We use genetic programming (GP) to determine the deformation modulus of rock masses. A database of 150 data sets, including modulus of elasticity of intact rock (Ei), uniaxial compressive strength (UCS), rock mass quality designation (RQD), the number of joint per meter (J/m), porosity, and dry density for possible input parameters, and the modulus deformation of the rock mass determined by a plate loading test for output, was established. The values of geological strength index (GSI) system were also determined for all sites and considered as another input parameter. Sensitivity analyses are considered to find out the important parameters for predicting of the deformation modulus of rock mass. Two approaches of sensitivity analyses, based on “statistical analysis of RSE values” and “sensitivity analysis about the mean”, are performed. Evolution of the sensitivity analyses results establish the fact that variable of UCS, GSI, and RQD play more prominent roles for predicting modulus of the rock mass, and so those are considered as the predictors to design the GP model. Finally, two equations were achieved by GP. The statistical measures of root mean square error (RMSE) and variance account for (VAF) have been used to compare GP models with the well-known existing empirical equations proposed for predicting the deformation modulus. These performance criteria proved that the GP models give higher predictions over existing empirical models.
The deformation modulus of a rock mass is one of the crucial parameters that must be considered in the design stage of surface and underground rock engineering structures. However, the determination of this modulus remains one of the most troublesome tasks in the field of rock mechanics. The direct procedures for estimating the modulus, such as plate jacking, plate loading, radial jacking, flat jack, etc., requires extensive, time consuming and difficult procedures.
Due to the difficulties encountered during the in situ tests, developing of predictive models to estimate the deformation modulus based on the rock mass properties was always an attractive study domain among the rock engineers [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18] and [19]. In this regard, there are too many parameters that affect the deformability of rock mass, and so it is generally impossible to develop a universal model that can be used in any practical way to predict the modulus of rock mass.
In recent years, new soft computing methods such as artificial neural networks (ANN), fuzzy logic and neuro-fuzzy systems were employed to estimate the modulus of deformation [16] and [17]. These techniques become more attractive because of the information processing characteristics of those, such as non-linearity, high parallelism, robustness, fault and failure tolerance and their capability to generalize. In spite of that, these methods are thriving in prediction; their insufficiency to clearly give prediction equations can cause problems in practical circumstances. Genetic programming (GP) is another soft computing method which can be a candidate to overcome this problem. However, a genetic programming model to determine the modulus of rock masses is still not available. The present study involves application of the genetic programming concept, as the first attempt to predict the deformation modulus of rock masses. The main advantage of GP based approaches is their ability to generate prediction equations which can be manipulated in practical circumstances without any difficulty.
The purpose of the current research involves selection of the input parameters, among the rock mass properties, for preparing GP model with the aid of sensitivity based neural network analyses, construction of new prediction formulae for estimation of the modulus based on GP approach using plate loading test data, and comparison between the results of GP models and existing empirical equations.
This study supplies a new and efficient approach for the formulation of deformation modulus using genetic programming concept for the first time in the literature. The experimental database used for GP modeling is based on in situ measurements of modulus and laboratory studies of rock mass parameters acquired from several dam sites and power house locations founded on Asmary Formation.
Sensitivity analyses based neural network methods were employed to select the predictors for GP models. The results show that rock mass properties of UCS, GSI, and RQD meaningfully control finding modulus of deformation which was regarded as the independent variables driving the data set. After training the GP models, two predictive equations for deformation modulus has been extracted and compared with the some existing empirical models. The comparison demonstrates that using genetic programming provides best predictions than as empirical equations comparable to the plate loading modulus measurements. So, we can use these models safely for the modulus prediction problems. The successful application of GP in the current study may encourage its innovative use in rock engineering in the future.
