<p>Composite and voided rock masses are commonly encountered in underground excavations, where cavities, weak infill, and grouted inclusions significantly influence stress redistribution and failure behaviour. The deviatoric stress (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\({\sigma}_{d})\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>σ</mi> <mi>d</mi> </msub> <mrow> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> versus axial strain (<InlineEquation ID="IEq2"> <EquationSource Format="TEX">\({\varepsilon}_{a})\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>ε</mi> <mi>a</mi> </msub> <mrow> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> response for hollow and intact-composite cylindrical rock like cement-sand mortar specimens, with a weak inner core, at different confining pressures (<InlineEquation ID="IEq3"> <EquationSource Format="TEX">\({\sigma}_{3})\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>σ</mi> <mn>3</mn> </msub> <mrow> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> has been determined experimentally as well as numerically. Triaxial compression tests were carried out on cylindrical specimens for different values of <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\({\sigma}_{3}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>σ</mi> <mn>3</mn> </msub> </math></EquationSource> </InlineEquation> (upto 30&#xa0;MPa). Two different mixes of mortar, namely (i) strong mortar with 50% cement by mass, and (ii) weak mortar with 15% cement, both after a curing period of 28&#xa0;days, were employed. The diameter (<InlineEquation ID="IEq5"> <EquationSource Format="TEX">\({d}_{i}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>d</mi> <mi>i</mi> </msub> </math></EquationSource> </InlineEquation>) of the inner core/hole was varied from 10 to 25&#xa0;mm by keeping a constant outer diameter (<InlineEquation ID="IEq6"> <EquationSource Format="TEX">\({d}_{o})\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>d</mi> <mi>o</mi> </msub> <mrow> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> of 38&#xa0;mm and with a height of 76&#xa0;mm. Ultrasonic P and S waves tests were also performed on the intact specimens at different values of <InlineEquation ID="IEq7"> <EquationSource Format="TEX">\({\sigma}_{3}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>σ</mi> <mn>3</mn> </msub> </math></EquationSource> </InlineEquation>. Finite elements (FE) analysis, using linear elastic-perfect plastic constitutive model, and analytical based simulations were also carried out to predict the stress‐strain response of both hollow and intact-composite specimens from the measured stress‐strain plots of the intact specimens. Experimental results clearly reveal that an increase in the value of <InlineEquation ID="IEq8"> <EquationSource Format="TEX">\({d}_{i}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>d</mi> <mi>i</mi> </msub> </math></EquationSource> </InlineEquation>/<InlineEquation ID="IEq9"> <EquationSource Format="TEX">\({d}_{o}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>d</mi> <mi>o</mi> </msub> </math></EquationSource> </InlineEquation> for hollow and intact-composite specimens leads to a continuous reduction in the values of <InlineEquation ID="IEq10"> <EquationSource Format="TEX">\({\sigma}_{df}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>σ</mi> <mrow> <mi mathvariant="italic">df</mi> </mrow> </msub> </math></EquationSource> </InlineEquation> (deviatoric stress at failure) and <InlineEquation ID="IEq11"> <EquationSource Format="TEX">\({E}_{i}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>E</mi> <mi>i</mi> </msub> </math></EquationSource> </InlineEquation> (initial Youngs’ modulus). For hollow specimens, the reduction in <InlineEquation ID="IEq12"> <EquationSource Format="TEX">\({\sigma}_{df}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>σ</mi> <mrow> <mi mathvariant="italic">df</mi> </mrow> </msub> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq13"> <EquationSource Format="TEX">\({E}_{i}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>E</mi> <mi>i</mi> </msub> </math></EquationSource> </InlineEquation> with an increase in <InlineEquation ID="IEq14"> <EquationSource Format="TEX">\({d}_{i}/{d}_{o}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>d</mi> <mi>i</mi> </msub> <mo stretchy="false">/</mo> <msub> <mi>d</mi> <mi>o</mi> </msub> </mrow> </math></EquationSource> </InlineEquation> is primarily attributed to (i) a reduction in average effective lateral confining pressure, and (ii) an increased stress concentration around the cavity region. For composite specimens, the reduction in <InlineEquation ID="IEq15"> <EquationSource Format="TEX">\({\sigma}_{df}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>σ</mi> <mrow> <mi mathvariant="italic">df</mi> </mrow> </msub> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq16"> <EquationSource Format="TEX">\({E}_{i}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>E</mi> <mi>i</mi> </msub> </math></EquationSource> </InlineEquation> with an increase in <InlineEquation ID="IEq17"> <EquationSource Format="TEX">\({d}_{i}/{d}_{o}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>d</mi> <mi>i</mi> </msub> <mo stretchy="false">/</mo> <msub> <mi>d</mi> <mi>o</mi> </msub> </mrow> </math></EquationSource> </InlineEquation> is primarily on account of load area exhibited by the inner weak material. An increment in <InlineEquation ID="IEq18"> <EquationSource Format="TEX">\({\sigma}_{3}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>σ</mi> <mn>3</mn> </msub> </math></EquationSource> </InlineEquation> in all the cases leads to increases in the magnitudes of <InlineEquation ID="IEq19"> <EquationSource Format="TEX">\({\sigma}_{df}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>σ</mi> <mrow> <mi mathvariant="italic">df</mi> </mrow> </msub> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq20"> <EquationSource Format="TEX">\({E}_{i}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>E</mi> <mi>i</mi> </msub> </math></EquationSource> </InlineEquation>. The results from the present research using cement mortar with respect to the effect of <InlineEquation ID="IEq21"> <EquationSource Format="TEX">\({d}_{i}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>d</mi> <mi>i</mi> </msub> </math></EquationSource> </InlineEquation>/<InlineEquation ID="IEq22"> <EquationSource Format="TEX">\({d}_{o}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>d</mi> <mi>o</mi> </msub> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq23"> <EquationSource Format="TEX">\({\sigma}_{3}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>σ</mi> <mn>3</mn> </msub> </math></EquationSource> </InlineEquation> on stress‐strain response for hollow specimens, were found to have almost similar trend as that reported in literature for sandstone. These findings provide insight into the stability of voided and infilled rock media relevant to tunnelling, borehole stability, and ground improvement applications. Overall, the findings from the present research will provide the effect of confining stress in hollow and composite cylindrical systems, highlighting the role of geometric and material heterogeneity in governing mechanical behaviour and building guidelines for predicting the stress‐strain response till failure for hollow and intact-composite rock like cement mortar specimens.</p>

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Triaxial Stress Strain Response of Hollow and Intact Rock Like Cement Mortar Composite Cylindrical Specimens

  • Jyant Kumar,
  • Abhay Anand

摘要

Composite and voided rock masses are commonly encountered in underground excavations, where cavities, weak infill, and grouted inclusions significantly influence stress redistribution and failure behaviour. The deviatoric stress ( \({\sigma}_{d})\) σ d ) versus axial strain ( \({\varepsilon}_{a})\) ε a ) response for hollow and intact-composite cylindrical rock like cement-sand mortar specimens, with a weak inner core, at different confining pressures ( \({\sigma}_{3})\) σ 3 ) has been determined experimentally as well as numerically. Triaxial compression tests were carried out on cylindrical specimens for different values of \({\sigma}_{3}\) σ 3 (upto 30 MPa). Two different mixes of mortar, namely (i) strong mortar with 50% cement by mass, and (ii) weak mortar with 15% cement, both after a curing period of 28 days, were employed. The diameter ( \({d}_{i}\) d i ) of the inner core/hole was varied from 10 to 25 mm by keeping a constant outer diameter ( \({d}_{o})\) d o ) of 38 mm and with a height of 76 mm. Ultrasonic P and S waves tests were also performed on the intact specimens at different values of \({\sigma}_{3}\) σ 3 . Finite elements (FE) analysis, using linear elastic-perfect plastic constitutive model, and analytical based simulations were also carried out to predict the stress‐strain response of both hollow and intact-composite specimens from the measured stress‐strain plots of the intact specimens. Experimental results clearly reveal that an increase in the value of \({d}_{i}\) d i / \({d}_{o}\) d o for hollow and intact-composite specimens leads to a continuous reduction in the values of \({\sigma}_{df}\) σ df (deviatoric stress at failure) and \({E}_{i}\) E i (initial Youngs’ modulus). For hollow specimens, the reduction in \({\sigma}_{df}\) σ df and \({E}_{i}\) E i with an increase in \({d}_{i}/{d}_{o}\) d i / d o is primarily attributed to (i) a reduction in average effective lateral confining pressure, and (ii) an increased stress concentration around the cavity region. For composite specimens, the reduction in \({\sigma}_{df}\) σ df and \({E}_{i}\) E i with an increase in \({d}_{i}/{d}_{o}\) d i / d o is primarily on account of load area exhibited by the inner weak material. An increment in \({\sigma}_{3}\) σ 3 in all the cases leads to increases in the magnitudes of \({\sigma}_{df}\) σ df and \({E}_{i}\) E i . The results from the present research using cement mortar with respect to the effect of \({d}_{i}\) d i / \({d}_{o}\) d o and \({\sigma}_{3}\) σ 3 on stress‐strain response for hollow specimens, were found to have almost similar trend as that reported in literature for sandstone. These findings provide insight into the stability of voided and infilled rock media relevant to tunnelling, borehole stability, and ground improvement applications. Overall, the findings from the present research will provide the effect of confining stress in hollow and composite cylindrical systems, highlighting the role of geometric and material heterogeneity in governing mechanical behaviour and building guidelines for predicting the stress‐strain response till failure for hollow and intact-composite rock like cement mortar specimens.