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Dynamic Analysis of Tunnel in Weathered Rock Subjected to Internal Blast Loading

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Abstract

The present study deals with three-dimensional nonlinear finite element (FE) analyses of a tunnel in rock with reinforced concrete (RC) lining subjected to internal blast loading. The analyses have been performed using the coupled Eulerian–Lagrangian analysis tool available in FE software Abaqus/Explicit. Rock and RC lining are modeled using three-dimensional Lagrangian elements. Beam elements have been used to model reinforcement in RC lining. Three different rock types with different weathering conditions have been used to understand the response of rock when subjected to blast load. The trinitrotoluene (TNT) explosive and surrounding air have been modeled using the Eulerian elements. The Drucker–Prager plasticity model with strain rate-dependent material properties has been used to simulate the stress–strain response of rock. The concrete damaged plasticity model and Johnson–Cook plasticity model have been used for the simulation of stress–strain response of concrete and steel, respectively. The explosive (TNT) has been modeled using Jones–Wilkins–Lee (JWL) equation of state. The analysis results have been studied for stresses, deformation and damage of RC lining and the surrounding rock. It is observed that damage in RC lining results in higher stress in rock. Rocks with low modulus and high weathering conditions show higher attenuation of shock wave. Higher amount of ground shock wave propagation is observed in case of less weathered rock. Ground heave is observed under blast loading for tunnel close to ground surface.

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Abbreviations

ϕ :

Angle of internal friction

\(\psi\) :

Dilation angle at mean stress–deviatoric stress plane

\(\varepsilon\) :

Eccentricity parameter

\(\varepsilon^{ * }\) :

Dimensionless plastic strain

\(\dot{\varepsilon }\) :

Strain rate

\(\dot{\varepsilon }_{0}\) :

Reference strain rate

\(\varepsilon_{\text{t}}^{\text{pl}}\) :

Tensile plastic strain

\(\varepsilon_{\text{c}}^{\text{pl}}\) :

Compressive plastic strain

ν :

Poisson’s ratio

\(\rho_{\text{c}}\) :

Density of concrete

\(\rho_{\text{s}}\) :

Density of steel

\(\rho\) :

Current density

\(\bar{\rho }\) :

Ratio of density of explosive in the solid state to current density

\(\rho_{\text{sol}}\) :

Density of explosive in the solid state

β :

Parameter related to the angle of internal friction

\(\sigma\) :

Dynamic yield stress (J–C) model

\(\sigma_{\text{t}}\) :

Tensile stress

\(\sigma_{\text{c}}\) :

Compressive stress

\(\hat{\bar{\sigma }}_{\hbox{max} }\) :

Maximum principal effective stress

\(\sigma_{\text{b0}}\) :

Initial equibiaxial compressive yield stress

\(\sigma_{\text{c0}}\) :

Initial uniaxial compressive yield stress

\(\sigma_{\text{t0}}\) :

Uniaxial tensile stress at failure

\(\sigma_{1}\), \(\sigma_{2}\), \(\sigma_{3}\) :

Effective stress in x, y and z directions, respectively

A, B :

Magnitude of pressure (JWL EOS)

A, B, C, m, n :

Model parameters (J–C) model

c :

Cohesion

c v :

Speed of sound wave

d :

Hardening parameter

\(d_{\text{t}}\) :

Damage variable for tension

\(d_{\text{c}}\) :

Damage variable for compression

\(D_{\text{o}}^{\text{el}}\) :

Undamaged initial elastic modulus

E c :

Modulus of elasticity of concrete

E s :

Modulus of elasticity of steel

e int :

Specific internal energy at atmospheric pressure

f ck :

Compressive strength of concrete

f s :

Tensile yield strength

G p :

Plastic potential function

l :

Smallest element dimension

K :

Scalar parameter

K c :

Ratio of second deviatoric stress invariant on the tensile meridian to that on the compressive meridian at initial crushing for any given value of effective mean stress

p :

Pressure

\(\bar{p}\) :

Effective mean pressure

p′:

Mean stress

q :

Deviatoric stress

R 1, R 2, ω :

Material constants (JWL EOS)

r :

Third invariant of the deviatoric stress tensor

\(\bar{s}\) :

Deviatoric stress tensor

T*:

Homologous temperature

Δt :

Time increment

\(t_{w}\) :

Thickness of concrete lining

U :

Displacement perpendicular to plane

\(U_{\text{R}}\) :

Out-of-plane rotations

x, y, z :

Cartesian directions

W :

Charge weight

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Authors and Affiliations

  1. Department of Civil Engineering, Indian Institute of Technology (IIT) Delhi, Hauz Khas, New Delhi, 110 016, India

    Rohit Tiwari, Tanusree Chakraborty & Vasant Matsagar

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  1. Rohit Tiwari
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  2. Tanusree Chakraborty
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  3. Vasant Matsagar
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Correspondence to Tanusree Chakraborty.

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Tiwari, R., Chakraborty, T. & Matsagar, V. Dynamic Analysis of Tunnel in Weathered Rock Subjected to Internal Blast Loading. Rock Mech Rock Eng 49, 4441–4458 (2016). https://doi.org/10.1007/s00603-016-1043-8

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