Finite-element folds of similar geometry

Model folds of similar geometry have been produced by using the finite-element method and the constitutive relations of a layer of wet quartzite embedded in a marble matrix with an initially sinusoidal configuration and a 10° limb dip. The power law for steady-state flow of Yule Marble (Heard and Raleigh, 1972) is used for the matrix and our new law for Canyon Creek quartzite deformed in the presence of water is used for the layer. The equiv- alent viscosity of the wet quartzite is highly temperature-sensitive, giving rise to a strong temperature dependence of the quartzite: marble viscosity ratio which, at a strain rate of 10⁻¹⁴/sec, drops from 543 at 200° to 0.13 at 800°C. At 375°C (η_q/η_m = 10), concentric folds develop at all strains to 80% natural shortening and stress, finite strain and viscosity distributions are somewhat similar to those found previously. Raising the temperature to 550° C (η_q/η_m = 1), at any stage of prior amplification, causes the folds to flatten with increasing strain, accompanied by attenuation of limbs and thickening of hinges, leading to folds with similar geometries and isoclinal folds at extreme strains. The effects are more pronounced at higher temperatures and at 700° C (η_q/η_m = 0.3) limb attenuation is so severe as to give rise to unrealistic geometries. At temperatures below about 600° C (η_q/η_m = 2), similar folds do not form. It thus appears as if a viscosity contrast near unity is required to produce similar folds in rocks, under the conditions simulated and different temperature dependencies of viscosities of materials in layered sequences is one important means of reducing viscosity contrasts.     

经历剪切变形历史的岩石节理表面粗糙特性分析

基于两类岩石节理剪切试验，采用非接触式激光测距仪，实测了剪切前后节理表面粗糙数据，统计分析了岩石节理表面粗糙特性的三维粗糙参数的物理含义，并将这些参数与相应的二维参数进行了充分比较。结果表明，三维参数与二维参数间存在的近似线性关系，而多个三维参数相对比单一的二维参数更全面有效地描述了节理表面粗糙特性。     

Numerical modelling of coupled flow and deformation in fractured rock specimens

A dual-porosity poroelastic model is extended to represent behaviour in cylindrical co-ordinates for the evaluation of flow-deformation effects in cylindrical laboratory samples incorporating a central wellbore or non-repeating axisymmetric injection on the periphery. Nine-node quadratic elements are used to represent mechanical deformation, while eight-node linear elements are used to interpolate the pressure fields, which offers significant advantages over the behaviour of other non-conforming elements. The model presented is validated against simplified analytical results, and extended to describe the behaviour of homogeneous and heterogeneous laboratory specimens subjected to controlled triaxial state of stress and injection tests. Apparent from the results is the significant influence of stress-deformation effects over system behaviour. Copyright © 1999 John Wiley & Sons, Ltd.     

青藏高原壳幔形变数值模拟研究

现有数值模拟研究已在很大程度上较合理地给出青藏高原演化运动学和动力学过程的图像。利用连续介质快速拉格朗日分析方法,笔者进行了青藏高原壳幔形变数值模拟研究。据此得到的青藏高原三维壳幔形变特征反映纬向上主碰撞带远、近程效应的差异和经向上地壳物质“逃逸”的存在,印证了青藏高原形成过程中南北双向挤压、而且南部作用大于北部作用的可能应力场特征。青藏高原壳幔形变不仅强烈依赖于随深度变化的岩石力学性质及其距离挤压作用前锋带的远近,而且存在强烈的横向不均一性。同时,强应变(剪切)带的存在对高原岩石圈形变具有重要影响,高原形变过程中地壳尺度的耦合流及壳-幔解耦共存。但是,常规数值模拟研究尚存在很大局限性:(1)物理-力学模型单一;(2)几何模型简单;(3)边界形态与条件理想化;(4)模型内部块体划分粗糙;(5)不连续体介质处理困难。借助具有可处理大形变能力的4-D数值模拟方法,将观测资料与数值模拟相互补充是深入研究青藏高原壳幔形变的关键。     

Numerical modelling of gassy sand behaviour under monotonic loading

Acta Geotechnica - The mechanical behaviour of gassy sand is rather complex owing to the inherent complex nature of sand and the occluded/dissolved gas. For better understanding of the behaviour of...     

Calcite fabrics around folds as indicators of deformation history

In the Morcles nappe (lowermost Helvetic nappe in western Switzerland) two phases of folding have been established. In this article the relationship between the calcite fabrics present in folded limestones and the folding history is analysed. Calcite fabrics around the first- and second-phase folds are related to the second phase of deformation. The following fabric patterns have been found. (1) The fabric geometry around a second-phase fold from the most internal part of the inverted limb of the nappe (locality Saillon) can be related to an overall simple shear deformation sequence, the sense of shear being related to the last advance of the Morcles nappe over the underlying autochthonous sedimentary cover of the Aiguilles Rouges massif. (2) In more external parts of the inverted limb (locality Petit Pré) the fabrics around a second-phase fold are interpreted as indicating a change in the deformation history from simple shear to a strain regime which can account for shortening along the first-phase cleavage by the formation of buckle folds. This change in the local strain regime could be related to a ‘locking’ of the frontal folds of the nappe during the last overthrust shear movements. (3) In the normal limb of the nappe the fabrics around a late second-phase kink fold (locality Neimia) are earlier than the folding event and appear to be rotated passively by the fold. (4) The fabrics around a first-phase fold (locality La Routia) are later than the folding event and overprint the fold.     

How useful are ‘millipede’ and other similar porphyroblast microstructures for determining synmetamorphic deformation histories?

ABSTRACT Oppositely concave microfolds (OCMs) in and adjacent to porphyroblasts can be classified into five nongenetic types. Type 1 OCMs are found in sections through porphyroblasts with spiral-shaped inclusion trails cut parallel to the spiral axes, and commonly show closed foliation loops. Type 2 OCMs, commonly referred to as ‘millipede’ microstructure, are highly symmetrical, the foliation folded into OCMs being approximately perpendicular to the overprinting foliation. Type 3 OCMs are similar to Type 2, but are asymmetrical, the foliation folded into OCMs being variably oblique to the overprinting foliation. Type 4 OCMs are highly asymmetrical, only one foliation is present, and this foliation is parallel to the local shear plane. Type 5 OCMs result from porphyroblast growth over a microfold interference pattern. Types 1 and 2 are commonly interpreted as indicating highly noncoaxial and highly coaxial bulk deformation paths, respectively, during porphyroblast growth. However, theoretically they can form by any deformation path intermediate between bulk coaxial shortening and bulk simple shearing. Given particular initial foliation orientation and timing of porphyroblast growth, Type 3 OCMs can also form during these intermediate deformation paths, and are commonly found in the same rocks as Type 2 OCMs. Type 4 OCMs may indicate highly noncoaxial deformation during porphyroblast growth, but may be difficult to distinguish from Type 3 OCMs. Thus, Types 1–3 (and possibly 4) reflect the finite strain state, giving no information about the rotational component of the deformation(s) responsible for their formation. Furthermore, there is a lack of unequivocal independent evidence for the degree of noncoaxiality of deformation (s) during the growth of porphyroblasts containing OCMs. Type 2 OCMs that occur independently of porphyroblasts or other rigid objects might indicate highly coaxial bulk shortening, but there is a lack of supporting physical or computer modelling. It is possible that microstructures in the matrix around OCMs formed during highly noncoaxial and highly coaxial deformation histories might have specific characteristics that allow them to be distinguished from one another. However, determining degrees of noncoaxiality from rock fabrics is a major, longstanding problem in structural geology.     

Successive development of plane noncylindrical folds in progressive deformation

In the history of superposed deformations of the iron formations at the western border of the Kolar Gold Field in S India, an important event was the successive growth of broadly coaxial plane noncylindrical folds in course of a progressive deformation concomitant with development of ductile mesoscopic shear zones. The noncylindrical folds were initiated as active folds by the creation of a buckling instability at successive stages on newly developed foliation surfaces. The nucleation of noncylindrical folds and the subsequent axial-plane folding of the tightened mature folds are explained by the mechanical inhomogeneity of the rocks and the heterogeneous character of strain. The correlation between increasing tightness and increasing noncylindricity of the folds indicates that the initial curvatures of hinge lines were accentuated by an extension parallel to the subhorizontal stretching lineation. From the patterns of deformed lineations over folds of varying tightnesses, it is concluded that the passive accentuation of hinge-line curvatures was mostly achieved when the folds had already become isoclinal or very tight.     

Numerical modelling of a hybrid skirted foundation under combined loading

Offshore foundations are subject to combinations of vertical, horizontal and moment (VHM) loading. Different foundation solutions are appropriate, depending amongst others, on the expected load combinations. This paper investigates in detail the soil failure mechanisms and resulting foundation capacity under undrained VHM loading of a hybrid foundation concept. Comprising of a skirted mat combined with an internal caisson compartment, this foundation design is found to provide significantly increased horizontal capacity that is often critical in offshore applications, with key influences for increased moment capacity identified as well. The numerical study investigated both variations in the geometry of the internal caisson compartment and the soil shear strength profile. The paper concludes by proposing expressions that allow slightly conservative prediction of the combined capacity of a hybrid foundation.     

Construction and systematic assessment of relative deformation histories

The systematics of deformation histories have been investigated using basic combinatorial mathematics. Using this approach, the number of deformation histories and the number of relationships associated with a given number of structures can be calculated. The range of possible deformation histories can also be determined. Using this information, the ambiguous nature of all deformation histories is examined together with the impact of unobserved relationships. The number of possible deformation histories that are compatible with a collection of age relationships is used as a crude measure of confidence in those histories. A procedure is described for the construction of deformation histories that is systematic, repeatable and rapid and within which ambiguities can be easily recognised.     

单调荷载下砂土变形过程数值模拟及细观机制研究

采用离散单元法的颗粒流理论,模拟了松砂和密砂在单调荷载作用下的变形过程,研究了砂土渐进破坏过程中的宏观力学行为和细观组构参量的演化规律。采用PFC的FISH语言开发了细观组构统计程序,通过记录加载不同时刻试样的细观参量,如配位数、接触法向分布、粒间法向接触力、切向接触力等的演化,分析了砂土变形过程中细观组构变化与宏观力学响应之间的内在联系。应用表征上述量的组构参数研究了砂土的诱发各向异性,探讨了松砂剪缩、密砂剪胀的细观机制。研究成果对于揭示砂土变形的细观机制以及建立砂土的细观力学模型具有重要意义。     

Numerical modelling of soil nails in loose fill slope under surcharge loading

A plane–strain numerical model has been developed to mimic a nailed loose fill slope under surcharge loading. The model has been used to back-analyse a field test that was conducted to examine the behaviour of soil nails in loose fill slopes under surcharge loading. Incremental elasto-plastic analyses coupled with pore water diffusion have been performed to study the internal deformation, water content redistribution in the soil, and the performance of the soil nails during and after the application of surcharge loading. The model parameters describing the mechanical and hydraulic properties of the nailed slope were obtained from field or laboratory tests. Different modelling techniques and boundary conditions for mimicking soil–nail interaction in loose fill material have been examined. Comparisons between numerical predictions and field measurements demonstrate that a new interfacial model, denoted as the embedded bond–slip interface model, is more suitable for mimicking the interfacial behaviour. Despite the simplicity of the numerical model, the predicted responses are in close agreement with the field test results, in particular the mobilisation and distribution of nail forces in response to surcharge loading. Both the numerical and the field test results suggest that soil nails are capable of increasing the overall stability of a loose fill slope for the loading conditions considered in this study. The increase in confining stress along the soil nails near the surcharge area is central to the overall stabilising mechanism. On the contrary, the nail forces mobilised near the nail heads are much smaller, indicating that the beneficial effect of having a structural grillage system at the slope face is limited for the range of surcharge pressures considered in this study.     

Numerical modelling of clast rotation during soft-sediment deformation: a case study in Miocene delta deposits

A numerical model for a rotated clast in a sedimentary matrix is presented, quantifying the deformation in associated soft-sediment deformation structures. All the structures occur in a southwards prograding deltaic sequence within the Miocene Ingering Formation, deposited at the northern margin of the Fohnsdorf Basin (Eastern Alps, Austria). Debris flow and pelitic strata contain boudins, pinch-and-swell structures, ptygmatic folds, rotated top-to-S reverse faults and rigid clasts, developed under different stress conditions within the same layers. The deformation around a 24×10 cm trapezoid-shaped rigid clast, resembling the δ-clast geometry in metamorphic rocks, has been modelled using a 2D finite element modelling software. Under the chosen initial and boundary conditions the rotational behaviour of the clast mainly depends on the proportions of pure and simple shear; best fitting results were attained with a dominantly pure shear deformation (~65–85%), with stretching parallel and shortening normal to the bedding. In this specific model set-up, the initial sedimentary thickness is reduced by 30%, explained by stretching due to sediment creeping and compaction. The high amount of pure shear deformation proposed is compatible with the observed layer-parallel boudinage and pinch-and-swell structures. Rotated faults and ptygmatic folds were caused by the minor component of bedding-parallel simple shear.     

Numerical modelling of deformation and fluid flow in the Shuikoushan district, Hunan Province, South China

The Shuikoushan district, in Hunan Province, South China, contains major Pb–Zn–Au–Ag polymetallic mineralisation. Two groups of numerical models have been constructed to study the interactions between deformation and fluid flow in the district during the Yanshanian compression event (180 to 90 Ma). The first group includes district-scale conceptual models of coupled deformation and fluid flow during folding. The models show that fluid flow patterns are controlled by deformation within the fold system inferred for the district. During regional shortening and folding, fluids are generally focused towards the fold hinge/core areas along higher permeability layers (in particular Permian limestone units), in preference to flowing across the low permeability seal units (Permian and Jurassic terrestrial sequences). The efficiency of this fluid focusing can only be significantly increased if these folded seal units are allowed to undergo permeability increase as a result of tensile failure. The modelling results show that permeability enhancement localises mostly at fold hinges, dominantly within the silicified zone on the top of the Permian limestone unit. This process results in increased flow velocities and facilitates fluid focusing towards fold hinge/core locations at this silicified rock horizon. The second group includes deposit scale models for the Kangjiawan deposit, which is one of the two major deposits in the Shuikoushan district. The models show patterns of tensile failure, permeability creation, fluid focusing and mixing, and fracture development along a selected exploration cross section through the deposit. These results are consistent with the observed brecciation and mineralisation features. Regions of maximum brecciation in the district are associated with: (1) a combination of fold hinge and fault intersection locations (structural); and (2) the silicified zone and Permian limestone unit (lithological). Such brecciation zones are associated with extensive fluid focusing and mixing, and therefore represent the most favourable locations for mineralisation in the district. On the basis of this work, ideas for future research work and mineral exploration in the district are proposed.     

Numerical modelling of desiccation cracking

The ability to model and predict the formation of desiccation cracks is potentially beneficial in many applications such as clay liner design, earth dam construction, and crop science, etc. However, most studies have focused on statistical analysis of crack patterns and qualitative study of contributing factors to crack development rather than prediction. Because it is exceedingly difficult to capture the nonlinear processes during desiccation in analytical modelling, most such models handle crack formation without considering variation of material properties with time, and are unattractive to use in realistic modelling. The data obtained from laboratory experiments on clay soil desiccating in moulds were used as a basis to develop a more refined model of desiccation cracking. In this study, the properties, such as matric suction, stiffness and tensile strength of soil, and base adhesion, could be expressed approximately as functions of moisture content. The initial conditions and the development of suction due to desiccation and the varying material properties were inputted to UDEC, a distinct element code, using its internal programming language FISH. The model was able to capture some essential physical aspects of crack evolution in soil contained in moulds with varying lengths, heights, and materials of construction. Extension of this methodology is potentially beneficial not only for modelling desiccation cracking in clay, but also in other systems with evolving material properties such as concrete structures and road pavements. Copyright © 2010 John Wiley & Sons, Ltd.     

降雨入渗条件下非饱和路堤变形与边坡的稳定数值模拟

对于常常处于非饱和状态的路堤在降雨入渗条件下变形问题的数值模拟研究,由于涉及到非饱和土力学,一直是个热点和难点。现有的强度折减有限元法一般仅对强度指标进行折减,但折减后得到的路堤变形场与实际变形场存在一定差异。论文分析认为,在降雨入渗影响下非饱和路堤不仅强度参数会降低,而且变形参数也会随着应力水平和强度参数的变化而变化。采用基于变模量的弹塑性强度折减法,对不同降雨入渗深度下路堤的变形规律进行数值模拟,并与室内模型试验结果进行比较;同时采用强度折减法和极限平衡法中的Bishop法,分析了不同降雨入渗深度对非饱和路堤稳定性和滑弧变化特征的影响规律。     

The determination of progressive deformation histories from antitaxial syntectonic crystal fibres

Antitaxial, syntectonic crystal fibres are modelled here as ‘mechanically-passive’ features, the fibres representing displacement paths, forming within a homogeneously deforming material. Evidence that many fibres develop in this way is widespread: asymptotic curvature, thinning of fibres, and strained old fibres. A measuring technique is proposed by which the complete deformation history (excluding translation) may be determined. The method involves the iterative unstraining of two complete fibres whose development began and ended simultaneously. A source of error is introduced by assuming that each of the two fibres developed at constant proportional rates, although synthetic examples suggest this error to be minimal. It is suggested that the kinematics of non-passive fibres are unobtainable since the rheologies and boundary conditions of the material involved are relatively unknown, and cannot be determined from geometry alone. Analysis of natural fibres found within the Ordovician slates in New Jersey, U.S.A. indicates that volume losses of up to 50% may occur during the formation of some slates. General constraints concerning the geometrical analysis of syntectonic crystal fibres are briefly discussed, and it is concluded that deformation histories must be interpreted with some modicum of caution.     

Progress in the study and modelling of similar fold interferences

Similar fold interferences are examined in two different ways.

• 1.(1) We show the importance of taking into account the original position of the stratification with respect to the orientations of two interfering fold phases. Basin and dome cases correspond to particular orientations of the interfering phases with respect to each other. In all other cases, coaxiality may be achieved for particular positions of the original stratification.
• 2.(2) We have achieved a computer-aided modelling which allows the visualization by means of sections and block-diagrams of any two or three similar fold interferences. The program allows us to define the stratification, orientations of the various phases and their profiles (sinusoidal or drawn by hand), and orientations and dimensions of the selected section or block diagram. Faults may also be represented.This modelling method is a powerful research tool that we hope to apply in future to detailed studies of fold interferences, to achieve quantitative field models of multiply folded and faulted terranes.

     

Numerical modelling on water retention and permeability of compacted GMZ bentonite under free-swelling conditions

In this study, a solid–liquid–gas coupled equation was established to simulate water retention characteristics of highly compacted GMZ bentonite. Then, modelling results were compared with laboratory test results. Results indicate that GMZ bentonite has a strong moisture expansion (or a limit drying shrinkage) characteristic. The control equation can simulate the water absorption and deformation characteristics very well at high relative humidity (or low suction). Environmental scanning electron microscope (ESEM) observation reveals the course grain soil texture of the surface under low relative humidity (RH), while the surface of GMZ bentonite becomes smooth (more fine-grained soil texture) as RH increases. Differences were found between the porosities calculated by macroexperiment results and microscopic observations with ESEM method. This is because only the interaggregate pores can be observed by ESEM photographs. Additionally, we find that the simulated effective porosities are close to the results calculated by microscopic tests, while the effective porosity is considered as the main flow channel of flow. Further, the intrinsic permeability, the effective water and gas permeability are calculated based on the proposed model. The modelling results coincide well with the laboratory experimental results and support the reliability of the proposed model.