# Review on the Service Safety Assessment of Main Cable of Long Span Multi-Tower Suspension Bridge
## 3 The Contact and Slip Behaviors of the Saddle  
In the aspect of contact between main cable and saddle, [PERSON] et al. [39] developed three nodes space saddle element (Figure 1 in Ref. [39]), and obtained the cable force at the tangent point between main cable and saddle during the contact process. [PERSON] et al. [19,20] and [PERSON] [40] calculated the secondary stress of main cable bent around the saddle under dead and live loads of suspension bridge, respectively. Meanwhile, they found the separation and slip behaviors between steel wires and between strands in the main cable during the bending deformation of main cable, and proposed calculation methods of a layered element model of bent main cable and limited friction force between layers. [PERSON] et al. [41] proposed a cable saddle modeling method in order to finely simulate the separation, contact and slip behaviors between main cable and saddle. He found that, in the case of unbalanced cable force loading, the radial pressure and friction force of the saddle both increase with increasing cable force and increase from the non-loading side to the loading side. [PERSON] [42] established the refined contact model to discuss the lateral force distribution, layered sliding, force transfer mechanism and anti-sliding measures between main cable and saddle groove. He found that the lateral force of cable strand presented a negative exponential convergence curve distribution and the lateral force was the direct factor affecting layered sliding. According to the layered sliding, he proposed that the upper steel wire slipped easily as compared to the lower steel wire. As the bottom steel wire exhibited the gross slip, the cable strand would skid as a whole. It was revealed that settings of vertical and horizontal friction plates could effectively improve the anti-sliding ability of main cable but the application of horizontal friction plate was relatively limited.  
Considering the micro slip between main cable and saddle, [PERSON] et al. [43] established the three-dimensional elastic catenary elements based on micro slip between main cable and saddle (Figure 3 in Ref. [43]). [PERSON] and [PERSON] [44] proposed the criterion of slip time and showed that testing results of relative slip between main cable and saddle at the non-loading side of saddle groove were most sensitive to the slip and could be used as the slip criterion. Meanwhile, they measured the coefficient of friction between main cable and saddle with two or without diaphragms, i.e., 0.473 and 0.552, respectively. [PERSON] [42]explored effects of coefficient of friction, vertical or horizontal diaphragms, cable strand arrangement in the saddle groove on slip characteristics between main cable and saddle through numerical simulation.  
In conclusion, lots of scholars calculated the lateral force and secondary stress of main cable on the saddle, studied the separation, contact and slip behaviors between main cable and saddle, explored separation and slip characteristics of strands and steel wires in main cable during the contact between main cable and saddle, and investigated the effects of coefficient of friction, diaphragm, and cable strand arrangement on static slip characteristics and criteria between main cable and saddle.