Dynamic analysis of strain localization in water‐saturated clay using a cyclic elasto‐viscoplastic model

A computational framework is presented for dynamic strain localization and deformation analyses of water‐saturated clay by using a cyclic elasto‐viscoplastic constitutive model. In the model, the nonlinear kinematic hardening rule and softening due to the structural degradation of soil particles are considered. In order to appropriately simulate the large deformation phenomenon in strain localization analysis, the dynamic finite element formulation for a two‐phase mixture is derived in the updated Lagrangian framework. The shear band development is shown through the distributions of viscoplastic shear strain, the axial strain, the mean effective stress, and the pore water pressure in a normally consolidated clay specimen. From the local stress–strain relations, more brittleness is found inside the shear bands than outside of them. The effects of partially drained conditions and mesh‐size dependency on the shear banding are also investigated. The effect of a partially drained boundary is found to be insignificant on the dynamic shear band propagation because of the rapid rate of applied loading and low permeability of the clay. Using the finer mesh results in slightly narrower shear bands; nonetheless, the results manifest convergency through the mesh refinement in terms of the overall shape of shear banding and stress–strain relations. Copyright © 2013 John Wiley & Sons, Ltd.     

Fabric dilatancy and the plasticity modeling of granular media

A novel conceptual model of the mechanics of sands is developed within an elastic–plastic framework. Central to this model is the realization that volume changes in anisotropic granular materials occur as a result of two fundamentally different mechanisms. The first is purely kinematic, dilative, and is the result of the changes in anisotropic fabric. There is also a second volume change in granular media that occurs as a direct response to changes in stress as in a standard elastic/plastic continuum. The inclusion of the two sources of volume change results in three important datum states. When subjected to isotropic strains, the resulting stress state in granular materials is not isotropic but lies upon the kinematic normal consolidation line. There exists a state at which the fabric‐induced volumetric strain rate becomes equal to the stress‐induced volumetric strain rate making the total plastic volumetric strain rate equal to zero. Granular response changes from contractive to dilative at this phase transformation line. The third datum state is the one in which the stress‐induced volumetric strain rate is zero. The sand, however, continues to dilate at this state with the difference between stress and dilation ratio a constant as predicted by Taylor's stress–dilatancy rule. These predictions are shown in accordance with experimental data from a series of drained tests and undrained on Ottawa sand. Copyright © 2011 John Wiley & Sons, Ltd.     

On the efficiency and predictability of strain energy for the evaluation of liquefaction potential: A numerical study

Strain energy concept has been employed by the researchers for the assessment of liquefaction phenomenon which is a disastrous type of earthquake-induced failure in saturated soils. The efficiency and predictability conditions of strain energy concept for liquefaction potential assessment are investigated herein using effective stress numerical analyses. Several earthquake ground motions were introduced to the base of a calibrated numerical model using an advanced fully coupled constitutive model. Results of the numerical analyses indicate that earthquake-induced excess pore pressure is more rigorously proportional to strain energy compared with the other examined intensity measures. Subsequently, a simple relationship was derived using the results of dynamic analyses to predict cumulative strain energy density in terms of magnitude, source to site distance, and effective overburden pressure. This relationship, which tries to guarantee the predictability condition of strain energy demand, has demonstrated a successful capability in discrimination between the liquefied and non-liquefied case histories recorded after several well-known earthquakes. This study has provided a practical linkage between numerical analysis and field observations. Finally, it is concluded that although strain energy approach possesses a great conceptual efficiency in liquefaction potential assessment, its precise prediction in actual field conditions involves some difficulties.     

Rifting Attractor Structures in the Baikal Rift System: Location and Effects

The current geodynamics and tectonophysics of the Baikal rift system (BRS) as recorded in lithospheric stress and strain are discussed in the context of self organization of nonlinear dissipative dynamic systems and nonlinear media. The regional strain field inferred from instrumental seismic moment and fault radius data for almost 70,000 M_LH ⩾ 2.0 events of 1968 through 1994 shows a complex pattern with zones of high strain anisotropy in the central part and both flanks of the rift system (the South Baikal, Hovsgöl, and Muya rift basins, respectively). The three zones of local strain anisotropy highs coincide with domains of predominantly vertical stress where earthquakes of different magnitudes are mostly of normal slip geometry. Pulse-like reversals of principal stresses in the high-strain domains appear to be nonlinear responses of the system to subcrustal processes. In this respect, the BRS lithosphere is interpreted in terms of the self organization theory as a geological dissipative system. Correspondingly, the domains of high strain anisotropy and stress change, called rifting attractor structures (RAS), are the driving forces of its evolution. The location and nonlinear dynamics of the rifting attractors have controlled lithospheric stress and strain of the rift system over the period of observations, and the same scenario may have been valid also in the Mesozoic-Cenozoic rifting history. The suggested model of a positive-feedback (fire-like) evolution of nonlinear dynamical systems with rifting attractors opens a new perspective on the current geodynamics and tectonophysics of the Baikal rift system.     

Development of quartz c-axis crossed/single girdles under simple-pure shear deformation: Results of visco-plastic self-consistent modeling

Quartz c-axis fabrics are widely used to determine the shear plane in ductile shear zones, based upon an assumption that the shear plane is perpendicular to both the central segment of quartz c-axis crossed girdle and single girdle. In this paper the development of quartz c-axis fabric under simple-pure shear deformation is simulated using the visco-plastic self-consistent (VPSC) model so as to re-examine this assumption. In the case of no or weak dynamic recrystallization, the simulated crossed girdles have a central segment perpendicular or nearly perpendicular to the maximum principal finite strain direction (X) and the XY finite strain plane, and at a variable angle relative to the imposed kinematic framework that is dependent on the modeled flow vorticity and finite strain. These crossed girdles have a symmetrical skeleton with respect to the finite strain axes, regardless of the bulk strain and the kinematic vorticity, and rotate in a way similar to the shear sense with increasing bulk strain ratio. The larger the vorticity number the more asymmetrical their legs tend to be. In the case of strong dynamic recrystallization and large bulk strain, under simple shear the crossed girdle switches into single girdles, sub-perpendicular to the shear plane, by losing the weak legs. The numerical results in our models do not confirm the above-mentioned assumption.     

Liquefaction Analysis Using Viscoplastic Kinematic Hardening Constitutive Model

The dynamic response analysis combined with the generalized return-mapping algorithm is applied to the integration algorithms of viscoplastic constitutive relations including the effect of the shear band. The kinematic hardening model based on modified and extended soil model with isotropic strain-hardening–softening is employed. In this paper, the TESRA (temporary effect of strain rate and acceleration) model is employed for the nonlinear viscosity of sand. The constitutive equations of rate-dependent plasticity originally proposed by Duvaut–Lions are employed as the base of the solutions. Liquefaction of a buried pipe is analyzed by finite element method by employing the above mentioned constitutive relations and the calculated results are compared with experimental results. The dynamic response analysis is applied to the solutions of the problems. The kinematic hardening–softening viscoplastic constitutive relations for geomaterials are promising for the predictions of cumulative deformations and liquefaction of the buried pipe. A great deal of experimental results indicate that the stress is a unique function of irreversible strain and its rate.     

Fault-related fold kinematics recorded by terrestrial growth strata,Sant Llorenç de Morunys,Pyrenees Mountains,NE Spain

Foreland basin growth strata are ideal recorders of deformation rates and kinematics in tectonically active regions. This study develops a high-resolution chronostratigraphic age model to determine folding rates in the Eocene-Oligocene terrestrial growth strata of the Berga Conglomerate Group, NE Spain. The Berga Conglomerate Group was sampled for rock magnetic, magnetostratigraphic, and magnetic susceptibility (χ) cyclostratigraphy analyses. Analysis of rock magnetic measurements indicate a mixed mineral assemblage with both paramagnetic and ferromagnetic minerals. A new magnetic reversal stratigraphy constrains the time frame of folding and is in agreement with previous interpretations. Time series analysis of χ variations show statistically significant power at expected orbital frequencies and provides precession-scale (20 kyr) temporal resolution. Strain measurements including anisotropy of magnetic susceptibility (AMS) fabrics and bedding plane strain worm burrow distortion are consistent with fixed hinge, flexural folding kinematics. Fault-related folding was modeled using χ cyclostratigraphy timing and strain measurement kinematic constraints. The onset of folding was at 33.85 Ma and the end of deformation is less constrained but is younger than 31.06 Ma. Deformation and sediment accumulation rates are unsteady at 20 kyr time scales but appear artificially steady at polarity chron time scales.     

应力路径对地表变形特性影响的数值模拟

针对不同环境条件及工程因素对地表变形影响的不同特点,研究了不同应力状态下土的变形特性,得出其影响地表变形的基本规律。通过典型三轴试验对比分析了变形规律,由试验数据空间反演了各应力路径下的本构模型空间,编制相应的模块嵌入有限元程序,模拟了几种不同路径下地表沉降算例,得到了导致地表变形的几个基本规律：①不同的地表变形问题对应的应力路径千差万别,需要用不同的应力路径条件下的本构模型进行分析;②应力路径的影响是不可忽略的,甚至在诸多因素中起主导作用;③数值建模方法建立起来的模型通过权值系列的不同反映应力路径的影响,能较好应用于此类问题的分析;④CTC与TC路径极限体变相差近20 %;⑤CTC路径的剪缩区范围比CTE路径大,两种路径下剪缩体应变值最大相差近17.3 %;CTE路径较CTC路径的剪胀更为明显,剪胀体应变最大相对差值近98 %。     

‘Large Igneous Provinces (LIPs)’: Definition,recommended terminology,and a hierarchical classification

This article is an appeal for the adoption of a correct and appropriate terminology with respect to the so-called Large Igneous Provinces (LIPs). The term LIP has been widely applied to large basaltic provinces such as the Deccan Traps, and the term Silicic Large Igneous Province (SLIP) to volcanic provinces of dominantly felsic composition, such as the Whitsunday Province. However, neither term (LIP, SLIP) has been applied to the large granitic batholiths of the world (e.g., Andes) to which both terms are perfectly applicable. LIP has also not been applied to broad areas of contemporaneous basalt magmatism (e.g., Indochina, Mongolia) and sizeable layered mafic intrusions (e.g., Bushveld) which in many significant respects may also be considered to represent ‘Large Igneous Provinces’. Here, I suggest that the term LIP is used in its broadest sense and that it should designate igneous provinces with outcrop areas ≥ 50,000 km². I propose a simple hierarchical classification of LIPs that is independent of composition, tectonic setting, or emplacement mechanism. I suggest that provinces such as the Deccan and Whitsunday provinces should be called Large Volcanic Provinces (LVPs), whereas large intrusive provinces (mafic–ultramafic intrusions, dyke/sill swarms, granitic batholiths) should be called Large Plutonic Provinces (LPPs). LVPs and LPPs thus together cover all LIPs, which can be felsic, mafic, or ultramafic, of sub-alkalic or alkalic affinity, and emplaced in continental or oceanic settings. LVPs are subdivided here into four groups: (i) the dominantly/wholly mafic Large Basaltic Provinces (LBPs) (e.g., Deccan, Ontong Java); (ii) the dominantly felsic Large Rhyolitic Provinces (LRPs) (e.g., Whitsunday, Sierra Madre Occidental); (iii) the dominantly andesitic Large Andesitic Provinces (LAPs) (e.g., Andes, Indonesia, Cascades), and (iv) the bimodal Large Basaltic–Rhyolitic Provinces (LBRPs) (e.g., Snake River–High Lava Plains). The intrusive equivalents of LRPs are the Large Granitic Provinces (LGPs) (e.g., the Andean batholiths), although an equivalent term for intrusive equivalents of LBPs is not necessary or warranted. The accuracy and usefulness of the terms flood basalt, plateau basalt, and trap are also examined. The largest LBP, LVP, and LIP is, of course, the bulk of the ocean floor. It is contended that the proposed LIP nomenclature and classification will lead to more accurate and precise terminology and hence better understanding of the wide variety of Large Igneous Provinces.     

Strain memory of 2D and 3D rigid inclusion populations in viscous flows — What is clast SPO telling us?

We model the development of shape preferred orientation (SPO) of a large population of two- and three-dimensional (2D and 3D) rigid clasts suspended in a linear viscous matrix deformed by superposed steady and continuously non-steady plane strain flows to investigate the sensitivity of clasts to changing boundary conditions during a single or superposed deformation events. Resultant clast SPOs are compared to one developed by an identical initial population that experienced a steady flow history of constant kinematic vorticity and reached an identical finite strain state, allowing examination of SPO sensitivity to deformation path. Rotation paths of individual triaxial inclusions are complex, even for steady plane strain flow histories. It has been suggested that the 3D nature of the system renders predictions based on 2D models inadequate for applied clast-based kinematic vorticity gauges. We demonstrate that for a large population of clasts, simplification to a 2D model does provide a good approximation to the SPO predicted by full 3D analysis for steady and non-steady plane strain deformation paths. Predictions of shape fabric development from 2D models are not only qualitatively similar to the more complex 3D analysis, but they display the same limitations of techniques based on clast SPO commonly used as a quantitative kinematic vorticity gauge. Our model results from steady, superposed, and non-steady flow histories with a significant pure shearing component at a wide range of finite strain resemble predictions for an identical initial population that experienced a single steady simple shearing deformation. We conclude that individual 2D and 3D clasts respond instantaneously to changes in boundary conditions, however, in aggregate, the SPO of a population of rigid inclusions does not reflect the late-stage kinematics of deformation, nor is it an indicator of the unique ‘mean’ kinematic vorticity experienced by a deformed rock volume.     

Numerical Investigation of the Dynamic Compressive Behaviour of Rock Materials at High Strain Rate

The dynamic compressive strength of rock materials increases with the strain rate. They are usually obtained by conducting laboratory tests such as split Hopkinson pressure bar (SHPB) test or drop-weight test. It is commonly agreed now that the dynamic increase factor (DIF) obtained from impact test is affected by lateral inertia confinement, friction confinement between the specimen and impact materials and the specimen sizes and geometries. Therefore, those derived directly from testing data do not necessarily reflect the true dynamic material properties. The influences of these parameters, however, are not straightforward to be quantified in laboratory tests. Therefore, the empirical DIF relations of rock materials obtained directly from impact tests consist of contributions from lateral inertia and end friction confinements, which need be eliminated to reflect the true dynamic material properties. Moreover, different rocks, such as granite, limestone and tuff have different material parameters, e.g., equation of state (EOS) and strength, which may also affect the DIF of materials but are not explicitly studied in the open literature. In the present study, numerical models of granite, limestone and tuff materials with different EOS and strength under impact loads are developed to simulate SHPB tests and to study the influences of EOS and strength, lateral inertia confinement and end friction confinement effects on their respective DIFs in the strain rate range between 1 and 1,000 s^?1. The commercial software AUTODYN with user-provided subroutines is used to perform the numerical simulations of SHPB tests. Numerical simulation results indicate that the lateral inertia confinement, friction confinement and specimen aspect (L/D) ratio significantly influence DIF obtained from impact tests and the inertia confinement effect is different for different rocks. Based on the numerical results, quantifications on the relative contributions from the lateral inertia confinement and the material strain rate effect on DIF of granite, limestone and tuff material compressive strength are made. The effects of friction coefficient, L/D ratio and rock type on DIF are discussed. Empirical relations of DIF with strain rate for the three rock materials representing the true material strain rate effect are also proposed.     

Strain and competence contrast estimation from fold shape

A new method to estimate strain and competence contrast from natural fold shapes is developed and verified by analogue and numerical experiments. Strain is estimated relative to the nucleation amplitude, A_N, which is the fold amplitude when the amplification velocities caused by kinematic layer thickening and dynamic folding are identical. A_N is defined as the initial amplitude corresponding to zero strain because folding at amplitudes smaller than A_N is dominantly by kinematic layer thickening. For amplitudes larger than A_N, estimates of strain and competence contrast are contoured in thickness-to-wavelength (H/λ) and amplitude-to-wavelength (A/λ) space. These quantities can be measured for any observed fold shape. Contour maps are constructed using existing linear theories of folding, a new nonlinear theory of folding and numerical simulations, all for single-layer folding. The method represents a significant improvement to the arc length method. The strain estimation method is applied to folds in viscous (Newtonian), power-law (non-Newtonian) and viscoelastic layers. Also, strain partitioning in fold trains is investigated. Strain partitioning refers to the difference in strain accommodated by individual folds in the fold train and by the whole fold train. Fold trains within layers exhibiting viscous and viscoelastic rheology show different characteristic strain partitioning patterns. Strain partitioning patterns of natural fold trains can be used to assess the rheological behaviour during fold initiation.     

Origin and tectonic interpretation of multiple fault patterns

It is shown that in two-dimensional and three-dimensional deformation accommodated by fracture, the symmetry of the fault patterns is an intrinsic attribute because it reflects the symmetry of either stress or strain tensors. The deformation accommodated by sliding along pre-existing planes, when there is kinematic interaction between that planes, forms multiple fault pattern and multiple slickenline sets during a single deformation event. These fault patterns have no restrictions with respect to symmetry, number of fault sets or fault orientation.

The kinematic analysis developed here shows that an interacting system is formed by two cross cutting faults and three slickenlines. One slickenline must be parallel to the intersection line between the planes. Also, it is demonstrated that the slickenlines generally do not correspond to the shear stress solution on the planes. Thus, the interaction between planes does not satisfy the assumption of parallelism between shear stress and slip vector. We conclude that the inversion methods to calculate paleostress tensors can lead to erroneous interpretations in structurally complex zones with many pre-existing planes of weakness.

We propose four possibilities to form multiple fault patterns: (1) two or more events of faulting obeying Coulomb's law with a change of orientation of the principal stresses in each event; (2) reactivation of non-interacting planes according to the Bott (1959) model; (3) one three-dimensional strain event that obeys the “Slip Model”; this mechanism will form an orthorhombic four-fault pattern and two slickenline sets in a single strain event; and (4) one or more events obeying the interacting block model proposed here, with or without rotation of the principal stresses. We propose the last origin as the most common in continental regions.     

Model-Based Identification of Mechanical Characteristics of Sinosaurus (Theropoda) Crests

The paired cranial crests of Sinosaurus(Theropoda) have been hypothesized as too weak to resist mechanical loads during combat. Finite element analysis(FEA) is used to test this hypothesis, first with geometry obtained through direct laser scanning of a well-preserved fossil of the crest, and then with two conceptual FE models of both crests analyzing the structure-deformation effects of fenestration. In the original fossil model, under direct loading on the dorsal faces of the crest, we found that the areas surrounding cavities on the crest experience shear stress that implies a high chance of material failure – the fracture of bone. In the conceptual model, a series of computational studies were conducted with varying loading directions. One simulation found that the shear stress and strain in the material around the cavity presented more deformation compared with the conceptual model without the cavities, and under this morphologically realistic scenario the loading conditions would result in local bone fractures. These model-based computational results indicate that the crest could not resist high loads, because it could not effectively decentralize the loading stress. Future investigations need to focus on more comprehensive computational experiments with more conditions, e.g. dynamical loading conditions, and direct palaeontological evidence.     

动态扰动对应力松弛岩石变形行为影响的试验研究

利用自主研发的岩石松弛-扰动试验装置,测试了岩石加载、松弛、动态扰动和扰动后4个阶段的轴向应力、轴向应变和声发射响应,观察到了岩石试样在动态扰动后应变增加、应力降低的现象,砂岩试样的这种特征比花岗岩明显。初步分析认为,产生该现象的原因一方面由于松弛-扰动过程导致岩石内部出现不可逆的损伤,另一方面则是扰动去除后试样的残余变形。在初始压密和弹性阶段,砂岩试样的声发射撞击数少;在接近应变峰值阶段,撞击数骤增;在应力松弛阶段撞击数骤减;在动态扰动阶段,撞击数骤增。声发射是由于岩石损伤引起的,声发射数据反映了岩石的损伤是引起松弛试样在动态扰动后应变增加、应力降低的一个原因。另外,基于砂岩和花岗岩的准静态循环加、卸载试验,对砂岩、花岗岩在不同应变等级下的残余应变进行了定量化;砂岩的残余应变远高于花岗岩,这与砂岩试样在历经松弛-动态扰动后应变增加、应力降低较为明显的趋势相对应。同时,无论是松弛-动态扰动试验还是准静态循环加、卸载试验,岩石的残余变形都会随着卸荷初始应变的提高而增加。岩石的损伤与残余变形是密切相关的,两者的综合作用引起了动态扰动后岩石试样的应变增加、应力降低现象。