N.R. Morgenstern

THE ULTIMATE FRICTIONAL RESISTANCE OF ROCK DISCONTINUITIES

Abstract When a sand or clay is sheared to large strains, it will pass through a peak shearing resistance and will generally decline in resistance until a value is reached where deformation can continue with no further change in resistance. This is the residual strength and an important characteristic of the residual strength is that it is independent of the original state of the soil. When a rock is sheared to large strains it too will pass through a peak resistance which will decline to a value where deformation can continue with essentially no change on shearing resistance, at least on a scale of displacement larger than the asperities on the resulting discontinuity. While this has also been called the residual strength, this terminology is mistaken because the resulting resistance is a function of the surface roughness developed along the rock discontinuity during the failure process. The term ultimate frictional resistance is preferred. The same rock brought to failure in different ways, under different environments, will have different ultimate frictional resistances that depend upon surface roughness. In the laboratory, surfaces of the same rock prepared in different ways that result in different roughness will also display different ultimate frictional resistances. Laboratory data on the ultimate frictional resistance of limestone from the Frank Slide, Alberta, are given. Alternate measures of quantifying surface roughness are discussed and correlations between surface roughness and ultimate friction are presented. The influence of wear on surface roughness is also discussed. Evidence from natural discontinuities in support of the concept of ultimate frictional resistance is provided by noting that the ultimate resistance along a natural bedding plane in the limestone is much greater than along a flexural slip surface. Flexural slip folding has reduced the roughness along certain bedding planes to values much less than those produced by shearing underformed bedding planes.

Interpretation of hydraulic fracturing breakdown pressure

Abstract Breakdown pressure is an important parameter obtained during hydraulic fracturing stress measurements. It is thought that the maximum horizontal stress can be calculated from the breakdown pressure, the minimum principal stress and the properties of the rocks. On the other hand, breakdown is a complex process. The breakdown pressure is rate-dependent, size-dependent, fracture fluid-dependent and σ 3 - dependent . As a result, many breakdown models prevail. This paper evaluates the various models experimentally and theoretically. The analysis shows that the classical breakdown model, the poroelastic model, the shear failure model and the point stress model cannot explain the observed abnormally high breakdown pressure. The fracture mechanics model is promising. The breakdown pressure appears to correspond to the onset of unstable fracture propagation. It should be stressed that the fracture criterion for the unstable fracture propagation is K I −K Ic = 0 and ∂( K I −K Ic )/∂L ⩾ 0 , not only K I −K Ic = 0 . Introduction of ∂( K I −KIc)/∂L ⩾ 0 makes it possible to explain several phenomena such as rate-dependent, size-dependent, fracture fluid-dependent and σ 3 - dependent responses and abnormally high breakdown pressures.

DEFORMATION OF SMALL TUNNELS - IV. BEHAVIOUR DURING FAILURE

Abstract Tests on small circular openings have been conducted to investigate the deformation processes near tunnels at large depth or in weak rock. The test equipment has been described in Part 1; typical test results documenting the behaviour of small tunnels in a jointed rock mass with time-dependent strength and deformation properties have been presented in Part II; and the pre-failure behaviour of these tunnels has been investigated in Part III. In this fourth part, results from one specific test on coal are used to discuss the behaviour of openings in a jointed rock mass during the failure process. The test results show that it is necessary to differentiate between two modes of behaviour, yielding and rapture, if overstressing of the rock mass near the opening occurs. The observed rock mass displacements and wall convergences are compared with predictions made by one analytical and one numerical model. It is concluded that existing design models do not satisfactorily simulate the transition from yielding to rupture and that both behaviour modes must be evaluated separately for proper tunnel design and selection of optimal construction techniques. Practical implications for tunnel monitoring and interpretation of oil well breakouts are also discussed.

Time-dependent deformation of small tunnels—II. Typical test data

Abstract Process simulation tests have been conducted to investigate the time-dependent deformation processes near tunnels at large depth or in weak rock. The test equipment has been described in Part I together with a presentation of the loading history adopted for the tests. This second Part includes a detailed description of typical test results and a discussion of the time-dependent processes, such as failure propagation and associated stress redistribution, which cause the observed behaviour. Both the time-dependent and time-dependent tunnel convergence and radial strain pattern inside the rock mass are presented in plots of field stress, strain or tunnel closure with time, and strain rate or tunnel closure rate. The performance of the tunnel in the pre-failure stress range, during the transition to an unstable opening and after a yield zone has developed is evaluated. Even though a detailed interpretation of the test results will follow in subsequent publications, several important conclusions can be made with respect to time-dependent processes controlling tunnel convergence, observation of the rock mass response to local yielding, position and type of instrumentation to detect time-dependent processes and propagation of instabilities in overstressed rock.

PHENOMENOLOGICAL MODEL FOR ROCK WITH TIME-DEPENDENT STRENGTH

Abstract Modelling of material behaviour constitutes a major part of the engineering design and construction process. Time-dependent deformation and failure mechanisms must often be considered, particularly in situations where the rock mass is stressed to relatively high stress levels. Under these conditions, it is necessary to model the time-dependent near failure and post-peak strength behaviour. A phenomenological model describing time-dependent failure process in strain-weakening rock has been presented, described and tested qualitatively on published test results from creep test, relaxation tests and variable strain rate tests. The model postulates that rock basically consists of a time-dependent and a time-independent resistance to deformation. Various parameter distribution functions are required to model different types of rocks or rock masses in detail, but it is shown that the proposed model describes essentially all observed time-dependent rock failure data.

An experimental investigation into hydraulic fracture propagation—Part 1. Experimental facilities

Abstract Since the development of hydraulic fracturing to enhance the production of oil or gas from a well, many fracture propagation models have been put forward. However, practical methods of evaluating the theoretical and numerical models have been few. For the above reasons, a set of hydraulic fracture tests was conducted on 350 × 305 × 305 mm and 610 × 584 × 305 mm gypstone blocks to produce experimental data for verification of hydraulic fracturing numerical models and evaluation of hydraulic fracturing theories for stress measurements. This paper, the first part of a series of publications, provides a general description of the experiments. It illustrates fabrication and properties of the artificial rock—gypstone, the test frame which applies the three principal stresses on specimens, the pump system that exerts bottomhole pressure on specimens, specimen size, well size, layout of wells and sealing of wells. Following that, instrumentation of the experiments (injection rate, bottomhole pressure, stresses, deformation of specimens) and testing procedures are presented. Finally, one representative experimental result is shown, and the effect of specimen size on breakdown pressure is examined by comparison of hydraulic fracture tests conducted in 305 × 305 × 305 mm with 610 × 584 × 305 mm block specimens. The experimental results show that this system is suitable for hydraulic fracture tests. No effect of specimen size on breakdown pressure is found for 305 × 305 × 305 mm block specimens.

Quantitative risk assessment of slope hazards along a section of railway in the Canadian Cordillera—a methodology considering the uncertainty in the results

Railway alignments through the Canadian Cordillera are constantly exposed to slope instabilities. Proactive mitigation strategies have been in place for a few decades now, and instability record keeping has been recognized as an important aspect of them. Such a proactive strategy has enhanced the industry’s capacity to manage slope risks, and some sections have been recognized as critical due to the frequency of instabilities. At these locations, quantification of the risks becomes necessary. Risk analysis requires knowledge of some variables for which statistical data are scarce or not available, and elicitation of subjective probabilities is needed. A limitation of such approaches lies in the uncertainty associated to those elicited probabilities. In this paper, a quantitative risk analysis is presented for a section of railway across the Canadian Cordillera. The analysis focused on the risk to life of the freight train crews working along this section. Upper and lower bounds were elicited to cope with the uncertainties associated with this approach. A Monte Carlo simulation technique was then applied to obtain the probability distribution of the estimated risks. The risk probability distribution suggests that the risk to life of the crews is below previously published evaluation criteria and within acceptable levels. The risk assessment approach proposed focuses on providing a measure of the uncertainty associated with the estimated risk and is capable of handling distributions that cover more than two orders of magnitude.

An experimental investigation into hydraulic fracture propagation—Part 2. Single well tests

Abstract This paper presents the experimental results of single well hydraulic fracture tests. The tests were conducted in dry gypstone blocks of 305 × 305 × 305 mm. True triaxial stresses were applied to the specimens. Leak-off was incorporated. The deformation of the specimens during injection was monitored to provide further data to characterize the fracture. The fracture and the oil penetration area were observed after testing. The influences of the least principal stress and the injection rate on fracture propagation were studied. The experiments produced considerable data on build-up of bottomhole pressure before breakdown, breakdown pressure under various states of stress and injection rates, behavior of fracture propagation post breakdown, and leak-off behavior. The monitoring of fracture propagation post breakdown and observation of leak-off provided data for a leak-off dominated material for use in numerical models.

Time-independent and time-dependent deformation of small tunnels—III pre-failure behaviour

Abstract Process simulation tests have been conducted to investigate the time-dependent deformation processes near tunnels at large depth or in weak rock. The tests equipment has been described in Part I together with a presentation of the loading history adopted for the tests. In Part II typical test results have been presented to document the behaviour of small tunnels in a jointed rock mass with time-dependent strength and deformation properties. A qualitative interpretation of the observed displacement pattern has been given. In this third part the measured tunnel closure and radial strain patterns are compared with those predicted from simple material models. The time-independent behaviour is compared with predictions assuming linear elastic material properties and the time-dependent tunnel response is compared with solutions assuming linear visco-elastic material properties. It is concluded that excessive deformations can be attributed to softening processes near the tunnel wall. The practical implications of this interpretation are discussed.

A Direct Shear Apparatus With Vibrational Loading

For some geotechnical design projects where soils are exposed to dynamic loads (vibrations), it becomes necessary to evaluate the strength and deformation characteristics of the soil under existing and/or anticipated vibrations. In order to investigate the effect of the vibrations on the strength and deformation properties of soils, representative samples should be collected and tested in laboratories and subjected to vibration of expected magnitudes. In this case, it is important that the laboratory equipment used is able to simulate field conditions as close as possible to provide the necessary parameters that can successfully be used in the design. A vibrational direct shear apparatus has been developed based on the conventional direct shear apparatus to evaluate the strength and deformation characteristics of soils (granular and cohesive) under a wide range of vibrational accelerations and frequencies. The apparatus makes it possible to test soils in both stress and displacement controlled modes. The design of the apparatus is such that it allows modification of the most commonly used direct shear apparatuses into the vibrational ones. The new apparatus was built and tested to prove its performance and reliability.