Laboratory measurements of rock strength provide limiting values of lithospheric stress, provided that one effective principal stress is known. Fracture strengths are too variable to be useful; however, rocks at shallow depth are probably fractured so that frictional strength may apply. A single linear friction law, termed Byerlee's law, holds for all materials except clays, to pressures of more than 1 GPa, to temperatures of 500°C, and over a wide range of strain rates. Byerlee's law, converted to maximum or minimum stress, is a good upper or lower bound to observed in situ stresses to 5 km, for pore pressure hydrostatic or subhydrostatic. Byerlee's law combined with the quartz or olivine flow law provides a maximum stress profile to about 25 or 50 km, respectively. For a temperature gradient of 15°K/km, stress will be close to zero at the surface and at 25 km (quartz) or 50 km (olivine) and reaches a maximum of 600 MPa (quartz) or 1100 MPa (olivine) for hydrostatic pore pressure. Some new permeability studies of crystalline rocks suggest that pore pressure will be low in the absence of a thick argillaceous cover.

Limits on lithospheric stress imposed by laboratory experiments

Experimental techniques commonly used for high strain-rate testing of concrete in compression, together with the methods used for measurement and recording of stress and strain, are critically assessed in the first part of this paper. The physical capability of each loading method is discussed and some consideration is given to the definitions used for specifying the loading rate. The second part reviews the dynamic compressive strength (mostly uniaxial rather than bi- or triaxial) of plain concrete, while in the third part a review on deformation behaviour indicates that uncertainty and disagreement exist concerning changes in axial strain at high strain rates.

Compressive behaviour of concrete at high strain rates

The purpose of this review is to discuss the development and the state of the art in dynamic testing techniques and dynamic mechanical behaviour of rock materials. The review begins by briefly introducing the history of rock dynamics and explaining the significance of studying these issues. Loading techniques commonly used for both intermediate and high strain rate tests and measurement techniques for dynamic stress and deformation are critically assessed in Sects. 2 and 3. In Sect. 4, methods of dynamic testing and estimation to obtain stress–strain curves at high strain rate are summarized, followed by an in-depth description of various dynamic mechanical properties (e.g. uniaxial and triaxial compressive strength, tensile strength, shear strength and fracture toughness) and corresponding fracture behaviour. Some influencing rock structural features (i.e. microstructure, size and shape) and testing conditions (i.e. confining pressure, temperature and water saturation) are considered, ending with some popular semi-empirical rate-dependent equations for the enhancement of dynamic mechanical properties. Section 5 discusses physical mechanisms of strain rate effects. Section 6 describes phenomenological and mechanically based rate-dependent constitutive models established from the knowledge of the stress–strain behaviour and physical mechanisms. Section 7 presents dynamic fracture criteria for quasi-brittle materials. Finally, a brief summary and some aspects of prospective research are presented.

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A Review of Dynamic Experimental Techniques and Mechanical Behaviour of Rock Materials

Review of experimental techniques for high rate deformation and shock studies

About the dynamic strength enhancement of concrete-like materials in a split Hopkinson pressure bar test

Deformation of a granite, a tonalite, and a limestone in a plane shock wave is compared with triaxial deformation at 10−5 sec−1 under the constraint of uniaxial strain. For granite and for limestone at moderate pressure, the stress-strain relation is nearly identical in the two tests; strain under these conditions was elastically recoverable. For the limestone at high pressure and for the tonalite at all pressures, volume decreases permanently. This permanent deformation, compared here for shock and slow strain-rate tests, had approximately the same strain-rate dependence as has been observed typically in fracture of rocks under triaxial conditions.

W. F. Brace

Papers

Comparison of uniaxial deformation in shock and static loading of three rocks