The algebraic evaluation of two-dimensional finite strain rosettes

Arrays or rosettes of lines along which the extension or relative extension can be determined constitute finite strain gauge rosettes. Expressions for the principal strains and their orientation in terms of three nonparallel gauge extensions can be established in a suitable form for algebraic evaluation, thus replacing graphical methods based on Mohr construction. Three types of strain rosette problems, including one which utilizes angles, are particularly relevant to the study of deformed rocks. These, together with their relation to grid methods, are discussed and simple examples of their use given. Finally, an approach to the problem of finding best-fitting solutions to overdetermined regular strain rosettes is discussed.     

Finite volume approach for finite strain consolidation

The paper presents the finite volume formulation and numerical solution of finite strain one‐dimensional consolidation equation. The equation used in this study utilises a nonlinear continuum representation of consolidation with varying compressibility and hydraulic conductivity and thus inherits the material and geometric nonlinearity. Time‐marching explicit scheme has been used to achieve transient solutions. The nonlinear terms have been evaluated with the known previous time step value of the independent variable, that is, void ratio. Three‐point quadratic interpolation function of Lagrangian family has been used to evaluate the face values at discrete control volumes. It has been shown that the numerical solution is stable and convergent for the general practical cases of consolidation. Performance of the numerical scheme has been evaluated by comparing the results with an analytical solution and with the piecewise piecewise‐linear finite difference numerical model. The approach seems to work well and offers excellent potential for simulating finite strain consolidation. Further, the parametric study has been performed on soft organic clays, and the influence of various parameters on the time ate consolidation characteristics of the soil is shown. Copyright © 2015 John Wiley & Sons, Ltd.     

多边形有限单元形函数的几何构造方法

根据非均质材料的细观结构,划分多边形的计算网格。采用多边形单元进行有限元分析,实现了基于材料真实结构的数值模拟。给出了多边形有限单元形函数的几何构造方法,构造了一个辅助多边形,采用散度定理推导出多边形单元形函数的表达式。分析总结了多边形Wachspress插值、Laplace插值和平均值插值的构造方法和性质。     

Correction: A parsimonious approach for large-scale tracer test interpretation

Hydrogeology Journal - A Correction to this paper has been published: https://doi.org/10.1007/s10040-021-02380-6     

A finite element approach to solve contact problems in geotechnical engineering

This paper presents a finite element approach to solve geotechnical problems with interfaces. The behaviours of interfaces obey the Mohr–Coulomb law. The FEM formulae are constructed by means of the principle of virtual displacement with contact boundary. To meet displacement compatibility conditions on contact boundary, independent degrees of freedom are taken as unknowns in FEM equations, instead of conventional nodal displacements. Examples on pressure distribution beneath a rigid strip footing, lateral earth pressure on retaining walls, behaviours of axially loaded bored piles, a shield‐driven metro tunnel, and interaction of a sliding slope with the tunnels going through it are solved with this method. The results show good agreement with analytical solutions or with in situ test results. Copyright © 2005 John Wiley & Sons, Ltd.     

A parsimonious approach for large-scale tracer test interpretation

Hydrogeology Journal - Dye tracing is an efficient method for spring watershed delineation, but is also used in surface waters to assess pollution migration over several kilometers. The aim of this...     

An approach to interpretation of step drawdown tests

To understand the behaviour of drawdown with discharge under site-specific conditions, a step drawdown test (SDT) was conducted on a tubewell in alluvium near Delhi, India, and the data were analyzed to find the value of well efficiency. The entrance velocity of groundwater into the well screen was computed to see if it exceeded the safety limit of 0.03 m/s. Reynold's number (Re) was also calculated to study the nature of flow at the well screen. The decrease in efficiency of the well at higher discharge was attributed to an increase in turbulence and curvature of the flow path of water. An alternative, more efficient approach has been put forward, using a spreadsheet programme to fit a polynomial trend line on a plot of drawdown versus discharge and deriving a polynomial trend line equation. This equation predicts the behaviour of drawdown with discharge under site-specific conditions. The calculated efficiency of the tubewell can, at best, be regarded as a reflection of head loss on account of the laminar flow from the aquifer.     

A quantitative study of deformation mechanisms and finite strain in quartzites

The Weverton quartzites in the Maryland Blue Ridge are deformed by one major period of greenschist-grade deformation. The components of finite strain due to different independent mechanisms have been measured for these rocks. The total strain is split up into two major components: $$\varepsilon ^t = \varepsilon ^p + \varepsilon ^d .$$ The finite natural strain caused by dislocation creep (? ^d ) is measured by a new technique using folded and stretched rutile needles which are good strain markers within the quartz crystals. Pressure solution strain (? ^p ) is measured from the ratio of the area of new crystals and fibers to the whole rock area in principal sections. Grain boundary sliding is a dependent process which accompanies both mechanisms. Pressure solution obeys a linear Newtonian flow law, \(\left| {\dot \gamma _0^p } \right| = A_p \left| {\tau _0 } \right|\) , while dislocation creep obeys a power law of the form \(\left| {\dot \gamma _0^d } \right| = A_d \left| {\tau _0 } \right|^n \) where \(\dot \gamma _0^p ,\dot \gamma _0^d \) are octahedral shear strain rates, τ₀ is the octahedral shear stress and A _p , A _p and n are constants. A direct correlation between finite strain measurements and the operating flow laws can be made. Application of these methods and principles to a few field examples indicates that the rocks obey a flow law partly governed by each mechanism. Any set of physical conditions defines a unique flow law and there is a transition in creep behavior from dominantly Newtonian to a power law with increasing strain rate.     

Directional properties of polygons and their application to finite strain estimation

An eigenmethod for characterising the directional properties of convex polygons is described. Given a polygon, regular in the undeformed state, its image following a homogeneous strain transformation is an irregular polygon whose eigensolution (an ellipse) has the axis ratio and orientation of the strain ellipse. The eigenmethod can therefore be used for finite strain estimation using polygonal strain markers, and is compared with alternative methods recently proposed by Roder (1977) and Sanderson (1977).     

A finite element approach to the simulation of hydraulic fractures with lag

We presented a finite‐element‐based algorithm to simulate plane‐strain, straight hydraulic fractures in an impermeable elastic medium. The algorithm accounts for the nonlinear coupling between the fluid pressure and the crack opening and separately tracks the evolution of the crack tip and the fluid front. It therefore allows the existence of a fluid lag. The fluid front is advanced explicitly in time, but an implicit strategy is needed for the crack tip to guarantee the satisfaction of Griffith's criterion at each time step. We enforced the coupling between the fluid and the rock by simultaneously solving for the pressure field in the fluid and the crack opening at each time step. We provided verification of our algorithm by performing sample simulations and comparing them with two known similarity solutions. Copyright © 2012 John Wiley & Sons, Ltd.     

A hybrid finite element-spectral boundary integral approach: Applications to dynamic rupture modeling in unbounded domains

The finite element method (FEM) and the spectral boundary integral method (SBI) have both been widely used in the study of dynamic rupture simulations along a weak interface. In this paper, we present a hybrid method that combines FEM and SBI through the consistent exchange of displacement and traction boundary conditions, thereby benefiting from the flexibility of FEM in handling problems with nonlinearities or small-scale heterogeneities and from the superior performance and accuracy of SBI. We validate the hybrid method using a benchmark problem from the Southern California Earthquake Center's dynamic rupture simulation validation exercises.We further demonstrate the capability and computational efficiency of the hybrid scheme for resolving off-fault heterogeneities by studying a 2D in-plane shear crack in two different settings: one where the crack is embedded in a high-velocity zone and another where it is embedded in a low-velocity zone. Finally, we discuss the potential of the hybrid method for addressing a wide range of problems in geophysics and engineering.     

Stress/strain variability in fractured media: a fracture geometric study

Geotechnical and Geological Engineering - The presence of natural fractures in fractured media plays a vital role in the in-situ stress state, which is predominantly influenced by tectonic stresses...     

A residual force finite element approach to soil–structure interaction analysis

An iterative process based upon a hybrid ‘residual force’ method is presented for solving elasto–plastic soil–structure interaction problems. In this approach the soil and the structure are treated as separate bodies and related only by compatibility of displacements and equilibrium of forces at the soil–structure interface. This scheme enables a significant improvement in numerical stability and rate of convergence over the conventional initial stress method. It is also shown that various interface conditions such as shear failure, slip and breakaway, and frictional and dilatant behaviour can be readily accounted for. Some practical aspects associated with the proposed scheme are emphasized for a number of numerical examples.     

一种解岩土工程变形体-刚体接触问题的有限元法

大多数的岩土工程问题都会涉及到岩土体-结构之间的相互作用,它们之间界面的合理模拟对计算结果有重要的影响。目前常用的Goodman节理单元、Desai薄层单元等虽然简单好用,但也存在着明显的缺陷。相比之下,作为接触问题计算,可更为合理地模拟接触面的力学行为。针对变形体-刚体这种特殊的接触问题,应用变形体的虚功原理建立了相应的虚功方程,在此基础上得出有限元计算公式,并建立了弹塑性接触问题有限元计算的实现方法。通过对刚性条形基础基底压力分布和刚性挡墙土压力分布等算例的计算,验证了该法的正确性和求解工程问题的有效性。