随机场理论在地基可靠度分析中的应用研究
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摘要
工程设计是在存在大量不确定性和某些未知因素的情况下进行的。对于这种不确定性,较之传统采用的定值设计法,可靠度的设计方法更为先进和科学。然而,由于岩土工程的特殊性和复杂性,目前国内外对于地基可靠度的研究与应用远落后于结构工程。其主要原因是算得的可靠度指标过小,对应的失效概率太大,常常超过10%,即使对已证明是安全稳定的工程也是如此。造成这种理论与实际情况背离的主要原因,是由于现在常用的数理统计方法忽略了岩土材料具有自相关性的特点,导致其方差估算偏大。本文针对这一问题,将随机场理论引入岩土工程的地基可靠度分析之中,研究土的相关性在概率分析中对土性的影响。
本文首先根据随机场理论,结合天津港地区的大量现场勘察资料,建立起天津港地基土性剖面的随机场模型,并对其土性剖面的平稳性和各态历经性进行了检验;对现有的求解相关距离的递推空间法和相关函数法进行比较和研究,从理论上证明当样本容量足够大时,两种方法的计算结果可以得到统一;并分别对其作出改进,提出波动函数法、加权拟合相关函数法和拟合折减函数法,使相关距离的计算更加简便易行且精度有所提高。
应用改进的相关函数拟合方法和相关距离计算方法,通过大量计算分析和数值模拟,证明天津港典型土层垂直方向和水平方向的土性剖面随机场的相关函数都为指数余弦型,并通过统计分析得出天津港地区典型土层相关距离的范围值。将随机场理论引入抗剪强度指标的统计方法,提出了按随机场统计的传统法、简化相关法、正交变换法,可分别从不同角度对土性指标的自相关性和互相关性加以考虑。
提出了随机场的另一种特征尺度——“完全不相关距离”的概念;探讨了在土工可靠度计算中如何正确选取并合理应用方差折减函数;并根据相关距离、完全不相关距离、有效影响深度的关系,提出了方差折减函数的确定原则;根据分析统计的天津港地区典型土层的相关特性,确定了本地区标准差折减的范围值。
将研究得到的相关函数和方差折减函数,应用到港口边坡稳定可靠度分析中,重新验算和校核现有工程的安全性指标,分析结果表明随机场理论的应用对地基可靠度起到了重要作用,按照方差折减函数的确定原则对强度指标进行方差折减后得到的可靠度指标与工程的实际安全程度较为匹配,可为港口工程地基可靠度规范的修订提供一定的理论依据。
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.
本文首先根据随机场理论,结合天津港地区的大量现场勘察资料,建立起天津港地基土性剖面的随机场模型,并对其土性剖面的平稳性和各态历经性进行了检验;对现有的求解相关距离的递推空间法和相关函数法进行比较和研究,从理论上证明当样本容量足够大时,两种方法的计算结果可以得到统一;并分别对其作出改进,提出波动函数法、加权拟合相关函数法和拟合折减函数法,使相关距离的计算更加简便易行且精度有所提高。
应用改进的相关函数拟合方法和相关距离计算方法,通过大量计算分析和数值模拟,证明天津港典型土层垂直方向和水平方向的土性剖面随机场的相关函数都为指数余弦型,并通过统计分析得出天津港地区典型土层相关距离的范围值。将随机场理论引入抗剪强度指标的统计方法,提出了按随机场统计的传统法、简化相关法、正交变换法,可分别从不同角度对土性指标的自相关性和互相关性加以考虑。
提出了随机场的另一种特征尺度——“完全不相关距离”的概念;探讨了在土工可靠度计算中如何正确选取并合理应用方差折减函数;并根据相关距离、完全不相关距离、有效影响深度的关系,提出了方差折减函数的确定原则;根据分析统计的天津港地区典型土层的相关特性,确定了本地区标准差折减的范围值。
将研究得到的相关函数和方差折减函数,应用到港口边坡稳定可靠度分析中,重新验算和校核现有工程的安全性指标,分析结果表明随机场理论的应用对地基可靠度起到了重要作用,按照方差折减函数的确定原则对强度指标进行方差折减后得到的可靠度指标与工程的实际安全程度较为匹配,可为港口工程地基可靠度规范的修订提供一定的理论依据。
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.
引文
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