This study presents an analysis of deformation around interacting tunnels excavated in intact and jointed rock masses. The study examines the behavior of twin parallel interacting horseshoe-shaped tunnels, which are widely used in underground construction projects such as hydroelectric power plants and transportation systems. The analysis, conducted using 2D plane strain elasto-plastic finite element modeling, investigates the effects of varying in-situ stress ratios (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">$K_0$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>K</mi> <mn>0</mn> </msub> </math></EquationSource> </InlineEquation>) and pillar width-to-diameter ratios (W/D) on stress redistribution, deformation patterns, and yielding zones in the surrounding rock mass. Three pillar width-to-tunnel diameter ratios (<InlineEquation ID="IEq2"> <EquationSource Format="TEX">$W/D = 0.3$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>W</mi> <mo stretchy="false">/</mo> <mi>D</mi> <mo>=</mo> <mn>0.3</mn> </mrow> </math></EquationSource> </InlineEquation>, 0.6, and 1.2) and three in-situ stress ratios (<InlineEquation ID="IEq3"> <EquationSource Format="TEX">$K_0 = 0.5$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>K</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>0.5</mn> </mrow> </math></EquationSource> </InlineEquation>, 1.0, and 1.5) were evaluated to examine spacing and stress variations. Elasto-plastic analyses were performed, incorporating a simultaneous excavation scenario. For the elasto-plastic analysis, the Hoek–Brown yield criterion was applied, using field data from a river valley project in India. The study further extends to elasto-plastic analysis of single and twin horseshoe tunnels in jointed rock masses, considering two discontinuity sets oriented at <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$45^\circ /45^\circ$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mn>45</mn> <mo>∘</mo> </msup> <mo stretchy="false">/</mo> <msup> <mn>45</mn> <mo>∘</mo> </msup> </mrow> </math></EquationSource> </InlineEquation>. The impact of joint orientation, in-situ stress ratio, and pillar width on stress distribution and deformation is reported to provide insights into optimal design and excavation approaches for interacting tunnels in complex rock conditions. The results demonstrate that smaller W/D ratios and higher in-situ stress ratios (<InlineEquation ID="IEq5"> <EquationSource Format="TEX">$K_0$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>K</mi> <mn>0</mn> </msub> </math></EquationSource> </InlineEquation>) significantly amplify deformation and yielding, particularly in jointed rock masses. Interaction effects are found to diminish with increasing W/D ratios, while <InlineEquation ID="IEq6"> <EquationSource Format="TEX">$K_0 = 1.0$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>K</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>1.0</mn> </mrow> </math></EquationSource> </InlineEquation> results in minimal yielding. In contrast, <InlineEquation ID="IEq7"> <EquationSource Format="TEX">$K_0 = 1.5$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>K</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>1.5</mn> </mrow> </math></EquationSource> </InlineEquation> and 0.5 induces more pronounced yielding in both intact and jointed rock.

Elasto-Plastic Analysis of Interacting Tunnels in Jointed Rock Masses Under Varying In-Situ Stress Ratios and Pillar Width-to-Diameter Ratio

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发表日期：

2025年9月1日

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Rajnish Kumar Tiwari,
Imran Ahmad Khan,
R. K. Srivastava

摘要

This study presents an analysis of deformation around interacting tunnels excavated in intact and jointed rock masses. The study examines the behavior of twin parallel interacting horseshoe-shaped tunnels, which are widely used in underground construction projects such as hydroelectric power plants and transportation systems. The analysis, conducted using 2D plane strain elasto-plastic finite element modeling, investigates the effects of varying in-situ stress ratios ( $K_0$ $K_{0}$ ) and pillar width-to-diameter ratios (W/D) on stress redistribution, deformation patterns, and yielding zones in the surrounding rock mass. Three pillar width-to-tunnel diameter ratios ( $W/D = 0.3$ $W / D = 0.3$ , 0.6, and 1.2) and three in-situ stress ratios ( $K_0 = 0.5$ $K_{0} = 0.5$ , 1.0, and 1.5) were evaluated to examine spacing and stress variations. Elasto-plastic analyses were performed, incorporating a simultaneous excavation scenario. For the elasto-plastic analysis, the Hoek–Brown yield criterion was applied, using field data from a river valley project in India. The study further extends to elasto-plastic analysis of single and twin horseshoe tunnels in jointed rock masses, considering two discontinuity sets oriented at $45^\circ /45^\circ$ $45^{\circ} / 45^{\circ}$ . The impact of joint orientation, in-situ stress ratio, and pillar width on stress distribution and deformation is reported to provide insights into optimal design and excavation approaches for interacting tunnels in complex rock conditions. The results demonstrate that smaller W/D ratios and higher in-situ stress ratios ( $K_0$ $K_{0}$ ) significantly amplify deformation and yielding, particularly in jointed rock masses. Interaction effects are found to diminish with increasing W/D ratios, while $K_0 = 1.0$ $K_{0} = 1.0$ results in minimal yielding. In contrast, $K_0 = 1.5$ $K_{0} = 1.5$ and 0.5 induces more pronounced yielding in both intact and jointed rock.