Study On Linear S-lnr Relation Of Regional Land Subsidence From Groundwater Withdrawl

Regional land subsidence from groundwater withdrawal is a very important global geologic hazard.The current literature about land subsidence from groundwater withdrawal are numerous.Some of which applying numerical computing methods can involve nonlinear constitutive relationship and complicated boundary conditions.Most of which based on layerwise summation method cannot considering frictional resistance caused by displacement difference.The rules of soil subsidence from groundwater pumping cannot be verified through case studies.The rule of s-lnr linear relationship of soil subsidence has been proved by several measured data at home and abroad.This rule of land subsidence in this paper can be used to predict vertical displacement for concerning points.It has comprehensive applications in engineering and practice.The governing equation were founded for the soil element in cylindrical coordinate with the assumption that the relation of soil deformation and load is one dimension and linear.The increase of effective stress comes from the decline of groundwater level and frictional resistance.Combining and solving differential equations,the approximate analytical solution shows that the relationship between soil subsidence and the logarithm of distance is linear.One of the main works in subsidence research is monitoring and forecast of land subsidence for control post.On the basis of subsidence formula for one pumping well,using superposition principle of linear differential equation,the regional land subsidence for group pumping wells was deduced,which has linear s-lnr relation.In spite of influence of complex geological structure,the subsidence funnel are not regular,linear s-lnr relation exist in every case referenced.The relation between land subsidence and pumping discharge is a key issue in the research of regional land subsidence from groundwater withdrawal.During the derivation of linear s-lnr relation:s?28?c₁?10?c₂ln r,it was found that the constant c₁?c₂and pumping discharge Q accord to the linear equations:c₁?28?k₁ Q?10?m₁ and c₂?28?k₂ Q?10?m₂.These two equations were proved by measured data from literature.The result of this paper is simple and applicable.The constant c₁?c₂ can be obtained by regression analysis from long-term monitoring data at one subsidence zone.