Rock Mechanics and Rock Engineering

The importance of discontinuities in controlling rock mass behaviour in any engineering project involving excavations calls for a sound and spatial characterization of the discontinuity structure present. Such a characterization necessitates field work that requires sufficient rock exposures in order to obtain an adequate number of data, time and considerable cost. Photoanalysis techniques can help in overcoming the above difficulties equally well or better than other techniques. This paper refers to simple photographic techniques and their implementation for computer aided analyses for the characterization of the rock mass fracturing features. In particular attention is focused on scale problems and on reconstruction of fracture density stereoplots on the basis of data collected from one or two images according to different lithologies and outcropping conditions. The methodology for evaluating the volumetric fracture intensity follows in a slightly modified way a technique previously suggested in the literature. Certain reported examples allow to validate the photoanalytical technique used and the proposed method of analysis. Furthermore, analyses on planar density, spacing, frequency, terminations in solid rock or against other discontinuities and spatial correlation have been implemented in a software to yield a more complete rock mass characterization. At the same time input data and analysis results are produced in data files available as input for numerical analyses.

Replicas were produced of 20 natural rock joints with different roughness. Factors affecting shear strength were examined and direct shear tests were performed using the replica joints to determine their quantitative shear strength characteristics. Results from the shear tests were best fitted by the power law equation, τ = Aσ n , where τ is the shear strength and σ n is the normal stress, and regression coefficients A and B were determined. The coefficient A (equal to τ when σ n is 1 MPa) is defined as the friction angle, and B, which determines the curvature of the plot of shear versus normal strength, is a factor that reduces the shear strength. The physical and mechanical properties of the coefficients A and B were defined, and the relationship between these coefficients and the factors affecting shear strength, such as roughness and joint wall strength, were analyzed quantitatively. A new equation, τ = σ n tan[ϕ b + ϕ J + s n], was suggested to measure and predict shear strength accurately based on results from these analyses, where ϕ b is the basic friction angle, ϕ J is the joint roughness angle, and s n is the shear component. Although the new shear strength equation is nonlinear, it is as simple to use as a linear equation and the shear strength can be estimated using only three easily measurable parameters (ϕ b , ϕ J , and σ j , the joint wall compressive strength). The failure envelope estimated using the new shear strength equation not only closely matches the measured shear strength, but also reflects the nonlinear relationship between the normal stress and shear strength.

A 3D particle-based DEM model was established taking into account the geometries of rock bridges. The model was used to investigate the shear behaviour of incipient rock joints. Fifty-seven direct shear tests were conducted under constant normal load (CNL) boundary conditions using the established model, in which rock bridges with 19 different geometries and incipient joints with various areal persistence (between 0.2 and 0.96) were involved. Our results show that, for the cases having a single rock bridge, cracks often initiated around the edges of the rock bridges and coalesced first in the middle of the rock bridge areas. While for other cases containing multiple rock bridges, cracks initially appeared at the connection points (located in the middle of the joint planes) of the rock bridges and then propagated to the edges. High crack initiation stresses were measured, which were often more than 60% of the shear strength of the tested incipient rock joints. Sudden failures of the rock bridges subjected to shearing were observed, accompanying dramatic increases in the number of cracks. Another important conclusion derived from this research is that both joint areal persistence and rock bridge geometry played significant roles in the shear failure of the simulated Horton Formation Siltstone joints. The present study has shown that shear strength increased gradually when joint areal persistence was decreased. Interestingly, different shear strength values were measured for rock joints with the same areal persistence (e.g. K = 0.5). Shear velocity was also found to have a significant influence on the shear characteristics of the Horton Formation Siltstone joints. A higher shear strength was measured when the shearing velocity was increased from 0.01 to 1 m/s.

The processes of deformation and failure in rocks are unavoidably accompanied by the absorption, storage, dissipation, and release of energy. To explore energy allocation during rock shear fracturing, two series of single loading and unloading preset angle shear tests at inclined angles of 60° and 50° were performed on red sandstone and granite by varying the experimental unloading level. The area integral approach was employed to interpret the load–displacement responses of the rock specimens via calculation of the energy parameters (referring to the external input energy, internal elastic energy and internal dissipation energy). The interpretations of the results revealed that the increase in the experimental unloading level nonlinearly increases the internal elastic energy, internal dissipation energy and external input energy; these relationships can be described by quadratic functions. It was also realized that under different experimental unloading levels, not only the internal elastic energy but also the internal dissipation energy is closely proportional to the external input energy. The proportional energy relationship can be used to quantify the internal elastic energy and internal dissipation energy at any expected experimental unloading levels, and a real-time calculation model for the internal elastic energy and internal dissipation energy in the pre-peak duration (including the peak point) was introduced. Meanwhile, an invariable feature for the ultimate internal elastic index Wed (the ratio of ultimate internal elastic energy to peak internal dissipation energy) was captured via quantitative analysis. Additionally, the energy allocation manner and transfer mechanisms of rocks bearing varied loading forms (including uniaxial compression, Brazilian splitting, point load, semicircular bending, and preset angle shear) were also comprehensively compared considering three basic rock fracture modes: the tensile, shear, and hybrid failure (mixed tensile-shear) modes. Thus, the proportional distribution patterns of internal elastic energy and internal dissipation energy or the linear correlations among the three energy parameters can be universally observed during the failure of homogeneous rocks, despite distinct loading forms under one-dimensional stress conditions.

This paper describes a novel procedure to assess fragmentation from automatic analysis of 3D photogrammetric models with a commercial software. The muckpiles from 12 blasts were photographed with a conventional drone to build 3D photogrammetric models; the flights were made with a relatively constant ground sampling distance (GSD) of 6.2 sd 0.92 mm (mean and standard deviation, respectively). A comparison with already published mass-based size distributions from 11 of these blasts, shows a good performance of automatic 3D-fragmentation measurements in the coarse range (P ≥ 60%), while deviations between mass-based and 3D model fragmentation analysis grow towards the central-fines range. As a solution, the Swebrec function is fitted to the reliable part of the size distributions, well above the GSD, and then is extended towards the fines, down to a percentage passing of 5–10%. The suitable fitting range is obtained iteratively from the mass-based fragmentation data; the lower fragment size considered is independent of the model’s resolution (i.e. GSD) with mean of 357 mm (equivalent to a passing in the range 66–86%, and well above the GSD of our models). The resulting distributions match properly mass-based size distributions with relative errors in percentile sizes of 15.5 sd 3.4%, and they can be represented with the simplest form of the fragmentation-energy-fan. As a guideline for reconstruction of size distributions and fines assessment when mass-based data is not available, the lower-fitting limit of 357 mm yields reasonable results (mean errors in pass in the range 5–36%) for the present case. The errors are limited enough to keep a sound description of the variation of fragmentation with change in blast design.

Detailed descriptions of the CSIR “doorstopper” and triaxial rock stress measuring instruments are given, including the procedures involved in making measurements with them. The derivations of the theoretical formulae which are used to calculate the rock stresses from the strains measured with the instruments are also included in the paper.