Study Of Using Random Field Theory In Soil Foundation Reliability Analysis

The engineering design is usually undertaken with a great deal of uncertainties and unknown factors. Therefore, the reliability theory based design method is more advanced and reasonable compared with the traditional determination design method. However, the research and application of using reliability theory in soil foundation design is much more complicated and far behind that in structure engineering at present. The dominant problem is that when designing a soil foundation with the reliability procedure, the calculated reliability index is often too small to be accepted, which gives the corresponding failure probability greater than 10%, even for the foundations that have been proved in safe conditions. The main reason why the theory deviates from actual conditions is that the auto-correlation of soil properties is ignored when using the common statistic method, which results in the over estimated variance of the parameters used for design. In this dissertation, the random field theory is applied to the reliability analysis of foundations in geotechnical engineering and the effect of correlation of soil on probability analysis is studied.According to the random field theory, some theoretical models are established for the soil profiles in Tianjin Harbor based on a large amount of investigation data, including the unit weight, water content, compressibility index and mechanical indexes, such as cohesion and inner frictional angle of foundation soils. Then the stationarity and ergodicity of soil profiles are examed, which should be the basic principle of the random theory. The conception of correlation distance is discussed and two traditional different methods for estimating the correlation distance are compared and studied. It is proved that the results obtained by both methods are approximately the same if the number of samples is large enough. In addition, both methods are improved respectively in order to make the calculation easier and get a more precise result.It is proved that the correlation functions of the random field models for the vertical and horizontal soil profiles in Tianjin Harbor can be expressed with exponential-cosine type and the representative values of correlation distance of local area are provided based on a great deal of calculation and curve fitting.The random field theory is also introduced into the statistical methods for characteristics of shear strength. The improved traditional method, the simplified correlation method and the cross transform method are presented in order that both of the auto-correlation and cross-correlation of the shear strength of soils can be considered in reliability analysis.The irrelated distance is presented as another characteristic parameter for the random field. How to correctly choose the reduction function of variance and how to reasonably apply it to the reliability analysis are discussed in very detail. Thereafter, the principle for determinating the reduction function of variance is presented according to the relationship of correlation distance, irrelated distance and effective depth in soil mechanics. The representative reduction function of variance of local area is put forward based on the statistic analysis on correlation characteristic of typical soil stratum in Tianjin Harbor.The correlation function and reduction function of variance are applied to the probabilistic slope stability analysis and the reliabilities of some practical projects are recalculated. It is proved that the reliability indexes obtained by reducing the variance of shear strength indexes according to the method developed in this thesis agree well with the reliability of practical engineering. The developed method may give guidance to apply the theory of random field to the reliability analysis of soil foundations.