Flow and fracture of rocks under general triaxial compression

Recent laboratory studies of the flow and fracture of rocks under general triaxial compression are reviewed. New developments in laboratory techniques have made it possible to measure three principal stresses and strains under general triaxial stress states, in which all three principal stresses are different.Strength and ductility of isotropic rocks are markedly affected not only by the least compression ₃, but also by the intermediate compression ₂, although these two effects are rather additional in strength, but opposite in ductility. The experimental results show that dilatancy is highly anisotropic under the general triaxial stress states.Deformational properties of anisotropic rocks have been also measured under the general triaxial compression. In this case, the effect of the intermediate compression markedly depends on the orientations of the weak planes.     

True triaxial cyclic behavior of concrete and rock in compression

Results from true triaxial cyclic tests on concrete are presented and compared with corresponding ones for dense rocks (mainly marbles) obtained under the same laboratory conditions. Common basic characteristics are confirmed regarding the essential effect of intermediate stress, the cataclastic mode of deformation under low confinement, the coupling between volumetric strain and deviatoric stress, the dependence of the equivalent modulus E_q and the hysteresis loops. Common characteristics are also revealed in meridian and deviatoric sections of peak strength surfaces, moreover a stress invariant and its work conjugate plastic strain increment are approximately equal. Concrete behavior is different on the postpeak plastic contraction under high confinement, on the creep rate, on the validity of the condition of convexity and on the considerable degree of violation of the condition of normality. A simple empirical equation is proposed and experimentally verified for predicting deviatoric sections of strength surfaces.     

Fracture of sedimentary rocks under a complex triaxial stress state

Most sedimentary rocks have layered structure, and their strength properties are therefore anisotropic; as a consequence, the rock strength depends on the direction of the applied stresses. In this case, various fracture mechanisms are possible. The following two possible fracture mechanisms are considered: actions along the bedding planes, which are weakening surfaces, and along the planes where stresses exceeding the total rock strength are attained. A triaxial independent loading test bench was used to study the fracture conditions for layered rocks composed of productive oil-and-gas strata in complex true triaxial loading tests. The study shows a good qualitative agreement between experimental results and theoretical estimates.     

A micromechanical damage model for rocks and concretes under triaxial compression

Based on analysis of deformation in an infinite isotropic elastic matrix containing an embedded elliptic crack, subject to far field triaxial compressive stress, the energy release rate and a mixed fracture criterion are obtained by using an energy balance approach. The additional compliance tensor induced by a single closed elliptic microcrack in a representative volume element and its in-plane growth is derived. The additional compliance tensor induced by the kinked growth of the elliptic microcrack is also obtained. The effect of the microcracks, randomly distributed both in geometric characteristics and orientations, is analyzed with the Taylor＇s scheme by introducing an appropriate probability density function. A micromechanical damage model for rocks and concretes under triaxial compression is obtained and experimentally verified.     

Experimental investigation on strength and failure behavior of pre-cracked marble under conventional triaxial compression

Fractures in natural rocks have an important effect on the strength and failure behavior of rock mass, which are often evaluated in rock engineering practice. The theoretical evaluation of mechanical behavior of fractured rock mass has no satisfactory answer due to the role of confining pressure and crack geometry. Therefore, in this paper, conventional triaxial compression experiments were carried out to study the strength and failure behavior of marble samples with two pre-existing closed cracks in non-overlapping geometry. Based on the experimental results of a number of triaxial compression tests, the effect of crack coalescence on the axial supporting capacity and deformation property were investigated with different confining pressures. The results show that intact samples and flawed samples (marble with pre-existing cracks) have different deformation properties after peak stress, which change from brittleness to plasticity and ductility with the increase of confining pressure. The peak strength and failure mode are found depending not only on the geometry of flaw, but also on the confining pressure. The strength of flawed samples shows distinct non-linear behavior, which is in a better agreement with non-linear Hoek–Brown criterion than linear Mohr–Coulomb criterion. For a kind of rock that has been evaluated as a Hoek–Brown material, a new evaluation criterion is put forward by adopting optimal approximation polynomial theory, which can be used to confirm more precisely the strength parameters (cohesion and internal friction angle) of flawed samples. For intact samples, the marble leads to typical shear failure mode with a single fracture surface under different confining pressures, while for flawed samples, under uniaxial compression and a lower confining pressure (σ₃ = 10 MPa), tests for coarse and medium marble (the coarse and medium refer to the grain size) exhibit three basic failure modes, i.e., tensile mode, shear mode, and mixed mode (tensile and shear). Shear mode is associated with lower strength behavior. However, under higher confining pressures (σ₃ = 30 MPa), for coarse marble, the axial supporting capacity is not related to the geometry of flaw. The friction among crystal grains determines the strength behavior of coarse marble. For medium marble, the failure mode and deformation behavior are dependent on the crack coalescence in the sample. The present research provides increased understanding of the fundamental nature of rock failure under conventional triaxial compression.     

Confinement-sensitive plasticity constitutive model for concrete in triaxial compression

In this paper, a confinement-sensitive plasticity constitutive model for concrete in triaxial compression is presented, aiming to describe the strength and deformational behaviour of both normal and high-strength concrete under multiaxial compression. It incorporates a three-parameter loading surface, uncoupled hardening and softening functions following the accumulation of plastic volumetric strain and a nonlinear Lode-angle dependent plastic potential function. The various model parameters are calibrated mainly on the basis of a large experimental database and are expressed in terms of only the uniaxial compressive concrete strength, leading to a single-parameter model, suitable for practical applications. The model’s performance is evaluated against experimental results and it is found that both the increased strength and deformation capacity of confined concrete are properly captured.     

三向受压混凝土的动态特性研究

为探究混凝土在三向受压状态下的动态特性,利用自行研制的大型多功能三轴材料试验机,进行不同应变速率(10-5/s、10-4/s、10-3/s、10-2/s)下混凝土不同定侧压比(1∶1、2∶1、3∶1、4∶1)的动态真三轴抗压试验,研究了混凝土在动态抗压下的强度和变形特性.结果表明:混凝土在三向受压状态下表现出明显的应变...     

Analytical evaluation of stress-strain test data

An analytical model for deducing the actual stress-strain properties from laboratory test results is discussed. As an illustration, an elastic bilinear material is used for unconfined cylindrical compression test conditions, as simulated with a finite element analysis. The results obtained are applicable for assisting in evaluating measured strength and stiffness properties of some clay soils, concrete test cylinders, concrete cores, and rock cores.The quantitative results of this study can be used for interpreting measured stress-strain data for unconfined compression test conditions. The error in measured results is shown to be influenced by Poisson's ratio, length-to-diameter ratio of the specimen, end condition, and ratio of inelastic modulus to initial elastic modulus. Curves for adjusting the measured results to the theoretical results are presented.Nomenclature D specimen diameter - E _i initial elastic stiffness modulus - E _y elastic stiffness modulus beyond the yield stress, plastic or inelastic modulus - L specimen length - axial strain - _av average strain - _g gage length strain - _y yield strain - Poisson's ratio - compressive stress - _av average stress - _t theoretical compressive stress - _y yield stress - _ym measured stress at the yield strain     

Properties of rocks tested in one-dimensional compression

An apparatus has been developed and used to obtain static stress-strain data on rock and soil samples in one-dimensional compression. This paper describes the design and method of use, and reports test results obtained on several types of rock and sand specimens. A 4-in.-diam specimen with height up to 2 in. is contained in a thin-walled steel cylinder. This cylinder is contained in the main pressure vessel which has a pressure cavity surrounding the specimen. Load is applied through a load cell on top of the specimen by a hydraulic press. An operator maintains a constant zero balance on strain gages bonded to the thin, steel cylinder containing the specimen by pumping hydraulic fluid into the pressure cavity, thus nullifying the tendency of the test specimen to expand laterally as it is compressed axially. Axial load and deflection are recorded on anx?y plotter from signals received from the load cell and a deflectometer mounted on the load cell. This apparatus has been successfully used to obtain data on rocks to axial stresses of 75,000 psi and on sand to 30,000 psi. Test data for both rocks and sand are presented in this paper.     

Damage constitutive for high strength concrete in triaxial cyclic compression

A constitutive relationship for high strength concrete in triaxial monotonic and cyclic compressions is developed based on the continuum damage mechanics. The bounding surface concept is employed in the formulation of the theoretical model. An experimental program was undertaken in order to establish databases for high strength concrete under triaxial monotonic and cyclic compressions. The stress-strain responses of high strength concrete subjected to triaxial monotonic and cyclic compressions were acquired through an experimental program. Comparison of the stress strain results indicates good agreement between the theoretical model and the experimental data.     

Construction of a theory of failure of composites in triaxial and biaxial compression

Conforms to the test of a paper delivered at the Internal Conference on Fracture and Fracture Mechanics (Shanghai, Chinese People's Republic, 1987). The paper was not submitted for publication in the conference proceedings.     

Determination of plastic stress-strain behavior by digital-image-processing techniques

This work explores the application of digitalimage-processing techniques to the measurement of large plastic strains. Two sample problems have been selected, namely the uniform tensile deformation of aluminum-sheet metal strips and the post-necking deformation of copper circular rods. Images of these gridded metallic test pleces were captured, digitized and analyzed in a fully computerized way to evaluate strain distributions, anisotropic parameters and plastic stress-strain flow curves. For post-necked test pieces, Bridgman stress correction has been easily applied by defining the neck profile contour from the automated processing of digitized images. Results compare satisfactorily with those based on displacements measured by conventional microscopy. The presented technique, with added improvements, can consititute a viable one for accurate and fully computerized measurement of large deformations.     

Soil failure under undrained quasi-static and high speed triaxial compression test

Experiments were conducted in unsaturated silty loam and sandy loam soils under undrained conditions. Soil failure under quasi-static and high speed triaxial compression were studied. The amount of energy used in breaking soil specimens was found to be a function of soil moisture content. During undrained quasi-static triaxial compression tests, two cases of brittle failure, a general shear failure and a fragmentation were observed. The test soil specimen broke more by fragmentation than by general shear failure. During undrained high speed triaxial compression tests, the energy use for breaking the soil specimen increased with increase in loading speed up to a certain critical speed range of 4.5–5 m/s, and then it decreased. Two types of soil failure, brittle failure and plastic flow, which were a function of the loading speed, were noticed. At lower speed, dilation of shearing along a slip plane was observed. However, at higher speed, barreling of the cylindrical specimen with top and bottom conical shaped wedges, or only a single wedge with a small crack or fluidization, was observed.     

Fracture mechanics of a tension-shear macrocrack in rocks

Fracture in rocks is influenced by anisotropy and existence of faults. Fracture initiation and propagation is often under the combined presence of sliding and opening of preexisting cracks. Linear-elastic fracture-mechanics (LEFM) has been used as a model for describing the propagation of a main crack in materials such as rocks, concrete, ceramics, etc. However, the presence of the fracture process zone which includes interlocking of grains and ligament connections results in deviations from perfectly brittle behavior. These effects are more pronounced in mixed-mode fracture, which involves crack initiation under the combined presence of tension-shear or compression-shear stresses.Specimens of Indiana limestone with a preexisting inclined notch were studied to observe the fracture process under a mixed-mode state of stress. Experimental monitoring involved using the electronic speckle-pattern interferometry (ESPI) technique to monitor strains and crack-propagation paths with high sensitivity. A scanning electron microscope (SEM) was used to examine the specimen for the presence of microcracks. Experimental results were subsequently evaluated using a mixed-mode fracture theory and finite-element computations.It was possible to visually observe the pre-peak and post-peak development of the fracture process zone. Developments in the crack-tip strain concentration were observed at and beyong the peak load. While the experiments conducted involved tension-shear cracks, the possibility of extending the concepts to compression-shear cracks was also explored. The possibilities and limitations of using the fracture-mechanics approach to understanding fracture in rocks were subsequently discussed.Paper was presented at the 1991 SEM Spring Conference on Experimental Mechanics held in Milwaukee, WI on June 9–13.     

Fracture mechanics of composites in compression along cracks

Conclusions Thus, based on the concepts in [5–7], the beginning of fracture of a composite in compression along a plane containing cracks can be represented as follows. If the material has not fractured already, then local fracture necessarily occurs next to the cracks at a value of compressive load corresponding to surface instability. Here, the upper limit of the ultimate theoretical strength corresponds to the minimum value of the shear modulus. This fracture mechanism can be seen in composites reinforced with high-modulus fibers. It should be noted that fracture can also take place on free surfaces of the material at these load values as a result of surface instability [1]. If the area of the free surface (lateral surface) of the material is substantially less than the total area of the cracks present throughout the volume of the material, then obviously the cracks will be the deciding factor in the fracture mechanism. The above-noted conclusions and quantitative abalysis were made only for a linearly elastic, orthotropic material with a high shear stiffness (brittle fracture), while the general results obtained in the present article also pertain to nonlinearly elastopiastic models. The results can be refined for more complex models. It must also be noted that the theoretical ultimate strength may be reduced substantially if the interaction of cracks located in parallel planes during instability is considered. This feature of the fracture mechanism was noted in note 6 in the article [6]. Composite materials generally have a fairly large number of cracks in planes and surfaces along the reinforcing elements. In connection with this, for composites it is best to allow for interaction of cracks located in parallel planes, which in turn should lead to a substantial reduction in the theoretical ultimate strength value obtained in the present article.Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Prikladnaya Mekhanika, Vol. 18, No. 6, pp. 3–9, June, 1982.     

Experimental investigation of plastic deformations of argillaceous soil with triaxial compression

The article describes the change in the loading surface during the process of simple loading. A study is made of the direction of the vector of the increment in the plastic deformation at different points of the loading surface. The experimental data were obtained in tests on the controlled triaxial compression of hollow cylindrical samples of argillaceous soil. The applicability of the theory of increments in the form of an association law is established.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 123–127, March–April, 1971.