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The prediction of dynamic energy behavior of a Brazilian disk containing nonpersistent joints subjected to drop hammer test utilizing heuristic approaches

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Abstract

Crack development initiated from nonpersistent joints in rock mass plays a key role in the instability of rock structures. In particular, the dynamic behavior of nonpersistent discontinuities can result in the coalescence and failure of rock structures. The effect and contribution of such joint parameters on rock structures’ failure under impact loading have not been thoroughly investigated by researchers. In this paper, 68 concrete Brazilian disks, manufactured to include several nonpersistent joints and joint sets, are subjected to impact loading to explore the impact of joint continuity factor, joint spacing, bridge angle, and loading direction on the required dynamic energy for crack initiation (DECI) and coalescence (DECC). Artificial neural network (ANN), adaptive neuro-fuzzy inference system (ANFIS), and its combination with particle swarm optimization (PSO) and genetic algorithm (GA) have been developed to predict the energy indexes. The performance of the models was evaluated using statistical indicators. The results show that intelligent methods can predict both energy indexes and that their outputs are consistent with laboratory results. The R-squared index for the test data of the ANN, ANFIS, and ANFIS-PSO/GA models to predict DECI parameters is 0.97, 0.96, 0.96, and 0.97, respectively, and for DECC is 0.98, 0.96, 0.96, and 0.93, respectively. The ANN have the best performance for the test data based on all statistical indexes. In addition, multiple parametric sensitivity analysis shows that both the joint continuity and joint spacing have the most significant effect while bridge angle and loading direction have the minimal effect on the energy indexes.

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Abbreviations

d :

Joint spacing (cm)

γ :

Bridge angle (°)

β :

Loading direction with respect to joint angle (°)

L j :

Joint length (cm)

L j :

Rock bridge length (cm)

k :

Joint continuity factor \(\left( {k = \frac{{L_{j} }}{{L_{j} + L_{r} }}} \right)\)

V 0 :

Initial velocity

\(f_{h}\) :

Objective function

\(\delta_{h}\) :

Independent relative importance of each parameter

\({\varvec{\gamma}}\) :

Sum of independent relative importance of each parameter

DECI:

Dynamic energy for crack initiation (kN mm)

DECC:

Dynamic energy for crack coalescence (kN mm)

MPSA:

Multiple parametric sensitivity analysis

DOE:

Design of experiments

ANN:

Artificial neural network

ANFIS:

Adaptive neuro-fuzzy inference system

PSO:

Particle swarm optimization

GA:

Genetic algorithm

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Authors and Affiliations

  1. Department of Mining Engineering, Hamedan University of Technology, Mardom Street, 65155-579, Hamedan, Iran

    Jamshid Shakeri, Mostafa Asadizadeh & Nima Babanouri

  2. Department of Mining and Nuclear Engineering, Missouri University of Science and Technology, Rolla, MO, 65409, USA

    Mostafa Asadizadeh

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  1. Jamshid Shakeri
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Correspondence to Mostafa Asadizadeh.

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Shakeri, J., Asadizadeh, M. & Babanouri, N. The prediction of dynamic energy behavior of a Brazilian disk containing nonpersistent joints subjected to drop hammer test utilizing heuristic approaches. Neural Comput & Applic 34, 9777–9792 (2022). https://doi.org/10.1007/s00521-022-06964-5

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