## 4 Understanding of TBM Performance
### Current Developments in Performance Prediction
#### 4.2.2 Empirical Model  
Empirical formulas have proven to be valuable tools during the feasibility, design, and construction stages of a project, as they are more practical and easier for construction personnel to understand compared to theoretical analyses. In geotechnical engineering, empirical formulas based on statistics are widely used to predict target variables. Empirical models can be broadly categorized into two main groups, simple and complex models. Sim  
Figure 6: Classification of TBM performance prediction models.  
ple empirical models typically consider only one or two rock mechanical parameters, such as uniaxial tensile strength, compressive strength, or hardness of the rock, for simplicity and convenience. For instance, [PERSON] [42] estimated the total rock hardness using Schmidt hammer bounce hardness and Tabor abrasion hardness and examined the relationship between PR and total hardness for limestones, shales, and sandstones with a total hardness ranging from 2 to 242. [PERSON] [43] developed a calculation formula by considering the cutter feed per revolution as a function of the single cutter thrust and the uniaxial compressive strength of the rock. [PERSON] and [PERSON] [7] proposed a prediction model based on eight examples of TBM tunnel construction performance data and geological information, which uses the average single cutter thrust and the rock tensile strength to calculate the cutter feed per revolution. [PERSON] [44] studied the relationship between rock structure scoring (RSR) systems and TBM performance, while [PERSON] et al. [8] enhanced the model proposed by [PERSON] [44] based on five TBM tunnel construction performance data sets and geological information, using 112 sets of valid data obtained from a 19 km tunnel. The upgraded model considered the effect of uniaxial compressive strength of the rock in the PR prediction model. [PERSON] et al. [5] developed a TBM feed per revolution prediction model based on four sedimentary rock TBM tunnelling performance data sets and geological information, and they found that PR was not only related to rock type, but also to the single cutter thrust. They therefore proposed a correlation formula between total rock hardness and in situ penetration index. Based on construction performance data and geological information from two TBM tunnels in Australia, [PERSON] [45] showed that PR could be well predicted using Schmidt hammer bounce hardness, total TBM thrust, NCB indentation hardness, and shear angle. However, these simple models are now mostly obsolete due to their low predictive accuracy.  
Empirical models developed at a later stage have created a large database of TBM performance by collecting numerous rock and machine parameters and using advanced techniques such as multiple regression analysis, fuzzy mathematics, and neural networks to develop complex empirical models. Well-known examples include the NTNU model [4], probabilistic model [5], [PERSON] model [6], neuro-fuzzy model [30], [PERSON] model [46], and special case model [47; 48; 49]. Furthermore, some researchers have attempted to develop new rock excavatability grading systems by linking TBM performance to rock excavatability grading systems, based on the concept of rock quality grading. Examples of such systems include the QTBM model [50] and the RME model [51; 52].