State-of-the-art predictive modeling of TBM performance in changing geological conditions through gene expression programming
Introduction
In our time, tunnel boring machines (TBMs) are frequently utilized in excavation of long infrastructural tunneling projects in a wide range of geological conditions. It is to ensure that the construction is completed with a reasonable time and cost, hence making the prediction tasks more crucial for planning and risk management purposes [96]. Among several technical and managerial parameters, TBM performance is of vital importance since it highly affects the time and cost of any tunneling project.
During the last four decades, several prediction models were proposed to estimate hard rock TBM performance using tunnel path geological parameters as inputs. Main output parameters suggested by prediction models are the rate of penetration (ROP), that is the penetration per revolution or per unit of time (this index is believed to be the most significant representative of the machine performance together with the other indicators; see, e.g., [52], the utilization factor (UF) (percentage of time in which the machine is excavating) and more recently the field penetration index (FPI) (the ratio of thrust per cutter and penetration rate per cutterhead revolution). Basically, two major approaches have already been followed to develop predictive models: (i) Analytical models which estimate the cutting force by studying the rock fragmentation process with indentation of mechanical tools. The most well-known developed models in this category are the Gehring’s model [34] and the Colorado School of Mines (CSM) model [80], [81]. The analytical models usually combine intact rock and the cutter characteristics, and they do not take into account rock mass structural properties that already proved to essentially contribute to TBM performance, such as rock discontinuities frequency and orientation; (ii) Empirical models based on databases of records of previous projects. Due to multiple number of influencing parameters on TBM performance and variability of field conditions, numerous models have been developed in this category. However, the most widespread empirical models are Norwegian University of Sciences and Technology (NTNU) model developed by Bruland [17] and recently updated by Macias [62], and the QTBM [11]. Other models have also been developed ranging from single factor models [25], [41] to multi-factor models [2], [4], [8], [16], [20], [21], [22], [26], [30], [31], [40], [45], [46], [47], [48], [49], [51], [55], [59], [61], [62], [64], [69], [71], [72], [74], [75], [76], [77], [78], [79], [82], [83], [84], [89], [90], [91], [92], [93], [94], [98], [99], [100], [101]. In addition, some researchers have tried to apply soft-computing solutions to the problem of TBM performance prediction mostly based on artificial intelligence (AI) techniques [1], [5], [6], [7], [15], [33], [37], [38], [63], [65], [67], [68], [87], [88] which resulted in development of kinds of black boxes without a practical potential for utilization in future applications, hence referred to as only “predictions” instead of model development attempts.
The present study aims to the prediction of TBM performance in changing rock mass environment with a relatively higher confidence compared to the previous similar models. Therefore, gene expression programming (GEP) [27], as an extension to genetic algorithm (GA) and genetic programming (GP) [10], [58], is utilized as an AI technique for this purpose. It is highly capable of developing functional relationships for predicting a specific output using multiple related inputs. In fact, based on the numerical experiments by Ferreira [29], the GEP approach is considered as an efficient alternative to traditional GP. Recently, there have been several scientific efforts directed at applying GEP to various civil and geotechnical engineering problems such as prediction of soil–water characteristic curve [53], estimation of compressive and tensile strength of different rock types [7], [13], [18], [23], [73], modeling of plate load test moduli of soil [70], predicting settlement induced by tunneling [3], estimation of air flow in a single rock joint [57], modeling of shear strength of concrete columns [14] and so on.
In this paper, the GEP approach is utilized to develop predictive equations for hard rock TBM performance with routine ground properties of tunnel path including intact rock and rock mass properties. The main aim of this recent modeling attempt is to increase the accuracy of estimations. Therefore, for the sake of comparison, a well-known database of TBM performance (the Queens Water Conveyance Tunnel #3, Stage 2, New York City, USA), which has previously been used to develop equations by other authors [2], [89], [90], [91], [92], [93], is selected and utilized in the analyses. Performance of proposed models of this research is directly compared to those of other researchers and the models based on mentioned database are eventually ranked.
Section snippets
Methodology
Genetic Algorithm (GA) was first presented by Holand [50] as an abstraction of biological evolution in the form of a stochastic optimization technique. The GA has then been further developed by Goldberg [39]. Chromosomes as symbolic strings of fixed length are the unique solutions in GA; they are usually evaluated using a fitness function and the algorithm stops once the output requirement is met [19]. Koza [58] presented the Genetic Programming (GP) which is derived from the extended version
Database of TBM performance
In this research, predictive modeling of hard rock TBM performance is to be conducted considering multiple influencing characteristics of the ground. To this end, a database compiled by Yagiz [89] from a hard rock mechanized tunneling project (the Queens Water Conveyance Tunnel #3, Stage 2) is employed which has already been widely used by other researchers for this purpose. Among other reasons for using this database such as the quality of measurements and good sort of influencing parameters,
Verification and discussion of the results
In order to have an idea about the predictive power of the developed GEP models, their performance indicators were compared with that of powerful statistical and soft computing-based models of TBM performance analysis. For the sake of a practical verification, models were chosen from the literature which have developed using the same database of this paper (The Queens Tunnel, No. 3, stage 2, NY, USA) with the exact number of observations (151 data points). This way, precision of the previous
Conclusions
Gene Expression Programming (GEP) is one of the best approaches for complex, nonlinear modeling. As the newest type of circulative algorithm, GEP gets the most of the capabilities of both GA and GP. This approach was utilized in this research to deal with complexity of modeling hard rock TBM performance in changing geological conditions in tunnel path. Enormous number of runs was conducted within an extensive program of modeling procedure in order to achieve the best models ever to describe TBM
Acknowledgements
The authors wish to express their deep sense of gratitude to Prof. Dr. Hanifi Copur, Head of Department of Mining Engineering, Istanbul Technical University (Turkey), for his meticulous suggestions and astute criticism in the revision phase of this article.
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