A Fully Analytical Solution of the Wellbore Stability Problem under Undrained Conditions Using a Linearised Cam-Clay Model

Charlez, Philippe; Roateşi, Simona

doi:10.2516/ogst:1999047

Cited by 20 publications

(4 citation statements)

References 11 publications

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“…Over the past few decades, much progress has been made to cavity expansion theory either in developing new solutions or extending its applications in modeling and interpreting practical geotechnical problems. Indeed, with appropriate imagination and simplification, a wide range of geotechnical problems can be tackled with cavity expansion theory, such as pile installation, 2–8 cone penetration tests, 9–14 pressure meter tests, 15–17 underground excavations and tunneling, 18–24 and wellbore stability 25–27 …”

Section: Introductionmentioning

confidence: 99%

A numerical investigation on undrained expansion of a cylindrical cavity under biaxial in situ stresses using anisotropic S‐CLAY1 model

Wang

2022

Num Anal Meth Geomechanics

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Cavity expansion under biaxial in situ stresses is commonly encountered in geotechnical engineering, which, however, has not been well-investigated at present. This paper numerically investigates the undrained expansion responses of a cylindrical cavity in S-CLAY1 soil under biaxial in situ stresses. The advanced anisotropic S-CLAY1 model is integrated by the semi-implicit scheme and implemented as a user-defined subroutine (UMAT) in the finite element model (FEM) to represent the elastoplastic behavior of the soil around the cavity during expansion. To validate and calibrate the FEM, a benchmark solution for cavity expansion under uniform in situ stress is specifically developed and compared with the FEM. Parametric studies are performed based on the FEM to numerically investigate the salient expansion responses under biaxial in situ stresses. The results reveal that the expansion responses, including the expansion pressures, the excess pore water pressures at the cavity wall, the distributions of the stress components around the cavity, are not only remarkably different with those under uniform in situ stress, but also different with the findings from the approximate analytical solutions. What is particularly surprising is that the positions of the maximum and minimum expansion pressures reverse with expansion of the cavity. The outcomes of present study reveal the significant mechanisms of undrained expansion of a cylindrical cavity under biaxial in situ stresses.

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Section: Introductionmentioning

confidence: 99%

A numerical investigation on undrained expansion of a cylindrical cavity under biaxial in situ stresses using anisotropic S‐CLAY1 model

Wang

2022

Num Anal Meth Geomechanics

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“…The formation around the borehole wall experiences deformation due to the relief of stresses, once the rock is removed, and then, replaced by the drilling fluid. The drilling fluid (or drilling mud) is a mixture of a fluid (water or oil based) and solid [22], used in the drilling operation to avoid the borehole closure and to fill the open space once occupied by the rock. The drilling fluid temporarily supports the borehole wall while drilling.…”

Section: Introductionmentioning

confidence: 99%

Stability analysis and uncertainty modeling of vertical and inclined wellbore drilling through heterogeneous field

Batalha¹,

Durán²,

Devloo³

et al. 2020

Oil Gas Sci. Technol. – Rev. IFP Energies nouvelles

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A stochastic two-dimensional geomechanical model developed by the authors and presented herein is used to analyze wellbore stability in heterogeneous formations. It consists of a finite element model and assumes linear elastic and isotropic material behavior under the plane strain state. The model simulates the stress state around vertical and inclined wellbore when a formation is submitted to internal drilling fluid pressure. This new state of stress may lead to rock failure, which is analyzed through a failure criteria. Since the exact variation of formation’s mechanical properties is not known, a spatially correlated field is used to evaluate the variability of a rock mechanical material property. The correlation between each pair of finite elements is determined by a covariance function. A two-dimensional spatially correlated field is used to verify the correlation between the elements of a vertical wellbore. A different approach, however, is necessary to model inclined wellbores. Once the direction and inclination of a wellbore are defined, a three-dimensional spatially correlated field becomes necessary to best simulate the formation field. Simulations using the stochastic model proposed herein and considering constant elastic modulus have been compared. It is observed that when considering the same elastic modulus along the field, the area of the plastic zone is symmetric at the borehole wall; when using the stochastic model, however, the plastic zone area surrounding the well is not symmetric; thus, the most vulnerable plastic zone may lead to premature failure. Stochastic simulations have been carried out with different heterogeneous fields for vertical and inclined wells, and distributions of the total plastic zone areas are obtained for each case. Based on the stochastic field probabilistic analysis, a distribution function is presented, which aims to define a stability framework analysis to best assist a decision making process in determining if a mud pressure is operationally acceptable or not.

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“…In addition to the Drucker-Prager, Mohr-Coulomb, and Hoek-Brown models (the latter two are quite suitable for modelling the granular geomaterials as they capture reasonably well the particle rearrangement and the frictional sliding between material particles), the analytical cavity contraction solutions based on the critical state plasticity models have also been developed, though quite limited. For example, Charlez and Roatesi (1999) derived an approximate analytical solution for the wellbore stability problem under undrained condition using a very simplistic, idealized Cam Clay model where the elliptical yield surface was replaced by two straight lines, and the solution is restricted to the volumetric strain hardening rocks with overconsolidation ratio less than 2. Concurrently, Yu and Rowe (1999) provided a set of comprehensive yet still approximate analytical/semi-analytical solutions for the undrained circular excavation problem using the well known Cam Clay critical state theories (Wood 1990).…”

Section: Introductionmentioning

confidence: 99%

Drained and undrained analyses of cylindrical cavity contractions by bounding surface plasticity

Chen

Abousleiman

2016

Can. Geotech. J.

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This paper develops a rigorous semi-analytical approach for drained–undrained cylindrical cavity contraction problems in bounding surface elastoplastic geomaterials. For undrained situations, the effective radial, tangential, and vertical component stresses can be solved directly from the constitutive governing differential equations as an initial value problem, the excess pore pressure subsequently being determined from the radial equilibrium equation. In contrast, for the drained case the Eulerian radial equilibrium equation must be first transformed into an equivalent one in a Lagrangian description via the introduction of an auxiliary variable, then solved together with the elastoplastic constitutive relation for the three stress components as well as the specific volume. It is observed that during drained–undrained contraction processes, plastic deformations occur immediately as a direct result of employing the bounding surface model, so outside the cavity there exists no purely elastic zone. The computed stress distributions and in particular the stress path prediction through an example analysis capture well the anticipated elastoplastic and failure behaviour of the geomaterials surrounding the cavity. The validity and accuracy of the proposed semi-analytical elastoplastic solutions are justified through comparison with ABAQUS numerical results, and their applicability to the tunnel excavation and wellbore drilling problems is also demonstrated.

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A Fully Analytical Solution of the Wellbore Stability Problem under Undrained Conditions Using a Linearised Cam-Clay Model

Cited by 20 publications

References 11 publications

A numerical investigation on undrained expansion of a cylindrical cavity under biaxial in situ stresses using anisotropic S‐CLAY1 model

A numerical investigation on undrained expansion of a cylindrical cavity under biaxial in situ stresses using anisotropic S‐CLAY1 model

Stability analysis and uncertainty modeling of vertical and inclined wellbore drilling through heterogeneous field

Drained and undrained analyses of cylindrical cavity contractions by bounding surface plasticity

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