driven by thermal loading leads to minor spalling. The thermal evolution, elastic behaviour and brittle failure observed in the experiment are well reflected by the models.

A coupled thermo-hydrologic-mechanical damage model and associated application in a stability analysis on a rock pillar

A numerical model of coupled thermo-hydrologic-mechanical damage (THMD) in the failure process of rock is proposed using elastic damage mechanics, thermal-elastic theory and seepage mechanics. In the proposed model, the mechanical deformation of rock subjected to thermo-hydrologic-mechanical loading is considered. The model includes the accumulation of damage applied to individual elements, which modifies the modulus, strength, permeability and thermal properties with the severity of the damage. This concept is introduced as a practical method to simulate progressive failure in heterogeneous and brittle rocks, obviating the need to explicitly identify crack tips and their interactions. The model is validated through comparisons of the simulated results with known analytical solutions. The proposed THMD model is implemented in the Rock Failure Process Analysis code (RFPA), and RFPA-THM is developed. Using RFPA-THM, numerical simulation is performed to investigate the stability of a hard rock pillar in the Äspö Pillar Stability Experiment (APSE). The numerically obtained stress field, failure pattern of the rock pillar and the associated Acoustic Emission (AE) events are all in agreement with the in situ experiment conducted at the Äspö Hard Rock Laboratory (HRL) and the phenomenological observations reported in previous studies.

Evolution of In Situ Rock Mass Damage Induced by Mechanical–Thermal Loading

To understand and predict the in situ brittle rock mass damage process induced by a coupled thermo-mechanical loading, the knowledge of rock mass yielding strength, scaling relationship between laboratory and in situ and microstructure characterization is required. Difficulties have been recognized due to the seldom availability of in situ experiment and appropriate numerical methodologies. The Aspo Pillar Stability Experiment was used to monitor the evolution of rock mass damage in a pillar of rock separating two 1.75-m diameter vertical boreholes. The loading of the pillar was controlled using the in situ stresses, excavation geometry, and locally increasing the rock temperature. The induced loading resulted in a complex discontinuum process that involved fracture initiation, propagation, interaction and buckling, all dominated by a tensile mechanism. Tracking this damage process was carried out in two steps. Initially, a three-dimensional numerical model was used to generate the stresses from the excavation geometry and thermal loading. The plane strain stresses, at selected locations where detailed displacement monitoring was available, were then used to track the evolution of damage caused by these induced stresses. The grain-based discrete element modeling approach described in Lan et al. (2010), which captures the grain scale heterogeneity of the rock, was used to establish the extent of damage. Good agreement was found between the predicted and measured temperatures and displacements. The grain-based model provided new insights into the progressive failure process.

Thermo-mechanical coupling analysis for DECOVALEX-2011 Task B, Äspö pillar stability experiment

Korea participated in DECOVALEX-2011, which is an international cooperation project for enhancing the reliability of computer simulations under the conditions of radioactive waste repositories, and modeled the laboratory compression tests and the in situ Äspö pillar stability experiment (APSE). From the comparison of the results with foreign research teams, it was possible to enhance the reliability of the computer simulation of the complex thermo-mechanical (TM) coupling behavior of rock mass. It was found that the two-step simulation with a full model and a submodel using FLAC3D was effective to combine the influence of in situ stress, tunnel excavation, deposition hole drilling, confining pressure, and thermal loading all together. One of the important results was the estimation of spalling strength of Äspö granite as 120 MPa after comparing the notch depth, notch length, and breakout angle of the notch with actual observation.

Numerical modeling of coupled thermo-mechanical response of a rock pillar

Understanding the rock mass response to excavation and thermal loading and improving the capability of the numerical models for simulating the progressive failure process of brittle rocks are important for safety assessment and optimization design of nuclear waste repositories. The international cooperative DECOVALEX-2011 project provides a platform for development, validation and comparison of numerical models, in which the Äspö pillar stability experiment (APSE) was selected as the modeling target for Task B. This paper presents the modeling results of Wuhan University (WHU) team for stages 1 and 2 of Task B by using a coupled thermo-mechanical model within the framework of continuum mechanics. The rock mass response to excavation is modeled with linear elastic, elastoplastic and brittle-plastic models, while the response to heating is modeled with a coupled thermo-elastic model. The capabilities and limitations of the model for representation of the thermo- mechanical responses of the rock pillar are discussed by comparing the modeling results with experimental observations. The results may provide a helpful reference for the stability and safety assessment of the hard granite host rock in China’s Beishan preselected area for high-level radioactive waste disposal.

The Äspö Pillar Stability Experiment: Part II—Rock mass response to coupled excavation-induced and thermal-induced stresses

A 1-m-thick pillar was subject to coupled excavation- and thermal-induced stresses to induce brittle rock mass yielding. The yielding strength of the heterogeneous and fractured rock mass consisting of Äspö diorite was evaluated at eighteen discrete locations using data from the displacement, acoustic emission, and thermal monitoring systems. The average rock mass yielding strength was determined to be 0.59 of the uniaxial compressive strength. The onset of dilation in uniaxial laboratory tests, determined from strain gauge data, was found to occur at approximately 0.45 of the uniaxial compressive strength. It was shown that that the onset of acoustic emission events in situ also occurred when the tangential stress exceeded 0.43 of the uniaxial compressive strength. For sites with absence of in situ data it is recommended that this lower-bound value determined from laboratory data may be used for assessing the in situ rock mass yielding strength. Visual observation and displacement monitoring showed that extent of rock mass yielding is sensitive to small changes in the tangential stress magnitudes. It was determined using three-dimensional modelling that changes in the tangential stress magnitude of approximately 1 MPa was sufficient to cause yielding of the pillar to propagate in what appeared to be intact rock. Observations suggest that without this small stress change yielding of the rock mass would not occur. In other words, there appeared to be a well defined boundary, and if the stresses reached this boundary yielding was observed. However, if stresses were only slightly below this boundary yielding or time-dependant processes were not observed over the monitoring period used in the experiment.

The Äspö pillar stability experiment: Part I—Experiment design

The Äspö pillar stability experiment was carried out to examine the failure process in a heterogeneous and fractured rock mass when subjected to coupled excavation-induced and thermal-induced stresses. The rock pillar was created by the excavation of two adjacent large-diameter boreholes. The pillar was loaded by a combination of excavation-induced stresses and heating of the surrounding rock by a rectangular heater pattern. The experiment was designed using the observation design method. The characterzation of the experiment volume showed that the experiment was located in a fractured water-bearing rock mass that was considered typical for the Äspö Hard Rock Laboratory (Äspö HRL) and for the Fenno-Scandinavian shield. Scoping calculations using two- and three-dimensional elastic stress analyses were carried out to reduce the uncertainty for the far-field in-situ stresses, establish the geometry for the access tunnel that would provide a elevated uniform stresses in the floor of the tunnel, and determine the optimum width of the pillar. It was concluded, based on the rock mass characteristics, that a 1 m-wide pillar formed by two 1.75 m diameter boreholes would meet the design objectives. Thermal modelling showed that thermally induced stresses in the pillar were adequate to elevate the pillar stresses above the stress magnitude required to initiate failure. Acoustic emission, displacement, and thermal monitoring systems were installed according to the experiment design without problems. No sensors were lost over the three month duration. After the experiment was completed, a laser scan of the pillar revealed the extent of the damaged pillar. The experiment commenced in January 2002 and was successfully completed in 2006.