Rock Mechanics and Rock Engineering

, Volume 51, Issue 10, pp 3029–3043 | Cite as

A Real-Time Back-Analysis Technique to Infer Rheological Parameters from Field Monitoring

  • Chongchong QiEmail author
  • Andy Fourie
Original Paper


The long-term stress analysis of engineering projects can be significantly expedited if we can determine an appropriate rheological model and its corresponding parameters. In the present contribution, we show that an accurate and real-time estimation of rheological parameters is possible by employing deep learning and metaheuristic algorithms. A real-time back-analysis technique was proposed using a deep long short-term memory neural network (DeepLSTM) as a substitute for numerical modelling and firefly algorithm (FA) to search for the optimum parameter. The performance of the proposed technique, the DeepLSTM-FA, was verified using a tunnel response with the FLAC 2D finite difference program. Furthermore, the application of the DeepLSTM-FA to an engineering instance, namely, the Adriatic Motorway near Draga Valley, was discussed in detail, revealing that the DeepLSTM-FA can provide practitioners with an accurate and real-time estimation of rheological parameters, thereby allowing for timely stress and stability analyses. We found that an accurate estimation of rheological parameters can be made using the first few points of displacement data instead of the whole displacement profile. This technique extends recent efforts to determine rheological parameters in real time and significantly accelerates the application of stress and stability analyses in the future.


Back-analysis Rheological parameters Deep long short-term memory Firefly algorithm 

List of symbols


Deep long short-term memory neural network


Firefly algorithm


Artificial intelligence


Burger-creep visco-plastic model


Feed-forward neural network


Recurrent neural network


Mean squared error


Absolute percentage error


Neural layer


Activation value for the neurons


Weight matrix




Activation function


Hidden sequence values



i, f, and o

Input, forget, and output gates


Cell activation

\({x_i}\) and \({x_j}\)

Fireflies i and j


Mutual distance between \({x_i}\) and \({x_j}\)


Attractiveness at \({r_{ij}}=0\)


Light absorption coefficient

\({\alpha _t}\)

Step size parameter

\({\epsilon _t}\)

Random number

\({\overline {Y} _i}\) and \({Y_i}\)

Predicted and field responses

\({\sigma _x}\) and \({\sigma _x}\)

In situ horizontal and vertical stresses

\({\gamma _r}\)

Unit weight




Internal friction angle

\({\sigma _t}\)

Tensile strength


Dilation angle


Bulk modulus


Maxwell shear modulus


Kelvin shear modulus

\({\eta ^{\text{M}}}\)

Maxwell viscosity

\({\eta ^{\text{K}}}\)

Kelvin viscosity



The first author was supported by the China Scholarship Council under Grant number: 201606420046.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Civil, Environmental and Mining EngineeringUniversity of Western AustraliaPerthAustralia

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