| Pile foundations with high pile cap are widely adopted as the first choice offoundation style in many key projects such as highway and railway bridgespassing over valleys or large rivers, due to its merits of high bearing capacity,small masonry and convenience for construction. This kind of high-pile-cap pilefoundation is most likely to generate large dynamic displacement, even thebuckling failure under the application of static loads comprising of the upperstructure loads and the self-weight of the foundation incorporating with thedynamic loads induced by the impact and the brake resistance of the vehicles orthe power equipments in motion, the wind, the wave and the earthquake. Theresulted engineering accident is often sudden that will bring about serverconsequence. It has become a hotspot issue with important significance both intheoretical and practical region focusing on the dynamic behavior of pilefoundation subjected to dynamic loads.For this end, based on the three-dimensional continuous medium model, theLaplace Transformation was introduced to convert the time domain issue ofpile-soil vertical vibration to the frequency domain of steady vibration and solvefor the dynamic impedance, the displacement and the frequency domain functionof velocity at the pile top of pile with steady vibration in homogeneous subsoil.The Inverse Fourier Transformation and the Convolution Theorem weresubsequently applied to derive the semi-analytical solution of the time domainresponse. The comparative analysis with the case example indicates that thelength-diameter ratio, the embedded ratio and the pile-soil wave velocity ratiohave a significant influence on the dynamic response at pile top, while otherparameters affect with a slight extent.Considering the heterogeneity of surrounding subsoil and the uncertainty ofthe constraints at the pile end, the stress dispersion effect of the soil at the pileend and the softening effect of the subsoil were incorporated into thethree-dimensional continuous medium model to derive the dynamic impedance,the displacement and the frequency domain function of velocity at pile top ofhigh-pile-cap pile. The Inverse Fourier Transformation and the ConvolutionTheorem were subsequently applied to derive the corresponding semi-analytical solution of the time domain response. The case study suggests that, theinfluence of the magnitude of the spreading angle for the soil stress on thedynamic response at pile top increases with the strengthening of the extent ofconstruction disturbance of the subsoil under pile toe.In order to investigate the stability of the vertical vibration for the pile, theenergy approach and the Hamilton Principle as well as the simplified flexuralfunction of pile body were introduced to establish the Mathieu equations for thedynamic stability of pile under the action of the harmonic loads, in which thehorizontal resistance model was calculated by the m approach and C approach,respectively. The Inverse Fourier Transformation and the Convolution Theoremwere subsequently applied to derive the corresponding semi-analytical solutionof the time domain response. The comparative analysis with the case historydemonstrates that, with the increasing of the length-diameter ratio, thedecreasing of the embedded ratio, the lengthening of the free section and thesoftening of the surrounding soil strength, the area of the instable dynamicregion of the pile will increase. On the contrary, the fixed loads P0affectsslightly. The above-mentioned change rules agree well with the engineeringpractice.The results of the laboratory model test for the dynamic response of thepile was used to verify the parametric resonance of the pile with the variousembedded ratios under the boundary condition of fixed constraint at both pileends. The calculated critical frequency of the external loads using the techniqueproposed in this paper when undergoing the parametric resonance of the pile isslightly larger than the measured data from the test. This difference can beadjusted by introducing a reduction factor k with the magnitude range of0.5-0.8,in which a bigger amplitude of dynamic load along with a deeper surroundingsubsoil will yield a smaller value of the k. |
