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Finite element-based probabilistic stability analysis of rock-fill tailing dam considering regional seismicity

  • A. HegdeEmail author
  • Tanmoy Das
Technical Note
  • 18 Downloads

Abstract

The recent tailing dam failure in Brazil has again emphasized the need of performing robust stability analysis prior to construction. This paper demonstrates the probabilistic dynamic stability analysis of tailing dams considering an existing rock-fill tailing dam in India. The stability analysis was performed using 2D finite element-based package RS2. In the probabilistic analysis, the strength parameters such as cohesion (c) and the friction angle (φ) were considered as random variables. In total, 3000 numbers of samples were generated assuming a normal distribution. Monte Carlo simulation was used to evaluate the probability of failure (PoF) and reliability index. Strength reduction method was used for the finite element analyses. A pseudo-static seismic loading was incorporated in the strength reduction analysis to check the seismic stability of the dam. A factor of safety (FoS) of 1.15 was observed from the deterministic analysis for downstream slope. For the same case, the probabilistic analysis provided a mean FoS of 1.19 with 5.46% probability of failure. The FoS values and the locations of the critical failure surface obtained by the limit equilibrium method and finite element method were compared. The observed FoS values were found to be higher than the values specified in the IS 7894-1975 (reaffirmed in 1997) and ANCOLD (1999). In the case of pseudo-static approach, the maximum displacement of 0.53 m was observed in the slope. Furthermore, nonlinear dynamic stability analysis was performed to simulate a true earthquake event. The permanent deformation of the slope after the earthquake was found to be 0.40 m. The zone of failure observed in both pseudo-static and nonlinear dynamic stability analyses was found to be the same. Overall, the results revealed that the spatial variability of the soil significantly influences the FoS values.

Keywords

Tailing dam Random variable Monte Carlo simulation Strength reduction method Spatial variability 

List of symbols

c

Cohesion (KPA)

cf

Factored cohesion (kPa)

CoVs

Coefficient of variation in normal random variables (dimensionless)

d

Standard normal deviate (dimensionless)

E

Young’s modulus (MPa)

Es

Spatial element size (m)

fmax

Maximum frequency (Hz)

f(s)

Probability density function of normal random variables (dimensionless)

G

Shear modulus of soil (GPa)

n

Number of random variables (dimensionless)

Ns

Number of sample having critical SRF less than or equal to 1 (dimensionless)

Ntotal

Total number of sample (dimensionless)

PoF

Probability of failure (%)

Rmin

Minimum number of realization (dimensionless)

RI

Reliability index (dimensionless)

s

Normal random variable (dimensionless)

SRF

Strength reduction factor (dimensionless)

Vs

Shear wave speed (m/s)

\( \alpha_{M} \)

Rayleigh alpha constant (s − 1)

\( \beta_{K} \)

Rayleigh beta constant (s)

\( \gamma \)

Unit weight of soil (kN/m3)

\( \varepsilon \)

Relative percentage error in estimating probability of failure (%)

\( \zeta_{i} \)

Damping ratio for mode i (%)

\( \lambda \)

Wave length associated with the highest frequency component (m)

\( \mu_{s} \)

Mean of normal random variables (dimensionless)

\( \mu_{{{\text{SRF}} }} \)

Mean of critical SRF values (dimensionless)

\( \nu \)

Poisson’s ratio (dimensionless)

\( \rho \)

Bulk unit weight of soil (kN/m3)

\( \sigma_{n} \)

Normal stress in soil (kN/m2)

\( \sigma_{s} \)

Standard deviation of normal random variables (dimensionless)

\( \sigma_{\text{SRF}} \)

Standard deviation of critical SRF values (dimensionless)

\( \tau_{f} \)

Shear stress in soil on the sliding surface (kN/m2)

\( \varphi \)

Friction angle (°)

\( \varphi_{f} \)

Factored friction angle (°)

\( \omega_{i} \)

Natural frequency of mode i (rad/s)

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Civil and Environmental EngineeringIndian Institute of Technology PatnaPatnaIndia

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