具有分数Kelvin模型的粘弹性岩体中水平圆形硐室的变形特性

在忽略体积变形的情况下进行水平图形硐室变形特性研究,建议采用分数代数Kelvin本构关系模拟岩体的粘弹性,提出了一种分析粘弹性岩体中水平圆形硐室变形特性的新思路,讨论了硐室位移及应变随时间变化的规律并与经典的Kelvin模型进行了比较。从分析的结果表明,分数代数能很好地模拟出粘弹性体松驰特性,通过改变分数代数的阶数又可以模拟各种粘弹性岩体、比经典粘弹性模型具有更大的适用范围。     

不同建模假定下岩石损伤黏弹模型的参数转换关系探讨

将外界因素对岩石变形的影响考虑为瞬间弹性损伤和长期蠕变损伤,并根据加载瞬间弹性模量及蠕变模量的劣化分别对瞬间弹性损伤变量和蠕变损伤变量进行定义,由此建立了考虑损伤的kBurgers模型。在此基础上,通过假定泊松比和体积模量为常量分别得到了对应的模型三维表达式,并得到了不同建模思路下模型参数间的换算关系。最后结合实际算例,对常体积模量假定下模型参数随含水率变化的损伤演化规律进行了分析,获得了常体积模量假定下模型的瞬间弹性损伤和长期蠕变损伤演化方程,检验了模型参数换算关系的有效性。     

连续排水边界下分数阶黏弹性饱和土体一维固结分析

采用分数阶Kelvin模型来描述饱和土体的流变特性,在连续排水边界条件下,利用Laplace变换推导出变换域内的饱和土体一维固结解析解,再通过Crump法对有效应力和固结沉降进行数值反演,得到了分数阶导数黏弹性饱和土体的一维固结半解析解。将连续排水边界退化到Terzaghi排水边界,退化后的结果与已有文献一致,验证了所得半解析解的可靠性。最后,基于所得解,分析了相关参数对土体固结的影响。结果表明,界面参数反映排水边界的透水性,从而影响土体中超孔隙水压力的消散速率;黏滞系数在固结后期对沉降发展影响较大,其值越大,沉降发展越慢;当阶次a不为零时,分数阶次越小,土体表现出的黏滞性越强,整体固结沉降发展越缓慢,次固结沉降发展也越缓慢。     

A nonlinear viscoelastic bend stiffener steady-state formulation

Bend stiffeners are essential components of a flexible riser system, employed to ensure a smooth transition at the upper connection and to protect the riser against over bending and from accumulation of fatigue damage. The highly nonlinear rate dependent behavior of these structures directly affects the integrity assessment of the riser in one of its most critical regions, the top connection. A steady-state formulation (disregarding inertial forces) and numerical solution procedure is developed in this work employing the perturbation method for a nonlinear viscoelastic bend stiffener large deflection beam model subjected to harmonic loading conditions. For stochastic loading conditions, the response is calculated employing the superposition principle by summing up the steady-state result of a number of individual frequency components. A time domain formulation is also derived employing the state-variable approach for the numerical solution of the resulting hereditary integral in the governing equations. A case study is presented for the top connection system of a 4″ ID flexible riser using relaxation and tensile experimental data obtained from a typical class of bend stiffener polyurethane. Harmonic and stochastic input loading conditions are employed for time and frequency domain model comparison/validation and to assess loading history and frequency influence in the curvature response.     

Semi-analytical solution for one-dimensional consolidation of fractional derivative viscoelastic saturated soils

This paper presents a semi-analytical solution to one-dimensional consolidation equation of fractional derivative Kelvin-Voigt viscoelastic saturated soils subjected to different time-dependent loadings. The theory of fractional calculus is first introduced to Kelvin-Voigt constitutive model to describe consolidation behavior of viscoelastic saturated soils. By applying Laplace transform upon the one-dimensional consolidation equation of saturated soils, the analytical solutions of effective stress and settlement in the Laplace transform domain are obtained. The present solutions are more general and have good agreements with available solutions from the literature, and are degenerated into ones for one-dimensional consolidation of elastic and viscoelastic saturated soils.     

Gravitational viscoelastic relaxation of eccentrically nested spheres

We present a semi-analytical solution to the 2-D forward modelling of viscoelastic relaxation in a heterogeneous model consisting of eccentrically nested spheres. Several numerical methods for 2-D and 3-D viscoelastic relaxation modelling have been applied recently, including finite-element and spectral-finite-difference schemes. The present semi-analytical approach provides a model response against which more general numerical algorithms can be validated. The eccentrically nested sphere solution has been tested by comparing it with the analytical solutions for viscoelastic relaxation in a homogeneous sphere and in two concentrically nested spheres, and good agreement was obtained.