Study On Cavity Expansion And Its Applications To Cone Penetration Test

The cone penetration test (CPT) has been used for decades to investigate the propertiesof soil in situ. It has been increasingly used because of important advantages it offers, such assimplicity, speed, and continuous profiling. Compared with other methods, it can providemore accurate properties of soil due to lower disturbance to soil in practice. Essentially, thetest consists of pushing a penetrometer with a standard geometry into the soil at a certain rate,while measuring a number of quantities which include the values of cone resistance q_c, porepressureâ–³u and the friction along a lateral sleeve f_s. Among the three measured parameters,the cone resistance q_c is adopted more widely. The versatility has further promoted the use ofthe CPT, but an important under-utilized advantage of the CPT is that the penetration processis amenable to theoretical model. This paper presents a theory based on cavity expansionanalysis for determining the cone tip resistance in sand, while including the effect ofintermediate principle stress on the strength of soil, which is necessary in practice engineering.Aditionally, cavity expansion analysis plays a significant role in modern soil mechanics. Theanalysis of many of the most important problems in the practice of geotechnical engineering(such as cone penetration testing, pile loading, or pressuremeter testing) rely to a large extenton cavity expansion analyses. Over the years, study on penetration mechanism of conepenetration testing limited to the rigid-plastic theory only considering pure sheafing. In orderto more reasonably interpret the results of the cone penetration whose mechanism results fromboth the plastic failure of the soil around the cone and outer elastic deformation, another goalof the paper is to develop and refine the cavity expansion theory. The main investigations andachievements are composed of following portions.1. Study on cavity expansion theoryIn order to incorporate the strain-softening and shear dilatation behavior of geomaterialsin the analysis, a strain-softening stress-strain model with stress-dropping and a simplifiedmodel ofε_v-ε₁ andε₃-ε₁ are adopted. Based on the extended spatial mobilization plane(SMP) theory and the governing equations of axial symmetry in the plane strain condition, thepartial differential equations for the boundary-value problem of cavity expansion in bothcohesive and cohesiveless soil are established and the closed-form solutions of stresses,strains, displacements in the elastic and plastic regions are obtained. Consequently, the maximum radius of plastic boundary and ultimate cavity pressure are solved for cylindricalcavity expansion in finite mass. Based on numerical results, the strain-softening rate and theeffects of soil dilatancy on expansion of cylindrical cavity are examined. Also comparativestudies are made for the present solution and current solution based on Mohr-Coulombcriterion in order to explain the effect of mediated principal stress. The result indicates thatthe effects of the strain-softening, the shear dilatation and the intermediate stress are obvious.Furthermore, in order to consider the effects of the large strain on the cavity expansion,logarithmic strain is adopted. Additionally, non-associated flow rule is used so as to introducethe effect of shear dilatation of soil and plastic flow in the plastic area. Based on the extendedspatial mobilization plane (SMP) theory, the governing equations of axial symmetry in theplane strain condition, and a strain-softening stress-strain model with stress-dropping, thepartial differential equations for the boundary-value problem of cavity expansion in cohesivesoil are established and the closed-form solutions of stresses, strains, displacements in theelastic and the solutions of stresses in plastic regions, and cavity expansion ratio r_u/r₀ areobtained. For comparison, the displacement formula from small strain theory is also given.The influences of using large or small strain theory, different dilation angles, differentsoftening extent were discussed. The analysis results show that using large strain theory isnecessary in case of relatively great expansion pressure, because using small strain theoryresults in great error; that higher extent of soil softening leads to greater expansion ratio,greater dilation angle leads to smaller expansion ratio under the same expansion pressure.Also comparative studies are made for the present solution and current solution based onMohr-Coulomb criterion in order to explain the effect of mediated principal stress.Consequently, one more time, the result proves the effects of the strain-softening, the sheardilatation and the intermediate stress on cavity expansion under large strain condition.2. Study on the approximate theory for cone resistanceCone resistance plays a very important role to obtain the properties of soil in conepenetration tests. This paper presents a general review of some presently available theories forcone penetration analysis, based on both bearing capacity theory and cavity expansion theory.Meanwhile, the applicabilities of the various reviewed method are compared. The resultsindicate that bearing capacity theory is simple, but it can not be used to simulate accuratelythe deep penetration of cone because it ignore the compressibility of soil and the increase ofthe intial stresses around the shaft. The theoretical cone factors based on bearing capacity wasproved to be smaller that experimental results. And cavity expansion theory is a simple andmore accurate method of analyzing cone penetration. The comparative study indicates that thecone factor depending on cylindrical cavity expansion, agrees well with with the cone factor observed in the field. It also shows that cylindrical cavity expansion theory is more suitable toestablish the theory for cone resistance than spherical cavity theory.In order to include the effect of intermediate principle stress, the spatial mobilizationplane (SMP) theory is adopted. Based on incremental elastic-plastic model to consider boththe incremental shearing dilation of sand under the large strain in the plastic area and thecompressibility of sand under the small strain in outer elastic area, together with thegoverning equations of the cylindrical cavity expansion, the approximate solutions for bothcritical depth in cone penetration tests and cone resistance below the critical are established.Meanwhile, the solutions are also obtained, based on Mohr-Coulomb failure criteria andcylindrical cavity expansion theory. By comparison among the solutions from three differenttheory, the results show that the solutions based on SMP criteria and cylindrical cavityexpansion theory agree best with the experimental results, the solutions based onMohr-Coulomb failure criteria and cylindrical cavity expansion theory are lower, thesolutions based on Mohr-Coulomb failure criteria and spherical expansion theory need to bemodified to go well.The finite software ABAQUS is applied to analyze the stress and displacement fieldaround the cone tip and along the cone shaft, considering the large strain and small strain ofsoil body respectively due to the penetration of the cone penetrometer. Moreover, the effectsof some soil parameters, the different strain definition, the penetrating depth, and the sizes ofcone on the various responses in the soil are discussed.