The paper presents the results of a micromechanical study using the Discrete Element Method (DEM) to critically evaluate the determination of the tensile strength of brittle rocks using the Brazilian test. The Brazilian test is performed on model cylindrical specimens loaded with two diametrically positioned plates and fails by splitting the cylinder. In the study, a series of DEM models of the direct tensile and Brazilian tests was conducted in controlled conditions to establish the relationship between the bond strength between rock grains/particles and the tensile strength from the Brazilian test. The modeling was focused on size effects and micromechanical insights into the splitting and fracture propagation processes in the Brazilian test. The results of the micromechanical study lead to a scaling relationship to account for the effects of Brazilian test specimen size, and for practical recommendations to obtain more accurate estimations of the nominal tensile strength of the rocks from the Brazilian test data.
The Brazilian test is the most widely used method to obtain the tensile strength of brittle rocks in practice. For many engineering projects, such as deep rock fracturing, there is a need to obtain rock mechanical parameters with accuracy using economical and rapid test methods. However, the governing failure mechanism in a Brazilian specimen is not an instantaneous breakage caused by reaching the peak-cross-sectional nominal strength, or plasticity theory, like in the direct-tensile test, but instead is propagation of a fracture or crack until the cylinder splits. Hence, the Brazilian test results are subjected to the fracture-mechanics size effect . In addition, experimental studies pointed out that loading rate, width of and friction between the contact between the sample and the loading plates have significant influence on the Brazilian tensile test results [2,3,4].
Carbon dioxide (abbreviated to CO2) sequestration in appropriate geologic formations (e.g., deep saline aquifers, deep unmineable coal seams, and depleted oil and gas reservoirs) is expected to be a promising technique to reduce CO2 emission its great storage potential. In geological sequestration projects, CO2 is supposed to be injected in the form of supercritical fluid which is denser than vapor state and less viscous than liquid state. Revealing d process of formation water by CO2 phase porous rock system is of importance to estimate storage capacity and ensure safe CO2 injection predict migration of CO2 in reservoirs, reservoir rocks need to be characterized in terms of the capillary pressure response and the relative permeabilities for formation water and CO2. In laboratories, the relative permeability curves are usually core tests in which a fluid phase is injected into core sample to displace another fluid phase paper has been published to discuss the curves such as relative permeability curves pressure curves, for multiphase processe sequestration and H2S disposal [1, 2, 3]. Typical quantities obtained in the core tests are pressures, flow rates, and fluid compositions measured at the inlet and outlet of the core samples. This paper presents a one-dimensional immiscible twophase fluid flow model in a porous rock system. The model parameter values are estimated by carrying out forward analysis to match the computed behavior with experimentally observed one. The experimental data used was obtained from high pressure core flooding test in which supercritical CO2 injection into geological CO2 reservoir is simulated. To investigate applicability of inverse analysis to the multiphase fluid problem, the relative permeability and capillary pressure curves were characterized through inverse analysis. Polynomial functions and Brooks-Corey capillary pressure model are assumed for the relative permeability and capillary pressure curves, respectively.
Rock masses invariably contain fractures of various lengths. Due to their geometry and mechanical weakness, the mechanical characteristics of the fractured rock masses are controlled by the fractures. However, the quantification of the mechanical behavior of fractured rock masses is very complicated, because fracture geometry and mechanical behavior are length scale dependent. However, this scale dependency has not been not fully analyzed. The main objective of this research is to perform a comprehensive parametric study on the effects of fracture geometry and length in the equivalent continuum elastic compliance behavior of fractured rock masses over a wide range of length scales. The study used a combination of Oda’s elastic compliance tensor, Monte Carlo Simulation (MCS), and different Probability Distribution Functions (PDFs). Fracture geometry parameters are based on field data obtained from different sources on studies of fracturing from varied geological sites. A key concept in the equivalent continuum method is a Representative Element Volume (REV). Using the combined analysis techniques, the validity of the REV assumption is extensively investigated, and a guideline is proposed on how to define a proper REV in terms of the equivalent continuum elastic compliance of fractured rock masses.
In nature, rock masses inevitably contain fractures. Thus, fracture mechanical behavior and geometrical distribution in a rock mass and the corresponding fracture properties, for example length, orientation, frequency, and stiffness, are key factors that control the mechanical behavior of fractured rock masses. However, developing the comprehensive correlation between fracture system geometry and the mechanical characteristics of fractured rock masses is very difficult, because of the complicated fracture distribution pattern in general. Since the 1950s, several numerical procedures have been developed for analyzing the mechanical behavior of fractured rock masses and the effect of different fracture patterns.
Brittle heterogeneous rocks emit Acoustic Emission (AE) events from fracture formation during loading which are associated with microstructure dislocation. Notched Beam Fracture Toughness (NBFT) tests were performed on samples of an analog rock and Colorado Rose Red Granite in order to characterize tensile fracture AE signals. All concrete specimen sizes were approximately 45x60x140 mm3 beams. Granite specimen sizes were 40x50x240 mm3 beams. Three point and four point loading methods were used on the concrete and granite samples respectively in order to generate maximum beam moment in the vicinity of an initiation notch. Six AE piezoelectric transducers manufactured by Physical Acoustics Corporation (PAC) were used. PAC’s AE source location software, AEwin, was used in order to triangulate event locations and perform waveform analysis. Attenuation analysis and curve generation was performed for each material tested in order to refine the event source location parameters. Load dependent stages of acoustic emission events were created. Four stages were used in order to characterize the micro crack development leading up to the main fracture formation. Crack location was verified visually post-test and a profilometer was used to generate a digitized fracture surface. An AE event estimated fracture surface was also created and compared with the profilometer data.
Acoustic Emission (AE) is the phenomenon in which a material or structure emits elastic waves caused by the sudden occurrence of fractures along discontinuous surfaces and grain boundaries. These elastic waves that propagate through the given material are more closely caused by a localized, and irreversible release of stress energy . AE signals were monitored throughout numerous Notched Beam Fracture Toughness (NBFT) tests. Three and four point loading schemes were used on analog rock (ultra high strength concrete) and granite samples, respectively. Two separate specimen sizes were tested: 45x60x140 mm3 and 40x50x240 mm3 beams.
Back-analysis is a systematic procedure to identify model parameters using the measured response from the construction. The use of back-analysis is particularly appropriate and useful for various tunneling projects, where more information on ground characteristics and monitored response become available as the construction progresses. Most often backanalysis requires that an optimization algorithm handles the task of identifying a set of model input parameters that will minimize the difference between predicted and measured performance. Predicted performance is typically obtained with the use of numerical analysis. The present paper explores the application of various optimization-based back-analysis techniques that are applicable to variable ground conditions and are directly coupled with the finite difference code FLAC. More specifically, this paper compares the performance of a traditional local optimization scheme versus global optimization strategies and outlines the characteristics and features of each method. The strength and importance of global optimization are discussed for geotechnical engineering applications along with the novel implementation of two global optimization algorithms in geotechnical parameter identification. This paper focuses on the use of these two novel algorithms, namely, the Simulated Annealing (SA) and the Differential Evolution Genetic Algorithm (DEGA) as candidate algorithms for back-analysis with FLAC. SA and DEGA belong to a broad class of heuristic-based methodologies for locating global solutions for non-linear optimization problems. Specific examples are given showcasing the convergence behavior and efficiency of these methods. It is shown that global optimization schemes are able to overcome the deficiencies of local search optimization methods, especially when non-linear geotechnical problems are investigated.
Back-analysis involves a procedure where different parameters and hypotheses of a trial problem, which can be expressed numerically, are varied in order for the results of the analysis to match a predicted performance as closely as possible.