【作者】 张业民；

【导师】 栾茂田；

【作者基本信息】 大连理工大学 ， 岩土工程， 2008， 博士

【摘要】 自然界中有许多现象都涉及不连续性。微积分学虽成功地解释了光滑的连续变化现象,但对于非连续问题有时就无能为力了。而突变理论是一种能够直接处理不连续性而无须联系任何特殊内在机制的数学工具。这使它特别适用于内部作用尚属未知的系统研究,并适合用于仅有的可信观察具有不连续性的情况。土工中结构突变、失稳、破坏等本身就是一种典型的突变现象。其中应用最多是尖点突变模型,因为它的临界面容易构造,且几何直观性很强。因此,论文主要以尖点突变模型为基础,对土工中突变现象及机理,如边坡失稳、地震液化、硬及软土应力-变形特性等,给予数学描述,并通过试验确定其可供应用的模型。论文主要研究内容及所取得的研究成果包括以下方面:1.应用突变理论尖点模型研究砂土的地震液化模型根据国内外实测液化资料、孔压的各类模型推导出在即将液化时,松土的超静孔隙水压力有突变,而密实土的超静孔隙水压力无突变这一现象,将尖点突变模型成功运用于对地震液化的判断。对Zeeman突变方程进行了重大修改。原始的突变方程是基于Zeeman突变机构得来的,这一模型目前被广泛应用。通过调整各系数可以使孔压、液化的发展更加精确地被方程所反映。通过逐步逼近的方法算出了方程中的参数,同时液化点和分叉曲线也被唯一地确定。通过对国内外液化资料的回判,可以看出此模型有较高的准确性。2.应用突变理论尖点模型研究土的静力工作状态(1)尖点突变模型描述静力载荷试验曲线的可行性及应用研究静力载荷试验主要用于测定承压板下应力主要影响范围内岩土的承载力和变形特性。但其试验时间很长,加载困难,试验结果也难确定。对于较硬土地基而言,当荷载大于某一数值时,基础急剧下降,地基发生突然破坏。而软粘土和松沙地基土的变形是渐变的,没有突变现象。根据静力载荷试验曲线的特点,定性地分析了利用尖点突变模型表达载荷-沉降曲线的可行性。通过坐标变换导出平板载荷试验的载荷-沉降曲线方程在沉降量、施加荷载及承载力因子三维空间中的表达式。根据土的破坏条件,确定出相应参数并建立其尖点突变模型。利用该突变模型对已有的试验进行了预测,预测结果和试验结果吻合较好。(2)尖点突变模型在边坡失稳中的应用研究总结目前国内外判别边坡稳定性的方法、分析各种判别方法的优缺点及适用范围。研究尖点突变模型模拟监测时间一坡体变形速率的可行性,提出用突变模型模拟目前国内外滑坡体实际监测数据思想和方法,并建立模型。结合各滑坡体实际监测数据定性的检验了模型研究的可行性,提出了预测的思想,并通过现有的数据对监测时间一变形速率进行了初步的预测。(3)土本构关系的描述及软粘土流动性的模型研究利用突变理论尖点模型建立的土的本构模型,该模型既可反映软土的渐变破坏,又能拟合硬土的突变破坏,使以往按土的松软或紧硬程度的区别分别建立的各自相应的本构关系,能够统一于同一个模型中。同时,该模型在求解土初始切线弹性模量上达到了实用上要求的精度,并且对土的应力应变路径进行了定性分析。在此基础上,对土尖点模型描述应力应变路径的可行性进行定量分析。通过分析推导和比较,表明突变理论中的尖点突变模型描述土的应力应变路径,在定量和定性上都是合理的,可行的。对饱和粘性土而言,仅当剪应力小于长期强度时,土体才呈现类似理想体那样的规律;而当剪应力小于长期强度时,土在恒定剪力作用下,变形渐趋停止。本文引用尖顶突变模式,建立了γ-τ-t的数学关系式,然后带入数据检验计算结果表明,理论和实测值吻合较好。由此可见该模型是可用的。3.对于建筑结构墙体共振振幅的突变性及细长杆突变失稳中点屈曲位移的研究(1)细长杆突变失稳中点屈曲位移的研究压杆失稳问题是工程中的突变问题。Euler公式基于小变形的近似方法,由于采用了曲率的近似表达式而无法求得中点屈曲位移δ。为此,本文利用突变理论原理及精确的曲率表达式建立了Euler杆在考虑几何非线性时的微分方程,通过算例揭示了压力大于分叉荷载时压力与中点屈曲位移的关系。研究结果表明,当压力达到荷载分叉点时,Euler杆不会立即丧失承载力,其承载力尚有微量的储备。研究结果与实验结果完全吻合。(2)本文还应用自创的共振仪对于建筑结构共振振幅的突变性进行验试印证。由作者申请专利的共振仪通过改变偏心块重量W或调节变频器使起振机电机的转速ω近似于连续变化,就可以使起振机获得不同的激振力。将共振机固定在悬臂梁模型顶部中央,在可调变频的共振机上,通过调节共振机的振动频率装置给系统加载。由试验成果可见,振动过程中顶点振幅存在跳跃现象,也即随着激振力增大,系统具有振幅突变特性。更多还原

【Abstract】 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.更多还原