Acoustic characterization of crack damage evolution in sandstone deformed under conventional and true triaxial loading

Abstract

We present a comparative study of crack damage evolution in dry sandstone under both conventional (σ1 > σ2 = σ3), and true triaxial (σ1 > σ2 > σ3) stress conditions using results from measurements made on cubic samples deformed in three orthogonal directions with independently controlled stress paths. To characterize crack damage, we measured the changes in ultrasonic compressional and shear wave velocities in the three principal directions, together with the bulk acoustic emission (AE) output contemporaneously with stress and strain. We use acoustic wave velocities to model comparative crack densities and orientations. In essence, we create two end‐member crack distributions; one displaying cylindrical transverse isotropy (conventional triaxial) and the other planar transverse isotropy (true triaxial). Under the stress conditions in our experiments we observed an approximately fivefold decrease in the number of AE events between the conventional and true triaxial cases. When taken together, the AE data, the velocities, and the crack density data indicate that the intermediate principal stress suppresses the total number of cracks and restricts their growth to orientations subnormal to the minimum principal stress. However, the size of individual cracks remains essentially constant, controlled by the material grain size. Crack damage is only generated when the differential stress exceeds some threshold value. Cyclic loading experiments show that further damage commences only when that previous maximum differential stress is exceeded, regardless of the mean stress, whether this is achieved by increasing the maximum principal stress or by decreasing the minimum principal stress.

A Directional Crack Damage Memory Effect in Sandstone Under True Triaxial Loading

“…However, in this study we are concerned with the evolution of crack damage that precedes ultimate failure. Our findings clearly show that such damage is a distinctly directional phenomenon, especially under true triaxial stress states (Browning et al, ). The fundamental and intrinsic attribute of any tensor invariant, that it is identical under any geometrical transformation, only serves to conceal the significance of this specific directionality (e.g., of sequentially evolving damage populations) with respect to the principal stresses and their orientations.…”

“…In the first of the three cycles, once a differential stress (Δ σ ) of 36 MPa has been reached, cracks form essentially parallel to σ zz and open essentially perpendicular to σ xx and σ yy and so are drawn as a colored girdle of poles in the x ‐ y plane. The breadth of the girdle is represented as 36° since it has previously been recognized that all fractures in the population do not form perfectly parallel to σ 1 but over a range of angles of about ±18° either side of σ 1 (see Browning et al, ). In the subsequent cycle, cracks form parallel to σ xx and open perpendicular to σ zz and σ yy , so this damage is represented as a girdle in the z ‐ y plane (with the same width of 36°) but is additional to the previous damage in the x ‐ y plane which remains.…”

“…All of these tests were conducted using uniaxial or conventional triaxial apparatus and so were unable to fully probe the directionality of the Kaiser effect. More recently, Browning et al () confirmed the presence of the Kaiser effect during true triaxial stressing experiments but concluded that the effect is more accurately a damage memory rather than a stress memory effect. In general, the state of stress in the crust is triaxial (i.e., σ 1 > σ 2 > σ 3 ; Zoback & Zoback, ), and results from experiments that recreate these more realistic stress conditions have noted significant effects on rock strength (Haimson & Chang, ), crack densities, crack orientations (Browning et al, ; Ghaffari et al, ), and fluid flow characteristics (Nasseri et al, ).…”

Dynamic Mechanical Behavior of Dry and Water Saturated Igneous Rock with Acoustic Emission Monitoring

“…Cyclic loading and unloading tests with acoustic emission monitoring are an effective approach to quantitatively measuring deformation and damage characteristics of various materials [11][12][13][14][15][16][17][18][19][20]. Sherif et al [12] captured and analyzed AE signals to characterize the crack formation and crack width development in the cyclic loading processes.…”

“…In addition to the fibre-reinforced composites and metallic materials, the AE method also is applied to research the mechanical behaviors of rock material. Browning et al [16] used cumulative AE hits and AE hits rate to evaluate the onset and evolution of new crack damage caused by inelastic processes in rocks under different loading conditions. Trippetta et al [17] found that there is a certain relation between the AE energy and the elastic moduli of seismogenic Triassic Evaporites subjected to cyclic stressing.…”