The Ultimate Bearing Capacity Of Strip Footings Based On Mohr-coulomb Failure Criterion

The soil is assumed to be a rigid plastic that follows to the associated flow rule,and the ultimate bearing capacity of strip footings on Mohr-coulomb soil is analyzed.The differential equations of slip-line are acquired according to the equilibrium equations at any point in soil.The bearing factor N? is calculated by numerical procedure,and the theoretical solutions of bearing capacity for smooth and rough footings are obtained based on some proper assumptions.Four main contents are focused in this paper:(1)The numerical procedures are written to compute the bearing capacity for smooth and rough footings by finite difference method.The numerical results are analyzed and compared with the values given by other researchers.The errors in calculating the bearing capacity factor N?for some known values are found that primarily result from the researchers'assumptions.The errors of bearing capacity between superposition method and numerical values are then discussed and an evaluation formula is proposed.lt is found the values of bearing capacity are underestimated 16%?24%for smooth footings and 17%?32%for rough footings by superposition method.The influence of surcharge ratio on failure surface and bearing factor N? is analyzed according to the numerical results.An approximate formula considering the surcharge ratio and friction angle simultaneously is proposed.The error between the approximate values and exact solutions are within 3%for smooth footings and 2%for rough footings.(2)The theoretical solutions of bearing capacity considering the weight of soil for smooth footings are deducedby slip-line method and upper-bound method based on some reasonable assumptions that are made in agreement with the numerical calculations.With the proper assumption of slip-line field,the formula of bearing capacity considering soil weight can still be written in classical forms.The bearing capacity factors Nq?Nc are exactly the same as analytic solution given by Prandtl.The formula of bearing capacity factor N? contains both the parameters of surcharge ratio ? and internal friction angle ?.The N? value got by the proposed formula is within an error of 2%compared to the numerical result.The kinematical field is constructed when both the bottom angles of smooth footing base are variable and the upper bound solution of bearing capacity is derived.The upper bound solutions are consistent with the classical ones if the basic angles equal to the traditional values.The upper bound solutions are discussed and the approximate equations are proposed in the circumstance that the two basic angles are equal or the apex angle of action zoneis equal to ?/2-?.(3)Analytical solution of the ultimate bearing capacity of rough stips is deduced with the limit equilibrium method.Assuming the angle of action zone is a variable and the shape of shearing transition zone is a modified logarithmic spiral,the formula of ultimate bearing capacity is then obtained with the consideration of two variables.If the variables are equal to the assumptions made by previous scholars,the solution is consistent with the classic one.When the shearing transition zone is a logarithmic spiral,the minimum values of the ultimate bearing capacity can be obtained by the approximate formula.The errors between the approximations are extremely small compared with exact solutions.The proposed approximate formula considering both surcharge ratio ? and internal friction angle(p is used to fit numerical results of other researchers.The fitting parameters and the approximate curves are compared with the results in this paper.It is proved that the approximate formula has a good fitting result and can be considered as the general formula when consider of the influences of ?and ?.(4)The application of calculating the ultimate bearing capacity and evaluating the safety factors is introduced in two cases:one is a roadbed relying on soft clay and the other is strip footing in a substation.The present computations are compared with the ones calculated by the classic formula.For clay with a relative large cohesion and small friction angle,the difference of calculationsbetween smooth and rough footings is small.As a result,it is useless to improve bearing capacity by increasing the roughness of the footing base.The approaches to improve the safety of foundation is increasing the width of the foundation to reduce the stress of the base or taking ground treatment measures to improve mechanical parameters.For sand soils with large friction angle and cohesionless,there is an obvious difference between the calculations for smooth and rough footing base,which shows that the roughness of footing base has significantly great influence on bearing capacity.In this circumstance,it's effective by enabling the roughness of footing base to improve bearing capacity.