Catastrophe Theory Applied In Several Geo-technic And Structure Engineering Area

Many phenomena in nature are of uncontinuity that can not be interpreted by calculus. While catastrophe theory can deal with uncontinuity directly and it is unnecessary to relate with any special internal mechanism, which makes it especially fit for the system that internal action is unknown and can be used in the condition that believable observation is discontinuous. The structures of geo-technic engineering break and failure are typically discontinuous phenomena. So the application of catastrophe theory in geo-technic engineering is promising to solve the uncontinuity. Especially the cusp model is characterized by simplify and practicality, which has two control variables, one state variable and an attainable critical surface. Therefore, the phenomena and mechanism in soil engineering, such as slope failure, liquefaction induced by earthquake, stress-strain of hard and soft soil, are described and predicted based on the cusp catastrophe models established by experiments data. The main investigations and achievements are composed of following portions.1. Estimation of liquefaction based on catastrophe theoryCusp catastrophe model was applied to construct a model to simulate occurrence of soil liquefaction induced by earthquake. In the proposed model, pore water pressure was looked as a state variable and capability of site anti- liquefaction and received earthquake energy were treated as two control variables. Comparison was made between site earthquake liquefaction information and the results obtained from the proposed method. It is shown that the suggested method is convincing, reliable and practical in the engineering. At the same time, stability problem including any soil body due to critical shear strength can be simulated conveniently. The cusp catastrophe model also has interesting implications for seismic dynamic intensity analysis of soil-structure interaction system and seismic stability analysis of earth dam and slope and so on.2. The applications of cusp model in static soil mehanics and engineering(1)Study on application and prediction of cusp-catastrophe model in plane-plate loading testBased on the property of loading- settlement curve obtained from static loading test, the feasibility of cusp-catastrophe theory applied to the simulation of the curve for plane plate loading test is qualitatively analyzed Through coordinate transformation, a curve equation of plane-plate loading test, which is illustrated in the space of axes settlement, load and factor of bearing capacity for soils is established. According to the failure condition defined by soil deformations, the parameters of model are determined and the model is built up. By analysis of test data, it indicated that the studied model is feasible. The cusp-catastrophe model is applied in the prediction of the relationship between load and settlement of several plane-plate loading experiments. Through comparison and verification, it is displayed that the predicted results by cusp catastrophe model are accordance with the test results in a degree.(2)Study on cusp catastrophe mutation of slope destabilizationIdentification methods of slope destabilization are summarized and theirs characteristic and application are pointed out. The feasibility of monitoring time-slope displacement is studied and the application of cusp model to actual monitored data is suggested. Combined practical data of slope the proposed model is tested, which demonstrates the feasibility. Moreover, the prediction of time-displacement rate is performed.(3)Description of soil constitutive relationship and analysis of flowing rule for soft clay with cusp catastrophe modelSoil constitutive mode that can represent both soft soil's gradual failure and hard soil's abrupt failure is established by using cusp catastrophe theory, which makes the hard and soft's soil model unified in one model. The precision on determining initial shear modulus using the model satisfies practical requirement. Qualitative and quantitive analysis of description of stress-strain relationship for soil with cusp-catastrophe model is made. Analysis and comparison represent that the proposed model is more effective. For saturated soft clay only when the shear stress is greater than the long-term strength, the soil obeys the ideal plastic rule. But when the shear stress is smaller than the long-term strength the deformation of the soil decays gradually under a constant shear stress. A "γ-τ-t" relation with the cusp catastrophe model is proposed which agrees with the test data.3. Get a series test data on the model with the resonant apparatus of own patent and the computation of middle displacement of Euler pole after bucking.(1)The computation of middle displacement of Euler pole after buckingPole's bucking is one of break problem in engineering. When pressure is smaller than bifurcate load, exoteric disturbance will make the pole deviate initial balanceable form. Allowing for non-linearity of Euler's pole, its differential equation by a precise expression of curvature is established. A program is written to compute it. The relationship between the load, when it is larger than critical load and the displacement of mid-pole is obtained. The study shows that Euler's pole does not lose its bearing capacity when the load is added up to the critical one. Its bearing capacity will be strengthened instead. The results agree well with the test.(2) The paper also get a series test results on the model of building structure with the resonant apparatus which the author had his own patent.The resonant apparatus adjusted its deviatonic or the inverter so as to get approximately continuously motor force while the motor roated velocityωcould change to any value in its restrict area .So did the motor force.In the dynmatic experiment, amplitude of the top had justment phenomenon.To that suddenly changed amplitude,the thesis gave a catastrophe theory idea constitution to explain the sudden changing amplitude.