The validity of the cubic law for laminar flow of fluids through open fractures consisting of parallel planar plates has been established by others over a wide range of conditions with apertures ranging down to a minimum of 0.2 µm. The law may be given in simplified form by Q/Δh = C(2b)3, where Q is the flow rate, Δh is the difference in hydraulic head, C is a constant that depends on the flow geometry and fluid properties, and 2b is the fracture aperture. The validity of this law for flow in a closed fracture where the surfaces are in contact and the aperture is being decreased under stress has been investigated at room temperature by using homogeneous samples of granite, basalt, and marble. Tension fractures were artificially induced, and the laboratory setup used radial as well as straight flow geometries. Apertures ranged from 250 down to 4µm, which was the minimum size that could be attained under a normal stress of 20 MPa. The cubic law was found to be valid whether the fracture surfaces were held open or were being closed under stress, and the results are not dependent on rock type. Permeability was uniquely defined by fracture aperture and was independent of the stress history used in these investigations. The effects of deviations from the ideal parallel plate concept only cause an apparent reduction in flow and may be incorporated into the cubic law by replacing C by C/ƒ. The factor ƒ varied from 1.04 to 1.65 in these investigations. The model of a fracture that is being closed under normal stress is visualized as being controlled by the strength of the asperities that are in contact. These contact areas are able to withstand significant stresses while maintaining space for fluids to continue to flow as the fracture aperture decreases. The controlling factor is the magnitude of the aperture, and since flow depends on (2b)3, a slight change in aperture evidently can easily dominate any other change in the geometry of the flow field. Thus one does not see any noticeable shift in the correlations of our experimental results in passing from a condition where the fracture surfaces were held open to one where the surfaces were being closed under stress.

/pdf/validity-of-cubic-law-for-fluid-flow-in-a-deformable-rock-2ynq4id3hq.pdf

VALIDITY OF CUBIC LAW FOR FLUID FLOW IN A DEFORMABLE ROCK FRACTURE - eScholarship

Keywords: Dimensionnement ; Classification ; Excavation ; Ouvrages souterrains ; Contrainte ; Ouvrages de soutenement Reference Record created on 2004-09-07, modified on 2016-08-08

Support of underground excavations in hard rock

Empirical estimation of rock mass modulus

A clumped particle model for rock

This paper presents a short history of the appraisal of laser scanner technologies in geosciences used for imaging relief by high-resolution digital elevation models (HRDEMs) or 3D models. A general overview of light detection and ranging (LIDAR) techniques applied to landslides is given, followed by a review of different applications of LIDAR for landslide, rockfall and debris-flow. These applications are classified as: (1) Detection and characterization of mass movements; (2) Hazard assessment and susceptibility mapping; (3) Modelling; (4) Monitoring. This review emphasizes how LIDAR-derived HRDEMs can be used to investigate any type of landslides. It is clear that such HRDEMs are not yet a common tool for landslides investigations, but this technique has opened new domains of applications that still have to be developed.

https://link.springer.com/content/pdf/10.1007%2Fs11069-010-9634-2.pdf

Use of LIDAR in landslide investigations: a review

Damage initiation and propagation in hard rock during tunnelling and the influence of near-face stress rotation

Spalling and strain bursting has long been recognized as a mechanism of failure in deep underground mines in hard rock and in deep infrastructure tunnels. The latter is a significant growth industry, particularly in Europe where subalpine base tunnels in excess of 10 m wide and dozens of kilometres long are being driven by tunnel boring machine (TBM) through alpine terrain at depths greater than 2 km. In more massive granitoid or gneissic ground, these tunnels have experienced significant spalling damage. En route to a practical predictive technique for this condition, the author utilizes a number of analytical and micromechanical tools to validate a simple empirical predictive model for tunnel spall initiation. The true nature of damage and of yield, as the result of extensile damage accumulation, in hard rocks is examined using these tools. Based on the resultant conceptual model, the author expands on the empirical damage threshold, using a spalling limit to differentiate stress paths that lead to crac...

The 2003 Canadian Geotechnical Colloquium: Mechanistic interpretation and practical application of damage and spalling prediction criteria for deep tunnelling

A review of the tensile strength of rock was conducted to determine the relationship between direct tensile strength (DTS) and Brazilian tensile strength (BTS) and to examine the validity of estimating tensile strength from other measured properties, such as the crack initiation (CI) threshold. A data set was gathered from the existing literature where tensile values could be reliably correlated with unconfined compressive strength or CI values. It was determined that the BTS obtained in standard testing is generally greater than the equivalent DTS and that this relationship is rock type dependent. CI yields a reasonable estimate of tensile strength and this correlation is improved when the BTS values are reduced to DTS values by rock type specific correlations. The factor f, in DTS = f BTS, can be considered to be approximately 0.9 for metamorphic, 0.8 for igneous and 0.7 for sedimentary rocks. The relationships presented demonstrate that there is wide scatter in the available data for estimating tensile strength likely due to both specimen variability and testing configuration, including platen geometry and relative stiffness. Estimates of tensile strength should only be used for preliminary design purposes and measurements should be made to confirm preliminary assumptions for each design.

A Review of the Tensile Strength of Rock: Concepts and Testing

The primary objective of this work was an examination of the complimentary roles of tensile damage and confinement reduction (or stress relaxation) on excavation response of “hard” rockmasses. Tensile damage and relaxation are examined with respect to structurally controlled or gravity driven failure modes as well as to strength controlled or stress driven rockmass damage and yield. In conventional analysis of both structurally controlled and stress driven failure, the effects of tensile damage and tensile resistance as well as the elevated sensitivity to low confinement are typically neglected, leading to erroneous predictions of groundfall potential or rock yield. The important role of these two elements in underground excavation stability in hard rock environments is examined in detail through a review of testing data, case study examination and a number of analytical and numerical analogues including discrete element simulation, statistical theory and fracture mechanics. This rigorous theoretical treatment updates, validates and constrains the current use of semi-empirical design guidelines based on these mechanisms.

Mark S. Diederichs

Papers

Empirical estimation of rock mass modulus

Damage initiation and propagation in hard rock during tunnelling and the influence of near-face stress rotation

The 2003 Canadian Geotechnical Colloquium: Mechanistic interpretation and practical application of damage and spalling prediction criteria for deep tunnelling

A Review of the Tensile Strength of Rock: Concepts and Testing

Manuel Rocha Medal Recipient Rock Fracture and Collapse Under Low Confinement Conditions