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_Journal of Structural Geology 32 (2010) 1701–1711_ _Contents lists available at ScienceDirect_ _Journal of Structural Geology_ _journal homepage: www.elsevier.com locate jsg_ _The effect of the intermediate principal stress on fault formation and fault angle in siltstone_ _BezaLeL Haimson a,*, John W. Rudnicki b a University of Wisconsin, Madison, WI 53706, USA b Northwestern University, Evanston, IL 60208, USA_ _article info_ _Article history: Received 6 February 2009 Received in revised form 5 July 2009 Accepted 25 August 2009 Available online 11 September 2009_ _Keywords: Bifurcation Fault angle Faulting Siltstone Mohr–Coulomb Shear localization Strength criterion True triaxial test_ _abstract_ We conducted true triaxial compression tests on specimens prepared from two siltstone core sections, one above and one below the Chelungpu Fault, Taiwan. For different constant s2 and s3 magnitudes, the maximum principal stress (s1) was raised until a post failure stage was reached, and a through-going fault had developed. Despite differences between the properties of the two cores, in all tests peak s1 increased as s2 was set at higher levels than s3, in contrast to Mohr–Coulomb condition predictions. The fault–normal vector was aligned with the s3 direction and made an angle (q) with s1 direction. The angle q, which corresponds to fault dip in case of normal faulting, increased monotonically with s2 for fixed s3, a variation that is also inconsistent with Mohr–Coulomb theory. The results of shear band localization theory are used with fault angles observed for axisymmetric compression and deviatoric pure shear to infer properties of the inelastic constitutive behavior. These properties are significantly different for the two cores. Using them to predict q for other deviatoric stress states yields good agreement with the observations for core II and acceptable agreement for core I. The results are used to predict the angle variation for constant mean normal stress (q decreases as the deviatoric stress state varies from axisymmetric extension to axisymmetric compression) and at fixed deviatoric stress state (q decreases monotonically with increasing mean normal stress)._ _? 2009 Elsevier Ltd. All rights reserved._ _1. Introduction_ Laboratory experiments simulating compressive failure and faulting in rocks are typically conducted on cylindrical specimens subjected to constant lateral confining pressure and a rising axial load until brittle fracture occurs. These ‘conventional triaxial tests’ replicate only a special case of crustal condition, that in which two of the principal stresses are equal. Conventional triaxial tests on rocks were conducted as early as the turn of the last century (Von Kármán, 1911). They gained acceptance because of the relatively simple equipment, specimen preparation, and testing procedure. The ubiquity of conventional triaxial testing can also be traced to the assumption that the intermediate principal stress (s2) has a negligible effect on rock failure characteristics as expressed, for example, in the Mohr or Mohr–Coulomb failure criteria (Jaeger et al., 2007). However, indications from the three major types of faulting encountered in the field, and results of numerous in situ stress measurements at depths reaching several kilometers (McGarr and Gay, 1978; Brace and Kohlstedt, 1980), point to a state of stress in the earth’s crust that is fully three-dimensional (s1 s s2 s s3). Murrell (1963), Handin et al. (1967), and Mogi (1967) compared results of conventional triaxial compression tests with those of conventional triaxial extension and deduced that the differences in rock resistance to faulting between the two modes of loading were due to the different magnitudes of s2 applied. Inspired by this evidence, Mogi (1971) introduced a true triaxial testing machine in which rectangular prismatic specimens were subjected to three different principal stresses. He found that indeed s2 affects the stress level at which faulting occurs, and hence the rock strength criterion, as well as the angle at which the fault develops. Little follow-up on Mogi’s seminal work took place until Haimson and coworkers carried out similar true triaxial tests in igneous rocks (Westerly granite, Haimson and Chang, 2000; Pohang rhyolite, Chang and Haimson, 2007); a metamorphic rock (KTB amphibolite, Chang and Haimson, 2000; Haimson and Chang, 2002) and a sedimentary rock (siltstone, Oku et al., 2007). They found that strength, deformability, and fault angle were affected by s2 in all the tested rocks. An exception was found in tests of Long Valley (California) ultra fine-grained hornfels and metapelite (Chang and Haimson, 2005), unusual rocks that appear to have no dilatancy, and develop no visible microcracks. Independently, building upon the antecedents of Hadamard (1903), Mandel (1966), Thomas (1961) and Hill (1962), Rudnicki and Rice (1975) (also, Rice, 1976; Besuelle and Rudnicki, 2004) suggested a description of failure as a bifurcation from homogeneous (spatially uniform) deformation that predicted a strong dependence on s2 (via the deviatoric stress state). More specifically, Rudnicki and Rice (1975) established conditions for which a solution corresponding to concentrated deformation in a planar band was an alternative to continued homogeneous deformation. The appearance of this localized mode of deformation is often essentially coincident with ‘‘failure’’ by development of a through-going fault or fracture, but in other cases it may be the precursor to a more extended evolution of localized deformation that ultimately requires significant additional strain for failure. Analysis based on this approach yields a relation among constitutive parameters required for the onset of bifurcation and hence depends strongly on how the homogeneous deformation prior to bifurcation, especially the inelastic portion, is modeled. The predictions of the failure stress by the bifurcation approach depend strongly on certain details of the constitutive behavior that are difficult to determine experimentally and, for various other reasons, are difficult to compare with experimental observations of failure (Besuelle and Rudnicki, 2004). However, the prediction for the fault angle is much less sensitive to these details and is more easily compared with observations in terms of the constitutive parameters for homogeneous deformation just prior to bifurcation. Rudnicki (2008a,b) has used and extended results from the bifurcation theory to interpret observations of failure plane inclinations in true triaxial tests of Westerly Granite (Haimson and Chang, 2000) and to infer aspects of the constitutive behavior. In this paper we describe two series of true triaxial tests conducted on samples of siltstone taken from the hanging wall and the footwall of the Chelungpu fault, Taiwan. The tests reveal a clear dependency of strength and fault angle on the magnitude of s2. The results are compared with predictions based on shear localization theory incorporating a yield surface and plastic potential that depend on three stress invariants (rather than two, as in Rudnicki and Rice (1975)). Dependences of the yield surface and plastic potential on mean stress are inferred from the fault angles observed in axisymmetric compression and deviatoric pure shear. These dependences are used to compare the predicted fault angles with observations for other deviatoric stress states and to predict the variation that would be observed with mean stress for fixed deviatoric stress state and with deviatoric stress state for fixed mean stress._ _2. Rocks tested_ _Rock specimens used in the true triaxial tests described here came from core recovered from the scientific hole A, near the northern end of the Chelungpu fault. The hole was drilled as part of the Taiwan Chelungpu Fault Drilling Project (TCDP). The project was undertaken to study the faulting mechanism behind the destructive Chi-Chi earthquake (1999; Mw ? 7.6), characterized as a thrust motion across the North-South striking Chelungpu fault (Shin and Teng, 2001; Lin et al., 2003). Core made available to us came from short sections centered at the depth of 891 m (core I) and 1252 m (core II), straddling the active fault, which was intercepted at 1111 m. Core I is a siltstone belonging to the early Pleistocene Cholan Formation, which persists to a depth of 1013 m; core II is also a siltstone, belonging to the Pliocene Chinshui Formation, which prevails at depths of 1013–1313 m. Thus, core II is representative of the rock traversed by the active Chelungpu fault. Core I comes from a somewhat younger formation. As shown below, there are distinct differences in mineral content, as well as in mechanical behavior between the two siltstones. We cannot tell whether the differences are related to their juxtaposition with respect to the fault and its activity or, what appears more likely, the consequence of their different deposition ages._ _The siltstone in core I contains 68% quartz, 19.5% clay, 9.5% feldspar, and 3% biotite; the siltstone in core II consists of 65% quartz, 25.5% clay, 7.5% feldspar, and 2% biotite. The only major difference is the amount of clay, and this may have a role in the disparity between the two core sections in some of their physical and mechanical properties (Table 1)._ _The 891 m siltstone is both stronger and stiffer in compression than the 1252 m core. Also notable is that core I rock has significantly larger grain size than core II. Although the siltstone is a sedimentary rock, no bedding planes were visible, and neither core showed signs of inhomogeneity. We examined the degree of anisotropy by running unconstrained (uniaxial) compression tests._ Ключевые слова: material, criterion, predicted variation, ?xed, prediction based, compaction, inelastic increment, prediction, solid, fault, decrease monotonically, localization, specimen, surface, constitutive parameter, compressive, compression, true triaxial, shear, haied, condition, isotropic material, band angle, siltstone belonging, strength, result, earth, thomas, deviatoric stress, mohr, brittle fracture, journal structural, term, lin, lode angle, principal stress, mandel, data set, parameter, inferred, plastic, rudnicki, engineering, bifurcation, journal, siltstone, testing, axisymmetric compression, true, international, stress invariant, based, isotropic, mechanics, experimental data, von, rudnicki journal, magnitude, compaction band, principal, data, linear, cook, rice, mohr–coulomb, behavior, constant, rudnicki rice, mode, inelastic, sin, theory, axisymmetric extension, strong dependence, oct, journal geophysical, eqs, deg, property, ii, yield condition, band, fault angle, mpa oct, chang haimson, decrease, case, angle, hill, structural, friction coefcient, observation, pure shear, figs, experimental result, mpa mpa, deformation, point, expression, pore pressure, brittle rock, triaxial, normal stress, geology, siltstone core, variation, potential, core, conducted, compressive strength, constitutive behavior, increment, rock mechanics, nadai domain, ql, elsevier, pure, plastic potential, borja, angle deg, yield, axisymmetric, failure surface, agreement, wa, north, paper, extension, predicted, dilatancy, conventional triaxial, strength criterion, faulting, faulting occurs, form, constitutive, society, dependence, yield surface, difference, nadai, strain, hadamard, failure, conventional, mogi, compressive stress, yield stress, increase, core core, direction, through-going fault, haimson rudnicki, rice expression, deviatoric, physical, subjected, triaxial strength, dilatancy factor, inelastic deformation, plane, test, yield function, stress, function, fracture, mpa, solids, haimson chang, slight increase, geophysical, eq, invariant, mohr criterion, normal, haimson, soct, chang, rock, structural geology, press, triaxial test