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In this study, mathematical formulations in the form of linear equations and corresponding rules for prediction of scour depth around bridge piers with debris accumulation are presented in Table 4. The proposed MT technique includes six input and one output parameters. MT technique was developed using five rules in the form of linear equations. A schematic diagram of tree-building of the MT approach in the form of rules for prediction of the scour depth around bridge piers with debris accumulation is illustrated in Figure 5. From the diagram, the splitting variable for providing Equations (16) and (17) (first and second LM) is and the corresponding value obtained is 6.93. In addition, with a value of 0.008 was considered as splitting variable for production of the third and fourth LM. In Equations (16) and (17), all input parameters except were taken into account in the prediction of the local scour depth with debris accumulation and also are considerably significant in developing the proposed LM. As well, , , , as input variables contributed in producing Equations (18) and (19) and this indicated these parameters have more important effects in comparison with other ones. In the fifth model (Equation (20)) given by the MT approach, , , and parameters play key roles in prediction of scour depth.
Table 4

General features of the proposed MT approach

Rules of MT approachLMLM no.Equation no.
D/d50 <= 96.429 : | h/D <= 5.892 : | | ΔA <= 6.93 : LM1 
formula
 
(1) (16) 
| | ΔA > 6.93 : LM2 
formula
 
(2) (17) 
| h/D > 5.892 : | | D/b <= 0.008 : LM3 
formula
 
(3) (18) 
| | D/b > 0.008 : LM4 
formula
 
(4) (19) 
D/d50 > 96.429 : LM5 
formula
 
(5) (20) 
Rules of MT approachLMLM no.Equation no.
D/d50 <= 96.429 : | h/D <= 5.892 : | | ΔA <= 6.93 : LM1 
formula
 
(1) (16) 
| | ΔA > 6.93 : LM2 
formula
 
(2) (17) 
| h/D > 5.892 : | | D/b <= 0.008 : LM3 
formula
 
(3) (18) 
| | D/b > 0.008 : LM4 
formula
 
(4) (19) 
D/d50 > 96.429 : LM5 
formula
 
(5) (20) 
Figure 5

Proposed MT structure for prediction of the scour depth around bridge pier with debris accumulation.

Figure 5

Proposed MT structure for prediction of the scour depth around bridge pier with debris accumulation.

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