Rotation Of Principal Stress Axes Research Articles

Stress direction history of the western United States and Mexico since 85 Ma

A data set of 369 paleostress direction indicators (sets of dikes, veins, or fault slip vectors) is collected from previous compilations and the geologic literature. Like contemporary data, these stress directions show great variability, even over short distances. Therefore statistical methods are helpful in deciding which apparent variations in space or in time are significant. First, the interpolation technique of Bird and Li [1996] is used to interpolate stress directions to a grid of evenly spaced points in each of seventeen 5‐m.y. time steps since 85 Ma. Then, a t test is used to search for stress direction changes between pairs of time windows whose sense can be determined with some minimum confidence. Available data cannot resolve local stress provinces, and only the broadest changes affecting country‐sized regions are reasonably certain. During 85–50 Ma, the most compressive horizontal stress azimuth 1H was fairly constant at ∼68° (United States) to 75° (Mexico). During 50–35 Ma, both counterclockwise stress changes (in the Pacific Northwest) and clockwise stress changes (from Nevada to New Mexico) are seen, but only locally and with about 50% confidence. A major stress azimuth change by ∼90° occurred at 33 ± 2 Ma in Mexico and at 30 ± 2 Ma in the western United States. This was probably an interchange between 1 and 3 caused by a decrease in horizontal compression and/or an increase in vertical compression. The most likely cause was the rollback of horizontally subducting Farallon slab from under the southwestern United States and northwest Mexico, which was rapid during 35–25 Ma. After this transition, a clockwise rotation of principal stress axes by 36°–48° occurred more gradually since 22 Ma, affecting the region between latitudes 28°N and 41°N. This occurred as the lengthening Pacific/North America transform boundary gradually added dextral shear on northwest striking planes to the previous stress field of SW‐NE extension.

増分非線形モデルの数学的構造・定式化と主応力軸回転時の挙動の検証

The incrementally nonlinear behaviors of engineering materials, in particular geomaterials, are often reported and formulated into constitutive models. We here discuss the mathematical structure of incrementally nonlinear constitutive models among stress rates, strain rates, and the rate of change in internal variables through the representation theorem of isotropic functions and their matrix forms. As the examples of incrementally nonlinear models we discuss the formulation of the multi-slip model and the modified elasto- plastic model leading to incremental nonlinearity. Both models are evaluated whether they can account for the behavior of sands during the rotation of principal stress axes and found to be satisfactory from a qualitative view point.

応力主軸回転を受ける粒状体の塑性ひずみ増分応答の考察

応力主軸回転を受ける粒状体の塑性ひずみ増分応答の考察

Stress Path Testing for Proper Characterization of Unbound Aggregate Base Behavior

Realistic pavement stresses induced by moving wheel loads were examined in granular base layers, and the significant effects of rotation of principal stress axes were addressed for a proper characterization of unbound aggregate behavior. Granular material resilient moduli are commonly determined at the centerline of wheel loading without taking into account the effects of moving wheel loads and the constantly rotating field principal stress states. Differences that exist between field- and laboratory-applied stress states were identified by comparing the field stresses simulated using a nonlinear axisymmetric finite element program, GT-PAVE, with the stress states commonly used in the standard resilient modulus test procedure, AASHTO T294-94. Three sets of complete triaxial test data obtained from testing aggregates under various realistic in situ stress paths caused by moving wheel loading were analyzed. Eight different granular material modulus models were developed from the experimental test data to include the applied mean stress, the applied shear stress, and the slope of stress path loading. Because of the complex loading regimes followed in the laboratory tests, characterization models that simultaneously analyzed the static and dynamic components of the applied mean and deviator stresses produced a high degree of accuracy. Models that consider the stress path slope variations predict the best stress path dependency of aggregate behavior caused by moving wheel loads. Such advanced models that allow for the effects of principal stress rotation better describe the granular material behavior under the actual field loading conditions.

The general stress strain relation of soils involving the rotation of principal stress axes

In the light of matrix theory, the character of stress increment which causes the rotation of principal stress axes is analysed and the general stress increment is decomposed into two parts: coaxial part and rotational part. Based on these, the complex three dimensional (3-D) problem involving the rotation of principal stress axes is simplified to the combination of the 3-D coaxial model and the theory about pure rotation of principal stress axes that is only around one principal stress axes. The difficulty of analysis is reduced significantly. The concrete calculating method of general 3-D problem is provided and other applications are also presented.

Effective Stress Analyses of Port Structures

ABSTRACT Effective stress analyses are performed on the seismic response of port structures during the 1995 Hyogoken-Nambu earthquake. The structures analyzed include: caisson type quay walls which moved up to 5 m maximum toward the sea; pneumatic caisson type bridge foundations which moved toward the sea, reducing the distance between the bridge foundations across a sea channel by a total of 0.8 m; and composite breakwaters which settled 2 m. Although these structures were all a rigid concrete type and shaken by the same earthquake, the mode and extent of deformation/failure were different depending on the backfill and embedment conditions of the structures. The constitutive model of soil used for the seismic analyses is a multiple mechanism model defined in strain space. The model can take the effect of principal stress axis rotation into account, which is known to play an important role in the cyclic behavior of sand under anisotropic stress conditions. The model parameters are calibrated based on in-situ and laboratory investigations, including in-situ freeze sampling. The results of the effective stress analyses are consistent with those measured, including the mode and extent of deformation/failure, suggesting that the cyclic behavior of soil, idealized through the effective stress model, can explain the variety of seismic response of the port structures in a unified manner.

How did the Meers fault scarp form? Paleoearthquake or aseismic creep?: A soil mechanical perspective

Studies confirm that the Meers fault in southwestern Oklahoma has been active in recent times. The most recent movement occurred about 1100 y ago in late Holocene. There is as much as 5 m vertical and possibly appreciably more left-lateral strike–slip displacements on the fault. During faulting, the Quaternary soils 1 Soil, in an engineering sense, is the relatively loose agglomerate of mineral and organic materials and sediments found above the bedrock, and at a particular site, it can be residual (that is, weathered in place) or transported (moved by water, wind, glaciers, etc.) ( Holtz and Kovacs, 1981). 1 along the fault were folded as well as ruptured. In some places, almost all of the deformation is accommodated by ductile folding of the soils. Having this kind of deformation with no record of an earthquake associated with the Meers fault during historical times raises the question whether the present scarp was formed seismically by earthquake event(s), or aseismically by slow deformation (aseismic fault creep). To determine how the scarp was formed, I have developed a multidisciplinary study which involved geological, soil mechanical, and soil micromorphological techniques. Geological mapping delineated the deformation, stratigraphy, and any features that might be associated with the faulting. The mapping was also needed to reconstruct the sequence of events that formed the scarp at the study site. Consolidation tests using the Casagrande (1936)method for finding maximum effective stresses were used to determine the states of stresses imposed on the soil deposits when they were first faulted. These states of stresses were then compared to the states of stresses needed to slowly deform or shear the soils in triaxial and direct drained shear tests. The direction of maximum principal stress was determined by Mohr's circle and soil micromorphological analyses. The results of soil mechanical analysis show that the faulting of the Quaternary soils along the fault had to be sudden or fast, which indicates that the scarp was probably created seismically. During faulting, the soils were anisotropically consolidated or compacted, thereby, recording in their structure the states of stresses that caused faulting to occur. The direction of the maximum principal horizontal stress is between N62°E and N72°E indicating rotation of principal stress axes. The technique developed for this study can be used in similar areas where active faults offset Quaternary soils with relatively unchanging moisture contents below some depth. Also, for shallow depths, this technique might give more reliable young tectonic stress measurements (both magnitude and orientation) than other techniques such as overcoring, hydraulic fracturing and wellbore breakouts because it is used on geologically recent units which, unlike lithified rocks, have not yet existed through millions of years of deformation.

Response of a Dense Sand Deposit During 1993 Kushiro-Oki Earthquake

In the 1993 Kushiro-oki Earthquake of Richter magnitude 7.8, simultaneous recording of earthquake motions was successfully made at the ground surface and at a depth of 77 meters in a dense saturated sand deposit. The peak horizontal acceleration was 0.47 g on the ground surface and 0.21 g at a depth of 77 meters. The acceleration record at the ground surface showed a distinctive ground response, which consisted of a cyclic motion having a period of about 1.5 seconds overlain by a spike at each peak of the motion. In order to study the mechanism of this peculiar ground response, effective stress analysis was conducted on the dense saturated sand deposit. The model used for this study was a strain space multiple mechanism model, which takes into account the effect of principal stress axis rotation. The recorded earthquake motion at a depth of 77 meters was used as the input earthquake motion for the analysis. Sampling after in-situ freezing was done in order to evaluate the properties of the sand. The results of the analysis indicated that the observed ground response was due to the effect of dilatancy of sand, which plays a significant role in the response of the dense saturated sand deposits during strong earthquake motions.

Seismicity and stress in the vicinity of Mount Spurr volcano, south central Alaska

Focal mechanism solutions and hypocenters for earthquakes near Mount Spurr volcano in south central Alaska reveal spatial perturbations in the regional stress field and in the maximum depth of seismicity. At the volcano, practically all the shocks during the dormant decade 1981–1991 have depths shallower than 5 km and are characterized by nearly pure normal slip. In contrast, earthquakes located outboard of the volcano mostly concentrate in the depth range 3–18 km and exhibit predominantly strike slip, oblique reverse slip, or reverse slip. The regional stress field is characterized by subhorizontal maximum principal stress directed N30°W, concordant with the direction of convergence between the North American and Pacific plates, whereas the maximum principal stress is probably more nearly vertical beneath the volcano. We suggest that the shoaling of seismicity beneath the volcano reflects localized elevation of the depth to the midcrustal transition from brittle failure to plastic flow. We attribute this localized elevation to relict magmatic heat associated with past volcanic eruptions. The available data are not sufficient to determine the cause of the suggested rotation of the maximum principal stress axis beneath the volcano; possible mechanisms include an increase in the vertical stress from the weight of the Mount Spurr massif and a decrease in the maximum horizontal stress associated with doming of the shallow crust from magmatic processes.

Couplled Geomechanical-thermal Simulation For Deforming Heavy-oil Reservoirs

Abstract The paper describes a novel numerical model for the solution of poro-elasto-plasticity and multiphase, thermal flow in unconsolidated heavy-oil and oil-sand reservoirs. The elasto-plastic deformation is calculated using a finite-element incremental plasticity model with Mohr-Coulomb and Drucker-Prager as the yield criteria. This model is coupled with CMG's thermal simulator STARS which is capable of handling many advanced thermal recovery processes. The geomechanical calculation is in fact an effective stress analysis which solves a set of force balance (equilibrium) equations based on total stresses. These are augmented by the elastic material behaviors, plastic yield criteria, plastic flow rule, work-hardening law, and the strain-displacement relationships. Besides volumetric deformation, the solution gives the displacements in each direction, stresses, and strain distribution in the reservoir. The behaviors of reservoir multiphase flow and heat transfer processes are most significantly affected by the volume change and the associated permeability increase. The volume change is calculated by the plasticity model, whereas the permeability increase is related to the volume change via tabular data. The prediction of shear failure region, the rotation of principal stress axis, and the reduction of effective stresses as a result of pore pressure increase, are all important phenomena affecting the placement of fluid and hear in the formation. Introduction Considerable experiences on the in-situ recovery of heavy oil and bitumen from unconsolidated media have been accumulated both in field operations and in laboratory research over the last two decades. The significance of geomechanical responses on the recovery of these reservoirs is now generally recognized. In order to understand the recovery processes, we must consider the complex interaction of multiphase fluid flow, heat transfer, changes in stress state, and formation deformation as a result of injection and production operations. Previous work on the coupling of stress modeling with reservoir simulation(1,2) uses linear elasticity. However, extensive experimental data on oil sands indicate extremely complex constitutive behaviors at elevated pore pressure and temperature(3–6). Oil sands are dense frictional materials which tend to dilate under shear. This dilatancy is the result of an increase in deviatory stresses which leads to the slippage and loss of grain-to-grain contacts. Since the original sand fabric is disturbed, strains thus accumulated are irrecoverable. More recent contributions to this class of coupled simulations(7–11) treat the nonlinearity and plasticity behaviors of oil sands with varying degrees or sophistication. The stresses and strains are related by the material constructive model which must be satisfied for the geomechanical calculation. In this work, an elastoplastic formulation is chosen such that plastic deformation as a result of shear dilatancy can he modeled. During cyclic steam stimulation, the sand matrix goes through several loading and unloading cycles. This leads to complex deformation history which must be properly accounted for. As a reservoir grid block is loaded in the elastic regime, elastic strains accumulate which are recoverable upon unloading. The stress space is delimited by the yield surface. As the stress state reaches the yield surface, additional loading will cause the material to yield plastically.

Description of clay anisotropy employing the concept of directional variation of porosity : Pietruszczak, S; Krucinski, S Proc 3rd International Symposium on Numerical Models in Geomechanics (NUMOG III), Niagara Falls, 8–11 May 1989P61–70. Publ London: Elsevier Applied Science, 1989

A mathematical framework has been developed for describing the effects of inherent and induced anisotropy in clays. The structure of governing equations permits, in general, the modelling of the sensitivity of soil response to the rotation of principal stress axes. The framework employs a continuum measure of material fabric, which is defined as an implicit function of the spatial distribution of porosity /void ratio. The set of classical functions describing the state of the material is thus enriched by new tensorial functions reflecting the orientation of the fabric. Such a formulation is advantageous over a conventional plasticity approach. It remains physically descriptive, in a sense that, the material response is a function of the specific manifestations of the microstructure. The presented approach is general and its applicability extends to other geological materials, provided the proposed evolution law (Chapter 2) is appropriately modified and the material functions are adequately selected. In its present form, the formulation does not account for irreversibility of both the plastic flow and the evolution of microstructure ouring histories experiencing stress reversals. However, the mathematical structure of the constitutive relations, as

Yielding and flow of sand under principal stress axes rotation : Pradel, D; Ishihara, K; Gutierrez, M Soils FoundV30, N1, March 1990, P87–99

Yielding and flow of sand under principal stress axes rotation : Pradel, D; Ishihara, K; Gutierrez, M Soils FoundV30, N1, March 1990, P87–99

Constitutive Relations for Sand Under Cyclic Loading Based on Elasto–Plasticity Theory

In this paper, constitutive relations for expressing the inelastic behavior of sandy ground expected at the time of a strong earthquake are proposed. These constitutive relations are formulated by a yield function in terms of effective stress ratio and by a plastic potential function which is derived from the stress ratio-plastic strain incremental ratio defined as a function of accumulated volumetric strain. These constitutive relations employ Sekiguchi and Ohta’s stress parameter to take account of the effects of rotation of principal stress axis on the deformation characteristics of sand. The Masing rule is modified in such a way that it can be used in the multi-dimensional stress field, and employed in the hardening function in order to express a hysteretic damping. Material constants contained in the proposed constitutive relations can be easily determined by the mechanical tests which are normally conducted in laboratory. The comparison between predicted behaviors by the constitutive relations and results of undrained cyclic shear tests shows that the dynamic strength-deformation characteristics of sand in a wide range of density can be simulated satisfactorily.

Yielding and Flow of Sand Under Principal Stress Axes Rotation

ABSTRACT In order to investigate the influence of inherent anisotropy on the yielding and plastic flow of loose and dense sand, a series of experiments involving a wide range of principal stress axes directions were carried out on hollow cylindrical specimens of Toyoura sand using a torsional shear test apparatus. Stress paths involving cycles of stress reversal and stress axis rotation were performed in order to identify the states of stress at which plastic flow begins to take place. The test results revealed well-defined families of yield loci having identical shapes in the stress space independent of the density of sand. Experimental evidence presented here shows that the direction of the plastic strains for different stress increments is not uniquely established indicating the non-existence of a unique plastic potential. Consequently, within the framework of conventional theory of plasticity, the yielding and flow of sand can only be explained with the concept of multiple yield surfaces.

Fabric Tensors in Constitutive Equations for Granular Materials

ABSTRACT In an effort to develop a constitutive equation associated with more deformation and failure features of granular materials, the constitutive formulation is studied taking into account the fabric tensors as internal variables and their evolution modes. In order to render the constitutive equation satisfy the principle of material objectivity, the representation theorem of isotropic functions is effectively used. The theorem is reviewed with a particular reference to the rate type constitutive equation which gives rise to the rate of deformation tensor as a function of the stress, stress rate and fabric tensors. After discussing the relationship between essential independent variables in constitutive equations and the state of granular materials from a viewpoint of the evolution mode of the fabric tensors, particular problems are studied with the result that: (1) Granular materials can show less summetry (more anisotropic) than orthotropic when the general stress states and paths are concerned; (2) In two dimensions, the introduction of the (anisotropic) fabric tensor is essential in order to describe the non-coaxial and dilatant behavior under the rotation of principal stress axes.

Strain Increment and Stress Directions in Torsion Shear Tests

The directions of the major principal strain increment, stress, and stress increment during rotation of the principal stress axes at any stress level are studied for \IK\N\do-consolidated clay using a torsion shear apparatus with individual control of the vertical normal stress, the confining pressure, and the shear stress on hollow cylinder specimens under undrained and drained conditions. The torsion shear tests are performed along predetermined stress-paths, which are chosen to cover the full range of rotation of principal stress axes from 0° to 90° relative to vertical. The test results indicate that the major principal strain increment directions coincide with the major principal stress directions at failure. The directions of major principal strain increment coincide with the directions of major principal stress increment at low stress levels and with the directions of major principal stress at higher stress levels. This indicates that the behavior of clay gradually changes from elastic to plastic as the stress level is increased. Elasto-plastic theory is therefore suitable for modeling the behavior of clay during rotation of principal stress axes.

Sand behavior under principal stress axes rotation : Toki, S; Miura, S; Miura, K Proc Eighth Asian Regional Conference on Soil Mechanics and Foundation Engineering, Kyoto, 20–24 July 1987V1, P113–116. Publ Japan: Japanese Society for Soil Mechanics and Foundations Engineering, 1987

Sand behavior under principal stress axes rotation : Toki, S; Miura, S; Miura, K Proc Eighth Asian Regional Conference on Soil Mechanics and Foundation Engineering, Kyoto, 20–24 July 1987V1, P113–116. Publ Japan: Japanese Society for Soil Mechanics and Foundations Engineering, 1987

Considerations on soil response to the rotation of principal stress directions

The paper evaluates various plasticity formulations in the context of their ability to describe the influence of the rotation of principal stress axes. The discussion extends to a new theoretical framework which incorporates an implicit measure of material microstructure, derived from the directional distribution of porosity.

Deformation prediction for anisotropic sand during the rotation of principal stress axes : Miura, K; Toki, S; Miura, S Soils FoundV26, N3, Sept 1986, P42–56

Deformation prediction for anisotropic sand during the rotation of principal stress axes : Miura, K; Toki, S; Miura, S Soils FoundV26, N3, Sept 1986, P42–56

Modelling soil behaviour under principal stress axis rotation : Towhata, I; Ishihara, K Proc 5th International Conference on Numerical Methods in Geomechanics, Nagoya, 1–5 April 1985V1, P523–530. Publ Rotterdam: A. A. Balkema, 1985

Modelling soil behaviour under principal stress axis rotation : Towhata, I; Ishihara, K Proc 5th International Conference on Numerical Methods in Geomechanics, Nagoya, 1–5 April 1985V1, P523–530. Publ Rotterdam: A. A. Balkema, 1985