Thermoelastic Stress in the Semi-Infinite Solid

Mindlin, R. D.; Cheng, David K.

doi:10.1063/1.1699786

Cited by 221 publications

(93 citation statements)

References 4 publications

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“…We compared the potentials for the two problems, and we also compared the displacement field produced by the cooling of the cylinder stack with the displacements at the free surface resulting from the cooling of a buried sphere [Mindlin and Cheng, 1950]. The difference between our approximate solution and the exact solution can be made to vanish by using suitably thin cylinders.…”

Section: Thermal Displacement and Stressmentioning

confidence: 99%

The evolution of impact basins: Cooling, subsidence, and thermal stress

1985

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Potentially important contributors to the topography and tectonics of multi-ring impact basins are the thermal contraction and thermal stress that accompany the loss of heat emplaced during basin formation. Heat converted from impact kinetic energy and contributed from the uplift of isotherms during cavity collapse are important components in the energy budget of a newly-formed basin. That the subsequent cooling may have been an important factor in the tectonic evolution of the Orientale basin is suggested by the deep central depression and by a surrounding region of extensive fissuring. To test these concepts, we develop models for the anomalous temperature distribution immediately following basin formation, and we calculate the resulting elastic displacement and stress fields that then would accompany cooling of the basin region. All models predict subsidence of the basin floor and a near-surface stress field consistent with fissuring. In addition, the rates of cooling and of accumulation of thermal stress are in agreement with the inferred timing of fissure formation in Orientale. The sensitivity of the predicted displacements and stresses to the initial temperature field allows us to place bounds on the quantity and distribution of impact heat emplaced during basin formation. In order to be consistent with the observed topography and the distribution of fissures in the Orientale basin, the buried heat deposited during the basin-forming event was between 1032 and 1033 erg. It is likely that most of this heat was concentrated within a distance of 100-200 km from the point of impact.

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Section: Thermal Displacement and Stressmentioning

confidence: 99%

The evolution of impact basins: Cooling, subsidence, and thermal stress

1985

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“…In order to account for a traction-free surface, additional displacements due to the corrective stresses applied in the plane defined by y = 0 (see Figure A1) need to be superimposed. This problem is a classical problem of theory of elasticity and can its solution can also be found in Sen (1950) and Mindlin and Cheng (1950). …”

Section: Appendix a Derivation Of Displacements Due To Corrective Sumentioning

confidence: 99%

“…Appendix B summarizes the derivation of 3-D ground movements for a spherical cavity point contraction embedded at depth, H, in an elastic half-space based on the method of singularity superposition (after Sagaseta, 1987;Sen, 1950;Mindlin & Cheng, 1950). The displacement components can be expressed as follows:…”

Section: Three Dimensional Effectsmentioning

confidence: 99%

Ground Movements due to Shallow Tunnels in Soft Ground. I: Analytical Solutions

Pinto

Whittle

2014

J. Geotech. Geoenviron. Eng.

103

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This paper presents simplified closed-form analytical solutions that can be used to interpret and predict ground movements caused by shallow tunneling in soft ground conditions. These solutions offer a more comprehensive framework for understanding the distribution of ground movements than widely used empirical functions. Analytical solutions for the displacement field within the ground mass are obtained for two basic modes of deformation corresponding to uniform convergence and ovalization at the wall of a circular tunnel cavity, based on the assumption of linear, elastic soil behavior. Deformation fields based on the superposition of fundamental, singularity solutions are shown to differ only slightly from analyses that consider the physical dimensions of the tunnel cavity, except in the case of very shallow tunnels. The Authors demonstrate a simplified method to account for soil plasticity in the analyses and illustrate closed-form solutions for a three-dimensional tunnel heading. A companion paper describes applications of these analyses to interpret field measurements of ground response to tunneling.

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“…They stated that two-dimensional DCFFT should be applied in residual stress computation. An alternative to Chiu's problem decomposition was advanced by Liu and Wang, (Liu & Wang, 2005), based on Mindlin and Cheng's results, (Mindlin & Cheng, 1950), involving derivatives of four key integrals. They also advanced an efficient algorithm to compute correlation products using convolution theorem, called Discrete Correlation Fast Fourier Transform (DCRFFT).…”

Section: Plastic Zone Contribution To Stress Statementioning

confidence: 99%