Study On Design Method Of Bridge Foundation In Sloping Ground Based On Strain Wedge Technique

With the implementation of “western development” and “Belt and Road”strategies in China,constructions of expressways and railways in the western mountainous area are developing rapidly,and some routes would inevitably cross the mountains.The complex geological conditions in mountain areas should be considered to ensure the engineering safety and reduce ecological damage.Therefore,many full viaducts or half-way bridges are adopted,pile foundations are constructed in sloping ground in these cases and the bearing characteristics are more complicated than piles in flat ground.So far,there is no corresponding design calculation method in China.This study is a part of the work carried out by grants from Western Transportation Construction Project of Transportation Ministry “Design and Construction Technology for Bridge Pile-column Foundation in High and Steep Cross Slope” and Construction Project of Transportation Ministry “Revision of Code for Design of Ground Base and Foundation of Highway Bridge and Culverts”,and would investigate the bearing mechanism,internal force and deformation of piles in sloping ground to refine the design calculation method.Firstly,the fundamentals of strain wedge technique are introduced and a model for three-dimensional lateral loaded single piles is modelled by finite element analysis software.The strain isoline nephogram of pile-surrounding soil is plotted for the verification of the strain wedge,and the basic parameters of strain wedge are estimated.Some conlusions are summed up as follows: With the increase of the lateral loads atop the pile,the strain in boundary,length and depth of the strain wedge increases,and the amplitude is similar.With the increase of internal friction angle of soil,the strain in boundary increases,the length and depth of strain wedge decrease,the amplitude is similar,and the fan angle does not change obviously.Then,the stability and reasonable pile spacing of anti-slide pile are investigated on the basis of comparisons with anti-slide piles and piles in sloping ground,and the failure mode of lateral loaded rigid piles in sloping ground are presented by finite element limit analysis software.On this basis,the corresponding ultimate failure modes of soil in front of piles under lateral uphill and downhill loads are presented,and the ultimate bearing capacity is derived.The results show that the lateral ultimate bearing ratio of rigid piles in sloping varies little with the cohesive and decreases with the slope angle.The lateral ultimate bearing ratio-slope inclination curve under different internal friction angles is almost straight line,and the boundary is relatively clear.Furthermore,the ratio increases nonlinearly with the slope distance,and it would be independent of the slope distance when the critical slope distance is reached.In addition,a modified strain wedge model and corresponding calculation method are proposed to evaluate the soil resistance in front of piles at the crest on the basis of the strain wedge in flat ground and model for the ultimate bearing capacity in sloping ground.It is calculated by the improved finite beam element method,considering the “P-?” effect,pile-soil interaction and shear modulus of soil.On this basis,the design calculation method of piles in the hillside is presented by employing the soil wedge theory to consider the possible extra earth pressure.The results show that reducing the foundation proportion coefficient(m?=1/2m)is a simple and practical way to analyze piles in sloping ground.It is suitable for predicting the lateral displacement of piles under small lateral loads,although it will underestimate the lateral displacement under large horizontal loads.Moreover,the results evaluated by modified strain wedge method are closer to the numerical results than m method and m?=1/2m method.Finally,a simplified model of the single pile under complex loads in sloping ground is established by considering extra earth pressure behind piles and their bearing characteristics,and the Pasternak two-parameter is employed to consider the influence of soil shear modulus.On this basis,the finite diffenrece solution of the single pile are derived.Furthermore,a simplified model for the analysis of internal forces and deformations of two-pile foundation in sloping ground is presented by considering their bearing characteristics and pile-soil-pile interaction,pile top deformation compatibility and boundary conditions.And the finite difference solution of internal forces and deformations of two-pile foundation in sloping ground is derived by considering “P-?” effect,the effect of tie beams,and continuous conditions between adjacent characteristic sections.