S - Kam Ng PhD Dissertation Final.pdf - Digital Repository of CCEE ...

Soil Resistance (R)40A’x’q Q=Quake = QuakeAStatic + DynamicS=Permanent SetBR u J s v pStressxR s J s v pStaticRxR s = K xR uRuOCStrainxSQqDeformationFigure 2.7: Stress strain diagram of the soil resistance at a pile point (after Coyle and Gibson,1970 and Smith, 1962).Smith (1962) described that the velocity of any particular pile segment at anyparticular time interval produces a displacement, which serves as a boundary condition forthe next time interval. Then, the displacements of two adjacent pile segments produce acompression in the spring between them and create a spring force. The spring force and theresistance acting on the particular segment produce a net force. This net force accelerates ordecelerates the segment and produces a new velocity which in turn produces a newdisplacement in the next succeeding time interval. This process is repeated for each segmentand each spring at each time interval until all downward velocities are dissipated. Thedisplacement of a pile given by Smith can be expressed by Eq. (2.17). The shaft resistancealongside of a pile can be expressed by Eq. (2.18), and the toe resistance can be expressed byEq. (2.19). The difference between the pile displacement and the corresponding grounddisplacement (D – D′) is represented by a soil quake (q). Soil quake along shaft (q s ) and soilquake at toe (q T ) are denoted to describe the difference in deformation alongside of a pile( ) and at the pile toe ( ), respectively.