Ship Bow Force-Deformation Curves for Ship-Impact Demand of Bridges considering Effect of Pile-Cap Depth

<table>Comparison of<i> P-a</i> curves for different shape impactors. The numerical model of the flat impactor is shown in Figure <a href="../fig10/#a">10(a)</a> at the depth of <svg height="12.4375" id="M113" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 48.512501 12.4375" width="48.512501" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,12.162)"><path d="M499 88q-41 -46 -83.5 -73t-68.5 -27q-41 0 -19 98l52 225q10 43 8 59.5t-16 16.5q-37 0 -112 -65t-117 -135q-14 -42 -38 -179q-36 -7 -75 -20l-7 8l127 594q8 40 2.5 49t-35.5 9h-35l5 25q36 3 71.5 13t56.5 18t25 8q11 0 3 -38l-88 -417h2q77 102 195 167q44 24 79 24
q61 0 30 -130l-52 -220q-8 -33 4 -33q8 0 31 14.5t43 33.5z" id="x210E"></path></g><g transform="matrix(.017,-0,0,-.017,13.543,12.162)"><path d="M535 323h-483v50h483v-50zM535 138h-483v50h483v-50z" id="x3D"></path></g><g transform="matrix(.017,-0,0,-.017,28.246,12.162)"><path d="M456 178h-96v-72q0 -51 12.5 -62.5t72.5 -16.5v-27h-256v27q65 5 78 17t13 62v72h-260v28q182 271 300 426h40v-407h96v-47zM280 225v295h-2q-107 -148 -196 -295h198z" id="x34"></path></g><g transform="matrix(.017,-0,0,-.017,36.406,12.162)"><path d="M113 -12q-24 0 -39.5 16t-15.5 42q0 24 16 40.5t40 16.5t40 -16.5t16 -40.5q0 -26 -16 -42t-41 -16z" id="x2E"></path></g><g transform="matrix(.017,-0,0,-.017,40.282,12.162)"><path d="M241 635q53 0 94 -28.5t63.5 -76t33.5 -102.5t11 -116q0 -58 -11 -112.5t-34 -103.5t-63.5 -78.5t-94.5 -29.5t-95 28t-64.5 75t-34.5 102.5t-11 118.5q0 58 11.5 112.5t34.5 103t64.5 78t95.5 29.5zM238 602q-32 0 -55.5 -25t-35.5 -68t-17.5 -91t-5.5 -105
q0 -76 10 -138.5t37 -107.5t69 -45q32 0 55.5 25t35.5 68.5t17.5 91.5t5.5 105t-5.5 105.5t-18 92t-36 68t-56.5 24.5z" id="x30"></path></g>
</svg> m; the numerical model of circular impactor is presented in the above figure at <svg height="12.4375" id="M114" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 48.512501 12.4375" width="48.512501" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,12.162)"><path d="M499 88q-41 -46 -83.5 -73t-68.5 -27q-41 0 -19 98l52 225q10 43 8 59.5t-16 16.5q-37 0 -112 -65t-117 -135q-14 -42 -38 -179q-36 -7 -75 -20l-7 8l127 594q8 40 2.5 49t-35.5 9h-35l5 25q36 3 71.5 13t56.5 18t25 8q11 0 3 -38l-88 -417h2q77 102 195 167q44 24 79 24
q61 0 30 -130l-52 -220q-8 -33 4 -33q8 0 31 14.5t43 33.5z" id="x210E"></path></g><g transform="matrix(.017,-0,0,-.017,13.543,12.162)"><path d="M535 323h-483v50h483v-50zM535 138h-483v50h483v-50z" id="x3D"></path></g><g transform="matrix(.017,-0,0,-.017,28.246,12.162)"><path d="M456 178h-96v-72q0 -51 12.5 -62.5t72.5 -16.5v-27h-256v27q65 5 78 17t13 62v72h-260v28q182 271 300 426h40v-407h96v-47zM280 225v295h-2q-107 -148 -196 -295h198z" id="x34"></path></g><g transform="matrix(.017,-0,0,-.017,36.406,12.162)"><path d="M113 -12q-24 0 -39.5 16t-15.5 42q0 24 16 40.5t40 16.5t40 -16.5t16 -40.5q0 -26 -16 -42t-41 -16z" id="x2E"></path></g><g transform="matrix(.017,-0,0,-.017,40.282,12.162)"><path d="M241 635q53 0 94 -28.5t63.5 -76t33.5 -102.5t11 -116q0 -58 -11 -112.5t-34 -103.5t-63.5 -78.5t-94.5 -29.5t-95 28t-64.5 75t-34.5 102.5t-11 118.5q0 58 11.5 112.5t34.5 103t64.5 78t95.5 29.5zM238 602q-32 0 -55.5 -25t-35.5 -68t-17.5 -91t-5.5 -105
q0 -76 10 -138.5t37 -107.5t69 -45q32 0 55.5 25t35.5 68.5t17.5 91.5t5.5 105t-5.5 105.5t-18 92t-36 68t-56.5 24.5z" id="x30"></path></g>
</svg> m and the diameter of 9.4 m.</table>

Shock and Vibration

fig12

Figure 12

Figure 12: Ship Bow Force-Deformation Curves for Ship-Impact Demand of Bridges considering Effect of Pile-Cap Depth 