Study On Shear Strength Of Sand Soil Based On Fractal Theory

The strength of the soil determines the stability of the foundation and has important theoretical reference significance in engineering design and construction.Relevant scholars have conducted theoretical and practical research on the strength of soil,and believe that to some extent,the change of soil pore ratio is one of the important factors that affect its shear strength.As the shearing process progresses,the soil pore ratio is constantly changing,but it is not clear how the physical structure of the soil particles changes.Fractal theory is a mathematical theory method that mainly studies complex or irregular objects in nature.The fractal dimension can quantitatively describe the internal structure of sand soil particles.In this paper,the porosity ratio is used as a functional relationship between the fractal dimension and the shear strength of the bridge,that is,based on the calculation formula of the shear strength of the sand soil based on the fractal theory.The indoor direct shear test is used to verify the feasibility of the formula for calculating the shear strength of sand soil deduced in this paper,which provides a theoretical reference for landslide stability analysis,mining,foundation pit support design and engineering prevention desogn.The main research contents and results of this article are as follows:(1)Fractal theory is a mathematical theoretical method that mainly studies complex or irregular objects in nature.It can describe the self-similarity,irregularity and fragmentation of objects well.Sand is a porous material with randomness and self-similarity,which can be well described quantitatively using fractal theory.As the shearing process proceeds,the pore ratio of the soil changes continuously,and the fractal dimension also changes.In this paper,the functional relationship between the pore ratio and the fractal dimension is derived based on the fractal theory of pore number-size fractal model,and the theoretical functional relationship between the shear strength of the sandy soil and the fractal dimension is established based on the critical state theory,the formula for calculating the shear strength of sand soil is obtained.(2)In order to verify the feasibility of the calculation formula deduced in this paper,this article selects Fujian standard sand for indoor direct shear test,measures the basic physical parameters of Fujian standard sand used in the test before the test,and draws the particle curve through the particle analysis test.Through calculation,the fractal dimension of standard sand can be obtained,and Zi in the derivation formula can be further obtained;the dry density interval of different particle sizes of standard sand can be obtained through specific gravity test and relative density test;different consolidation stress and soil body can be obtained through consolidation test.Through the consolidation test,the relationship between different consolidation stresses and the fractal dimension of the soil is obtained,and the ? in the derivation formula is obtained by function fitting.Finally,the direct shear test is carried out through standard sand with different particle sizes,and the test data is collated and analyzed.(3)Substitute the fractal dimension and physical indexes related to standard sand into the traditional formula of Khalili and the calculation formula derived from this paper,calculate the calculated values of the two formulas and compare with the actual measured values.It is found that the traditional Khalili formula differs greatly from the measured value of the direct shear test because the traditional calculation formula ignores the effect of the change of the void ratio on the shear strength,however,the error between the calculated value and the measured value of the calculation formula of the shear strength of the sand soil based on the fractal theory is smaller,better than traditional calculation formulas.The feasibility of the formula for calculating the shear strength of sand based on fractal theory is verified.