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SUMMARYRecently, a new type of time step integration algorithms using complex time steps has been proposed. For linear problems, the algorithms are higher order accurate, unconditionally stable and have directly controllable numerical dissipation. Solutions with high accuracy can be generated using large time steps. In this paper, the algorithms are extended to solve non-linear problems. The pseudo-force approach is adopted in treating the non-linear terms. To maintain the solutions accuracy, the pseudo-force is reconstructed by interpolation. Special treatments are required to compute the excitation at the complex time steps. Several numerical examples are analysed. It is observed that the complex time step method can be computationally more e cient than the Newmark method when very accurate numerical solutions are required.

Low-density polyethylene sheets (LDPE) were used in this study to investigate its effectiveness in reducing downdrag on cast in situ piles. Eight model pile pull-out tests were conducted using three reinforced concrete circular model piles with different surface conditions (smooth, smooth with necking and bulging, and rough) in combination with three different LDPE sheet arrangements (one-sheet, two-sheet, and three-sheet). The pile was embedded partially in Ottawa sand with a surcharge of 19.3 kPa on sand surface. The test results showed that an arrangement with 3 pieces of 0.25-mm thick LDPE sheet was most effective in reducing side friction up to an average of 89 %. It was also found that the effectiveness of LDPE sheets is independent of the concrete surface roughness. However, the presence of necking and bulging was found to increase the side resistance up to 40 % for the plain pile without LDPE sheets.