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On the Stability of Underground Caves in Calcareous Rocks Due to Long-Term Weathering

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Abstract

This paper addresses the problem of the stability of structures on calcareous rocks due to long-term weathering processes. The case study consists of a building resting on a calcarenite rock formation where two abandoned man-made caves exist directly under the structure. The boundaries of the caves were exposed to a slightly acidic environment inducing time-dependent weathering. Analyses were performed following a semi-decoupled approach, where the weathering process, driven by a reactive transport mechanism, was first solved and its results were fed to the mechanical problem which hence accounted for the spatial and temporal evolution or rock damage. For the mechanical problem, a nonlocal constitutive model was employed for the objective simulation of localised deformations. Relevant outcomes are obtained regarding the evolution of the structure’s stability and about the importance of regularising the finite element solution in the presence of brittle materials.

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Abbreviations

BVP:

Boundary value problem

CHM:

Chemo-hydro-mechanical

GDP:

Grain dissolution process

HMC:

Hyperbolic Mohr–Coulomb

LTD:

Long-term debonding

STD:

Short-term debonding

B :

Parameter in \(f_\text {d}\)

\(\text {CaCO}_{3(\text {s})}\) :

Calcium carbonate species in the solid phase

D :

Isotropic diffusion coefficient

\(D_{ij}\) :

Diffusion tensor

E :

Young’s modulus

\(\text {H}_3 \text {O}^+_\text {(aq)}\) :

Acid ions

\(J_2\) :

Second invariant of the deviatoric stress tensor

K :

Darcy isotropic permeability

\(K_1\), \(K_2\) :

Reaction rate constants

M :

Mass

\(N_\text {G}\) :

Number of Gauss points

\(S_\text {r}\) :

Degree of saturation

\(S_\text {r,cr}\) :

Minimum \(S_\text {r}\) for all the depositional bonds to suspend

Y :

Weathering function

\(Y_\text {dis}\) :

Component of the weathering function for the LTD process

\(Y_\text {sus}\) :

Component of the weathering function for the STD process

\(a_\phi\) :

Constant controlling the curvature of the hyperbolic hardening function

\(b_\text{c}\) :

Softening rate for the cohesion and tensile strength

\(b_\phi\) :

Softening rate for the friction angle

\(c^*\) :

Asymptotic cohesion

\(c^*_\text {ini}\) :

Initial asymptotic cohesion

\(c^*_\text {ini,uw}\) :

Initial asymptotic cohesion for \(\xi _\text {dis} = 0\)

f :

Yield function

\(f_\text {d}\) :

Function defining the shape of f in the deviatoric plane

\(l_\text {s}\) :

Length scale parameter

m :

Parameter in \(f_\text {d}\)

n :

Effective porosity

p :

Mean stress

\(\text {pH}\) :

Potential of the hydrogen

\(p_\text{t}\) :

Isotropic tensile strength

\(p_{t \text {ini}}\) :

Initial isotropic tensile strength

\(p_{t \text {ini,uw}}\) :

Initial isotropic tensile strength for \(\xi _\text {dis} = 0\)

\(q_i\) :

Component of the real seepage velocity along the i axis

\(r_{kl}\) :

Radial distance between the kth and lth Gauss points

\(s_{ij}\) :

Deviatoric stress tensor

w :

Normalised averaging factor

\(w_0\) :

Weighting function

\(\alpha\) :

Parameter in \(f_\text {d}\)

\(\delta _{ij}\) :

Kronecker delta

\(\epsilon _1\) :

Major principal strain

\(\epsilon _3\) :

Minor principal strain

\(\epsilon ^\text {p}_\text {eq}\) :

Equivalent plastic strain

\(\bar{\epsilon }^\text {p}_\text {eq}\) :

Nonlocal equivalent plastic strain

\(\epsilon ^\text {p}_{ij}\) :

Plastic strain tensor

\(\epsilon _\text {s}\) :

Shear strains

\(\theta\) :

Lode’s angle

\(\nu\) :

Poisson’s ratio

\(\xi _\text {dis}\) :

Normalised dissolved mass

\(\xi _\text {dis,cr}\) :

Corresponds to \(\xi _\text {dis}\) when all diagenetic bonds have been dissolved

\(\sigma ^\text {d}_\text {c0}\) :

Uniaxial compression strength under dry conditions

\(\sigma ^\text {w}_\text {c0}\) :

Uniaxial compression strength under wet conditions

\(\sigma _{ij}\) :

Stress tensor

\(\phi ^*\) :

Asymptotic friction angle

\(\phi ^*_\text {ini}\) :

Initial asymptotic friction angle

\(\phi ^*_\text {peak}\) :

Peak asymptotic friction angle

\(\phi ^*_\text {res}\) :

Residual friction angle

\(\chi\) :

Value of \(\epsilon ^\text {p}_\text {eq}\) separating the hardening and softening regimes

\(\psi\) :

Angle of dilation

\(\omega\) :

Constant controlling the volumetric component of plastic deformations

\([\cdot ]\) :

Bulk fluid concentrations

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Authors and Affiliations

  1. Institute of Engineering, National Autonomous University of Mexico, Mexico City, Mexico

    Miguel A. Mánica

  2. School of Science and Engineering, University of Dundee, Dundee, UK

    Matteo O. Ciantia

  3. Department of Civil and Environmental Engineering, Universitat Politècnica de Catalunya, Barcelona Tech, Barcelona, Spain

    Antonio Gens

Authors
  1. Miguel A. Mánica
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  2. Matteo O. Ciantia
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  3. Antonio Gens
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Correspondence to Miguel A. Mánica.

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Mánica, M.A., Ciantia, M.O. & Gens, A. On the Stability of Underground Caves in Calcareous Rocks Due to Long-Term Weathering. Rock Mech Rock Eng 53, 3885–3901 (2020). https://doi.org/10.1007/s00603-020-02142-y

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  • DOI: https://doi.org/10.1007/s00603-020-02142-y

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