Anisotropic yielding of rocks at high temperatures and pressures

The anisotropic deformation of foliated and linealed rocks has been investigated, primarily to predict the mechanical response of rocks surrounding buried magma chambers to the stress fields generated by deep drilling. The principal application in this regard has been to evaluate, the scientific feasibility of extracting geothermal energy from buried magma chambers. Our approach has been to perform triaxial extension and compression tests at temperatures and pressures representative of the borehole environment on samples cored along six selected orientations and to fit the data to an orthohombric yield criterion. We have investigated Four-Mile gneiss (a strongly layered gneiss with well defined lineation), a biotite-rich schist, and Westerly granite (using a block oriented with respect to the granite's rift, grain, and hardway). Progress has been made in three areas: the experimental determination of strength anisotropies for the three starting materials, theoretical treatment and modeling of the results, and characterization of fabrics surrounding magma bodies resulting from their diaperic emplacement into shallow portions of the Earth's crust. In addition, results have been obtained for the tensile fracture of quartzite, basal slip and anisotropy of biotite single crystals, and anisotropic flow of bedded rocksalt.


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INTRODUCTION
This progress report for the project entitled "Anisotropic Yielding of Rocks at High Temperatures and Pressures" presents: a summary of Energy (grant no. DE Drs. Andreas Kronenberg and James E. Russell. responses to s rocksalt has been submitted under a separate cover. our s manuscripts in press or submitted to referred journals and research funded in full or in part by the Department of Energy. We also provide a list of abstracts and brief descriptions of ongoing research on schist, granite, and bedded rocksalt, the results of We expect to complete two more manuscripts within the year, one on our continuing work on biotite schist and another on the forms of anisotropic yield criteria and their application to data acquired previously for slates and phyllites. We have completed experiments on Westerly granite, our isotropic end-member for comparison w i t h results obtained for Four-Mile gneiss. However, the results for schist are surprising in several respects and we propose to continue our studies of micarich metamorphic rocks, treating these as coarse-grained analogues to fine-grained, clay-rich sMes.
As a means of summarizing our work, we include those manuscripts that have been completed and submitted for publication during the current funding period, followed by brief descriptions of our ongoing studies and unpublished results.

ONGOING RESEARCH Deforman 'on of Biotite Schist
The experimental results we have obtained on Four-Mile gneiss have demonstrated that the yield behavior of quartzo-feldspathic rocks containing only a , provided the mica minerals exhibit a s of gneiss oriented such that resolved shear stresses on the foliation plane are percentage (10%) of mica can be large are considerably weaker than granites of similar grain size and composition, and this weakness is attributed to enhanced nucleation of microcracks in quartz and feldspar adjacent to mica grains that are suitably oriented for slip. We expect the yield behavior of rocks containing a higher proportion of phyllosilicates to be influenced by the strongly anisotropic nature of these minerals as well, although the strengths, temperature and pressure dependencies, and flow-controlling mechanisms in such rocks may be signifi Constant strain ra samples of a fine-grained schist (Idaho County, Idaho) rich in biotite (>75%) with 10-20% epidote and several percent chlorite and feldspar. The starting material exhibits a well-defmed, near-planar foliation and a consistent mesoscopic lineation. It lacks specimen scale; however, its distribution of biotite and section scale w i t h millimeter-scale layers of nearly pure (>95%) biotite alternating with zones which contain up to 50% epidote. The epidote-rich mnes are somewhat finer grained, and preferred orientations of biotite appear to be weaker within them (Fig. 1 gneiss and previous schist e ents (E3org and Handin, 1966) suggest that the experiments we p e r f o d on the biotite schist would capture its maximum strength anisotropy. To our surprise, the experimental data do not reveal any significant strength differences associated with ntations at any experimental conditions tested. Plots of differential stress versus axial stmin are presented in Figure 2 and compared with results for biotite the first 2% strain. E Y accommodated the total shortening imposed at constant differential stresses (within 20 percent of  L i those measured at 2 percent strain). Individual schist samples showed the entire range of behavior from strain hardening, steady strength, and strain softening post-yield behavior, but no systematic response was observed as a function of temperature or confining pressure in either orientation.
Differential stresses supparted by the schist beyond the yield point lie between those measured for biotite single crystals shortened at 900 and 45' to their (001) planes. The results of all of the experiments performed to date are assembled in Table 1.
Compressive strengths of biotite schist exhibit dependencies upon co-g pressure as well as upon temperature and strain rate, a result we may expect if deformation is accommodated both by brittle and by d u d e processes. Mohr circles representing differential stresses at 2 percent strain have been plotted for samples shortened perpendicular to foliation and at 45' to foliation ( . Thus, the lllechaxlical response and grain-scale defmticm mechanisms are both consistent w i t h defmtion in the transitional brittleductile field, in which both pressure-sensitive and thenmlly-aciivatcd mechanisms contribute significantly to the deformation. The transitional brittleductile def-tion of schist appears to be subject to history-and/or path-dependencies. The results of temperature-stepping experiments differ for those experiments in which the temperature was step-wise increased and decreased (Figure 6) with a change in apparmt   ------  Similarly, strain rate-stepping experiments have shown that the relationship between difFerential ss and strain rate is pathdependent, although it has been more difficulttomeasure.
-Both the isotropic nature and path dependence of defarmation of the biotite schist chosen for study have been smprising to us, and we have initiated detailed microstructural studies of defmned samples with the goal of understanding the mechanisms of defamation leading to this behavior. In part, we suspect that the mechanical anisotropies of foliated rocks, or lack thereof, may be reflected in the preferred orientations of layer silicates, their spatial distributions, and modal concentrations, and the mechanisms of defamation operative within neighboring phases. Path dependencies may be intrinsic to the processes of dislocation glide, kinking, firictional sliding and microcrack extension of layer silicates, or may reflect changing contributions of these mechanisms to the maaOScOpic defoxmation. Our microstructural studies, currently underway, should contribute to our understanding of other foliated and layered rocks as well. M e c h a n i c a l results for phyllites, slates, and shales have been analyzed only at the macroscopic level due to the extremely fine grain sizes Charactens ' tic of these rocks. We propose to continue our study of schist into the next project period treating it as a coarse-grained analogue to fine-grained, clay-bearing shales. We plan experiments on several schists we have collected, with Wering mica contents and p r e f d orientations. By examining their anisotropies and defmtion microstructures, we hope to identify those fabric elements which lead to directional behavior. We expect that microstnrcttlral and textural studies of fine-grained shales will be more d E c d t than our studies of schists and we may need to rely on those insights gained from these coarse-grained analogues.

on of Westerlv
For purposes of comparison with Four-Mile gneiss, we performed a series of compression expekmts on samples of Westerly granite cored in six orientations w i t h respect to the quarrying planes, the rift €2, the grain G, and the hardway H (Figure 7) at confining pressures of 0,50, and 100 Mpa Westerly granite resembles Four-Mile gneiss in composition with similar volume fractions of quartz and feldspars and a combined mica content (7% biotite and 2% muscovite) nearly identical to that &tentined for the gneiss (9% biotite and 1% muscovite). In contrast to Four-We

Figure7. ConstantstrainmecompressionexperinzentsonWestcrly
Cylindricalsampleswert bycaringpupendicularto the the grain G, and the -strain curve for Wcsteriy P,lOoMPa,and€= 10-3 t li G kj  Peng and Johnson (1972) for Chelmsfd granite. cyrindrical s were prepared and tcsted in orientations perpendicular to the rift R, grain G, and trardway H, and to surfaces prepared at 45" to R, G, and H (Figure 7). All of the experiments were performed at room tempemure and a strain rate of lO.5~-1. All samples failed by frstcture and exhibited similar stress-strain curves. However, peak frachne strengths varied from sample to % andexperiments were (as~yaslOtimesintw0 orientations).
The results are assembled in Table 2 and indicate that Westerly granite is very nearly isotropic. Unlike the variations in fracture strength of up to 20% repatexi for Chelmsford granite (Peng and Johnson, 1972 Table 3 for samples shortened perpendicular to bedding (labeled V), parallel to bedding (labeled H), the cxperi&ntal uncertainties. However, significant difftrences have beem g (labeled 45). Merential stresses measured in these three orientations are observed in the lateral strains of these samples, which suggest subtle departures from isotropic mechanical Properties (Figures 9 and 10). the differential stress and strain rate (i.e., w i t h n measure of anisotropy than do   whereas the permanent finite strain near the sample's center may be a p x h a t a k assuming strains a n sufficiently small to treat them as infinitesimal and neglect crrors associated with their nxxmmnent as engineering strains. We believe that these p l i m i~~~ results are promising and we will continue investigating the weaklyaefined anisotropy of bedded rocksalt until the end of the current project period

Students S u m e d
Three students in the Center for Tectonophysics have received support from this grant in the foxm of research assistantships. W f i a m Shea has been involved in the work on biotite schist and is expected to complete his Ph.D. thesis on 'The Roles of Micas and Fabric in the Deformation of Foliated Rock: An Experimental Study" within the upcoming year. Lin Peng @cnmcd the granite experiments and is expected to complete her US. thesis on 'The Interaction of Two Closely Spaced Cmks-Rock Models and Computer Simulations" by the end of May, 1990. Mchad TSCM has been involved in the work on salt defonnaton and has made excellent progress on his PkD. research, including experimental and observational results.
Richard Gouschalk received support from this grant in the form of a postdoctoral fellowship. In addition to cumpIeting a thorough investigation of Four-Mile gneiss, Rick eff&vely extended his education in structural geology and tcctoniCs to include a solid background in mechanics.