A Method for Modeling Variation of In Situ Stress Related to Lithology - PDF document

1 A Method for Modeling Variation of In Si
A Method for Modeling Variation of In Situ Stress Related to Lithology J. K. Whyatt Spokane Research Laboratory, National Institute for Occupational Safety and Health, Spokane, Washington, USA Assuring ground control safety in many mining and tunneling projects depends, at understanding of in situ stress conditions that will be encountered. Yet it is rarely practical to conduct more a very limited number of stress measurements. Stresses along the route of a ptypically concepts seeks to define a set of uniform regional loads. the rock massperience gained in Finally, factors affecting ERVIEW AND APPLICAAN ELLIPTICAL INCLUSION of an excavation in a naturally vable stress through intrusive st). In this example, it is al stress is primarily a function simplify the problem, it is assumed that region­al loads are aligned with ellipse axes. Clearly, the in situ stress field geometry induced stresses, illustrated in has been solved exactly (Donn biaxial solution. This relatip can be used to first back-calculate regionald then carry out the forward tunnel route 1.—Outline of modeling an-alyzed in light of lithologic inclusions to find Loads are thus applied to the model to determine stresses in of interest, in this case, the course of a robustness, or insensitivity to error, of solution. For instance, it asymptotically as the ellipse elongated (Figure 2). Thus, errors in estimating the Also, the elliptical problem solutigeometric unique property that stress throughout the inclusion (Sendeckyj, 1970). degree of stress concentration at a measure­ This is particularly convenient in cases where measurements the hardest available e case with many overcore measure­ recovery and linear geologic structures depart fromelliptical geometry (and its geometric limits). 3. SOURCES OF LOAD of a precise and direct link between particu­ load s

2 ources and stmodeling. by Hyett et al. (
ources and stmodeling. by Hyett et al. (1986). (i.e. gravitational, tectonic, thermal, and physico-chemical loads). : Reversible change in gravitational body forces as lines of symmetry. A unia. A uniaFh=(1/1-Lv) Fv]. Tectonic stress: Reversible change in the stress caused by application of tractions to rock mass boundaries. Does not include tractions in of boundary movement in reaction to applica­ induced by restraint of boundary movement in reaction to irreversible consequences of loading. state caused by che in the rock (e.g. recrystallization, absorption of groundwater levels) while are maintained as lines of sym­metry. Reversible caused by variation of rock temperature fr F) while rock mass boundaries are maintained as lines of symmetry. Figure 2.—Stress-concentrating effect of elliptical inclusion (plane stress). developing these definns, a uniaxial strain mon for regions relatively un­ in excess of this model. of two reasons. First, it may be that an alternative ation of horizontal stress, as a global model of gravitational loSheorey,ight be useful to apply any tendency toward viscous such a rock mass will tend to increase th uniaxial strain model). Such deformations are by a reduction in the total potential energy of rock mass. This reduction resultscrease in stored strain energy due to horizontal stress with loss in gravi­ potential energy (i.e. the rock mass slumps or viscous deformation). In a rock mass stress equal to stresses are only those that increase in Poisson’s ratio is just that– apparent– sources that bme apparent after gravitational is removed. In this ce remaining stress removed in two parts.aries are removed as tectonic loads. ning internal stress distri­ is removed as a residual stress state, leaving a also consider scale, since models necessarilyproject. sources must the bound

3 aries of this rock mass, es. Since resid
aries of this rock mass, es. Since residual stress is are removed, residual stress systems larger than kind of loading applied outs rules for behavior of rock mass boundaries are also required. These are— • Boundaries symmetry for application of • Changesoundary tractions caused by applica­ghboring sections of the crust be passed through rock mass f a batholith will rock mass that are functionally equivalent to tectonic boundary tractions. • Changes in boundary tractions caused by irre (i.e. that are not removed with load sources) are, in essence, part of a re system tinterest. They are treated as tectonic loads. nition of tectonic state of stress in the subject rock mass. REFERENCE STATE GENERATION OF A RESIDUAL STRESS FIELD and linear methods for applying allll the nonlinearity associated with of the in situ stress field is assi stress state. Given the complex of many raccurately.s alternative—directly mapping stress field—is usually impractical. to determine how closely it (in combinatiinduced by other load sources) matched approach requir more likely to if they are linkehe geometry of relevant geologic structures in a consistent and physically way. In a geologic seing should be associated with analysis be greatly simplified if a linear could be developed for generating these tributions, i.e. a method whereby a number of residual stress sta to fit a desired distribution of residual and tectonic by simply assigning a uniform initial stress elastically in the absence of load sources. Figure 3.—Tectonic () components of a uniform stress field in an elastic model of an elliptical soft inclusion point of this example the boundary load, Px, from a body with a stress state is revealed as the model adjusts to absence of loads and reaches eilibrium. This inclusion geometry. Since the resstress state

4 also be described by the original stre
also be described by the original stress), it may be more convenient to the residual stress state in terms of its ce state for the residual stress reference state concepirreversible processes that create a residual stress field. provides a framework for studying how the stress field relageometry of geologic structures. it is highly unlikely that accurate hope is simply that residual stficiently close to reality to be measures of the quality should provide insight into whether reasonable stress fields are being generated. Poor approx­ will result in poor matches between model and measurement. ring the potential for reference state esidual stress fields, it is useful to some characteristics of the relationship reference state residual stress field. These All reference states will g can be represented by a reference state. For contains several bars with various levels a completely the residual stress state). Re be attained exactly through relaxa­ of a reference state might be atta through deformation induced by an applied load initial stress Uniquenesste is not necessarily a generator of a residual stress field rock mass, every uniform initiatress field is a reference states would seem to diminish greatly with the addition of geologic complexity. reference state iscontext of elastic adjustment to the removal of all the relationship between reference state l changes in state should, therefore, cause only small type of reference state mass might provide sock mass were generated. For rocks are more highly the concentration of stress in high-modulu more quickly (i.e. with l rocks. One possible geologic interpreta­, then residual strcounteracts by loading. Thus, ate of stress is the reference state. One c interpretation is that long-term vis­nated or greatly reduced contrasts between rock types. Such viscous deformatio would lead

5 toward a lithostatic stress , then resi
toward a lithostatic stress , then residual stress incompletelynteracts or reinforces structural stress patterns. Thus, the reference state will loads. If residual stresses actually reinfe from applied loads. A tensile ass, while not intuitive, is appropriated necessary for achieving a residual by compressive loading. One possible geologicpretation shift loads from soft to TIMATING sources currently applied ion of interest, ing stresses from applied loads) is loads (including the regional reference state). ticularly encompassing all maller models with gravit gravity (or density of rock), which covers gravitational with depth. The final six are components stress field. These components may also be considered to vary linearly with depth. linear relationship load source component (inem. In the forward problem, the principle field within the model as a linear com­ of stresses induced by these unit l In the backwardred stresses. Fitting can be accomplished with any of a number of routines that reduce (e.g. a squared error measure as the sum of squares of normal stress component error plus twicehe sum of squares of shear component error. Double weighting preserves invariance with respect to coordinate system. supplied in the Excel spreadsheet program. PLICATIONDISTRICT OF NORTHERN IDAHO d’Alene Mining District of northern Idaho (Whyatt, 2000). This analysis sought to rec varying measurements of in situ stress (Table strict and, hopefully, help explain observed intensity of rockburstrelationship with depth or elevation (e.g. Figure 4). Table 1.—Summary of in situ stress measurements, Coeur d’Alene Mining District, USA, megapascals Lucky Friday Sunshine Mine breakouts 3300 level 7300 level 4250 level 5300 level 113.4 Bearing ............ .. N 20° W N 21° W N 38° W S 80° W N 80° W N 65° W *Measured/estimated *Measured vertica

6 l stress divided by an estimate of verti
l stress divided by an estimate of vertical stress based on depth of overburden. 4.—Observed magnitude of vertic in situ stress measurements at various depths. Variability that can attributed topography is indicated by the shaded region. geology of to the assumptions of this significant rock types have been (Whyatt et al., 1996). Three of these occur stratigraphic units while the fourth is characterized k types, makes up over 80% of the accessible rock types (sericitic, vitreous, and rgillite and are associated with econ typically provide better core ecovery and are isotropic than siltite-argillite been preferred host rocks for in situ stress meas­ Over the tectonic summarized as two periods of inte by three periods of intense faulting, harder isolated inclusions of various shapes and size stress field is assumeprimarily by graclay-rich rock should behave over geolo the method provided the best fit at well-silicified sites. of this method to these stress measurements provided a muimproved stress For exan the horizontal plane of the meas­ was more than an order of magnitude less hile successfully anticipating analysis (Table 2) generated a (Table 3). This result is well in line with how this Table 2.—Inferred regional loads at a depth of 1500 m Tectonic strain: = 1654 microstrain Bearing = N 41° W = 1239 microstrain Reference state in silicified rock: = 152 MPa (tension) Bearing = N 67° W = 49.6 MPa (tension) Table 3.—Estimated stress field in siltite-argillite rock far from quartzitic inclusions at a depth of 1500 m = 33.2 MPa Bearing = N 41° W = 40.7 MPa = 40.7 MPa tensile reference st for residual stress reflects the fact that silicified rocks are more highly imply. This result suggests increase rockburstbrittleness of this rock type. Moreover, it suggestsl stresses. Finally, analysis shows that crite

7 ria for measurement sites in the distric
ria for measurement sites in the district must as the potential for an accurateurement. 7. CONCLUSIONS AND DISCUSSION from a variety of stress measure­ within a naturally varying in situ stress field. method assumes that stress variation arises pri­asts in rock properties, particularly lus, and that unusually soft or hard por­ between load sources and resulting rev stress field. These definitions, and an approx­ method of ge of an initial uniform stressth method has been applied to an analysis of northern Idaho. It successfully loading conditions stent with a diverse reasonable is far from perfect, it does provide significant models of stress variation with elevation. Most into the spatial distribution of rockburst level, these scatter evident in likely a real variation that is associatedgeologicctures. Thus, consistency should be by direct extrapolation from available modeling of assoted stress variation should beneficial to most underground engineering projectsensitive to in situ stress conditions, but will particularly well suited to tunnels and mine drifextending through diverse geologic conditions. results also suggest that the number and distribution of stress measurements lute accuracy of the 8. ACKNOWLEDGMENTS author is indebted to Dr. Charles Fairhurst for his developing, my colleagues the Spokane Research Laory (NIOSH), parti­ Brian White Ted Williams, in applying this to the Coeur d’Alene District, is also gratefully 9. REFERENCES Donnell, L.H. 1941. Stresconcentrations due to elliptical discontinuities in plates under edgorces. Contributions to Mechanics and Related Subjects: Von Karman Anni­ena: California Institute of Technol­ogy, pp. 293-309. F. & Souley, M. 1997. Interprurements in a Provence mising a block modelling. In Proceedings of the International Symposium on , K. Sugawara and Y. Oba Kumamot

8 o, eds. Oct. 7-10, 1977). Rotterdam: Ba
o, eds. Oct. 7-10, 1977). Rotterdam: Balkema,Hyett, J.A. 1986. A critical of basic concepts associated with the existe stress. In Rock Stress and Rock Stress Measurements: Proceedings of International Symposium Rock Stress and Rock Stress Measurements, O. Stephans­ ed. (Stockholm, Sept. 1-3, 1986). Lulea, Sweden: Centek Publ., pp. 387-396. Konietzky, H. & Marschall, P. 1996. Excavations disturbed zone tunnels in fractured rock—Example from the Grimsel Geomechanics '96, Z. Rakowski, ed. Rotterdam: Balkema, pp. 235-240. . Characterizing in situ stress domains at the Research Laboratory. Geotech. J27:631-646. G.P. 1970. Elastic inclusioelastostatics. Intern. J. of Solid Structures, 6:1535-1543. P.R. 1994. A theory for in situ stresses in isotropic and transversely. Rock Mech. Min. Sci. & Geomech. Abstr. 311:23-34. Whyatt, J.K. 2000. Influence of geologic structures on stress variation for rock-bursting in mines with reference to the Lucky Friday Mine, Idaho. Ph.D. dissertation. Minneapolis: University of Minnesota, 203 pp. Whyatt, J.K. & White, B.G. 1998. Rock bund seismicity ramp development, Lucky Friday Mine, Mullan, Proceedings, 17th International Conference on Control in Mining Aug. 4-6, 1998.) Morgantown: Univ. of West Virginia, pp. 317-325. Whyatt, J.K., White, B.G. & Johnson, J.C. 1996. Strength and deformation properties of Belt strata, CoeurDistrict, ID. U.S. Bur. Report of Investigations 9619, Whyatt, J.K., Williams, T.J. & Blake, W. 1995. In situ stress atarts): 4. Characterization of in situ stress field. U.S. Bur. Mines Report of Investiga­tions 9582, 26 pp. Whyatt, J.K., Williams, T.J. & White, B.G. 2000. and the May 13, District, northern Idaho.Pacific Rocks 2000. Rock Proceedings of the Fourth North Mechanics Symposium (NARMS 2000),. Girard, M. eds. (Seattle, WA, July 31­Aug. 3, 2000). Rotterdam: Balkema, pp. 3