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Numerical analysis of localization phenomena with application in deep boreholes.

机译：局部化现象的数值分析及其在深孔中的应用。

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摘要

As boreholes are drilled deeper into the Earth's crust, increasing problems are encountered with failure of the borehole wall (breakout) due to the existing high stresses at great depth. In this thesis we have investigated this failure process numerically in a large scale finite element computation, carried out on the supercomputer Cray-2.;In the first part of this thesis rock is described by the equations of deformation theory of plasticity for a rigid-plastic, cohesive-frictional, incompressible material. The dependency of the borehole stability on the radius of the borehole (scale effect) was examined by extending the constitutive equations to continuum model with microstructure. These constitutive equations have been successfully applied for the case of hydrostatic far-field stress where the derived eigenvalue problem was solved semi-analytically, based on conventional solution methods and traditional perturbation methods. The detected possible bifurcation of the solution and the existence of the scale effect pursued the research further to post bifurcation analysis for more realistic constitutive modeling and loading conditions.;In the second part, rock is modelled by the elastoplastic constitutive equations of a flow theory of plasticity for cohesive-frictional, hardening-softening, dilatant material. These constitutive equations were fitted on true stress-strain data from triaxial compression tests on rock specimens. For the numerical solution of equations, we have developed a non-linear finite element code for a polar (Cosserat) continuum. The ill-posed boundary value problem of borehole stability in strain softening rock, was regularized since the Cosserat-continuum introduces a length scale into the problem and it numerically assures convergency of the elastoplastic code in the softening regime. Continuation methods with a systematic computer-aided analysis are used to investigate how solutions, their existence and their uniqueness change as geostatic stresses change. Results are presented for the case of hydrostatic as well non-hydrostatic far-stress fields. The present analysis enables us to model what is usually called a 'progressive' failure mechanism. Also due to the existence of an internal length in the constitutive model, 'small' holes fail at higher external stresses than 'large' holes. This 'scale' effect and the computed failure modes are in a very good agreement with the experiment.
机译：随着钻孔被钻入地壳的更深处，由于存在于大深度的高应力，钻孔壁破裂（突围）的问题越来越多。在本文中，我们在超级计算机Cray-2上进行了大规模有限元计算，并对这一破坏过程进行了数值研究。;在论文的第一部分中，岩石是通过塑性变形理论方程描述的，塑料，摩擦摩擦，不可压缩的材料。通过将本构方程扩展到具有微观结构的连续体模型，研究了井眼稳定性对井眼半径（尺度效应）的依赖性。这些本构方程已成功地应用于静水远场应力的情况下，其中基于传统的求解方法和传统的摄动方法，半解析导出的特征值问题。检测到的溶液可能出现的分叉和规模效应的存在使研究进一步展开，以便在分叉后进行分析，以获得更实际的本构模型和载荷条件。第二部分，利用流动理论的弹塑性本构方程对岩石进行建模。内聚摩擦，硬化软化，膨胀材料的可塑性。这些本构方程适用于岩石样本三轴压缩试验的真实应力-应变数据。对于方程的数值解，我们开发了一个极性（Cosserat）连续体的非线性有限元代码。由于Cosserat-continuum将长度标度引入到问题软化岩中，因此规范化了应变软化岩中钻孔稳定性的不适定边界值问题，并在数值上确保了软化过程中弹塑性规范的收敛性。连续方法和系统的计算机辅助分析用于研究解决方案，其存在性和唯一性如何随地应力的变化而变化。给出了静水和非静水远应力场的结果。本分析使我们能够对通常称为“渐进式”故障机制的模型进行建模。同样由于本构模型内部长度的存在，“小”孔比“大”孔在更高的外力作用下失效。这种“比例”效应和计算出的失效模式与实验非常吻合。

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  • 作者

    Papanastasiou, Panos Charilaou.;

  • 作者单位

    University of Minnesota.;

  • 授予单位 University of Minnesota.;
  • 学科 Civil engineering.;Petroleum engineering.;Mining engineering.
  • 学位 Ph.D.
  • 年度 1990
  • 页码 265 p.
  • 总页数 265
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

  • 入库时间 2022-08-17 11:50:30

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