Title

在簡單應力狀態下探討具空間變異性土壤的整體剪力強度

Translated Titles

On overall shear strengths of soil masses under simple stress states

DOI

10.6342/NTU.2012.02263

Authors

高炳勳

Key Words

隨機場 ; 空間變異性 ; 剪力強度 ; 關聯性長度 ; 有限元素分析 ; random field ; spatial variability ; shear strength ; scale of fluctuation ; finite element analysis

PublicationName

臺灣大學土木工程學研究所學位論文

Volume or Term/Year and Month of Publication

2012年

Academic Degree Category

碩士

Advisor

卿建業

Content Language

繁體中文

Chinese Abstract

土壤的剪力強度是具有空間變異性的,大部分的大地工程問題中,阻抗力是由土體的整體剪力強度所提供,通常會和整個特定區域的空間平均有關,舉例來說,土堤可以分為三個區塊(主動、漸變及被動),整體剪力強度及為此三區塊之平均。 具空間變異性的土壤性質可以用隨機場模型來模擬,隨機場模型為隨機函數所構成,可藉由改變固有期望值(Mean)、固有變異性(Variance)以及關聯性長度(Scale of fluctuation)產生不同的隨機場模型,Vanmarcke (1977)提出了隨機場區域內之平均特性,期望值會和固有期望值相同,變異性會小於固有變異性,此理論純粹為統計上之性質並沒有考慮到土體的力學機制,而土體的整體剪力強度卻是需要考慮力學機制的,因此本研究首先將利用有限元素分析釐清整體剪力強度和Vanmarcke (1977)所述之空間平均值的差異。 藉由MATLAB 及 ABAQUS等數值軟體進行模擬得到的樣本,本研究將提出一套簡單的公式,可以用來預估在單一應力狀態下具空間變異性土體的整體剪力強度之期望值及變異性,此公式可以清楚說明,在不同應力狀態下(軸向加壓或純剪力)及不同空間變異性分布(均向或層狀土壤),整體剪力強度之複雜行為,有兩個主要因素影響整體剪力強度:(1)沿潛在滑動面上之線平均效應,(b)不確定的破壞面路徑,從研究中可以推得真實滑動面即為許多潛在滑動面中之最小的線平均值,以及臨界關聯性長度是由這兩個因素互相制衡所造成。

English Abstract

Soil shear strengths vary in space. For most foundation engineering problems, resistances provided by soil mass are the overall shear strengths, which are typically related to spatial averaging over certain region. For example, the failure region for an embankment typically consists of three regions (active, transient, and passive), and the overall resistance is related to the averaging over these three regions. Spatial variabilities of soil properties can be simulated by random fields. Random fields are consisted by random functions and modeled by inherent mean value, inherent variance, and scale of fluctuation. Vanmarcke (1977) showed that the averaged property of a random field over a region has mean value identical to the inherent mean, while the variance of the average is less than the inherent variance. Vanmarcke’s theories of spatial averaging are purely statistical, not involving mechanisms. However, the overall shear strength of a soil mass should be governed by the mechanisms, hence the first purpose of this study is to understand the difference between the spatial average of Vanmarcke’s theories and the overall shear strength. After simulating the samples from MATLAB and ABAQUS, this study proposes a set of simple equations to predict the mean value and variance of the overall shear strength for spatially variable soil masses subjected to uniform stress states. These equations are rather effective in explaining the complicated behaviors for the overall shear strengths, regardless of stress states (e.g., compression or shear), spatial variability patterns (e.g., isotropic or anisotropic). Two factors that affect the behaviors of the overall shear strength are identified: (a) the line averaging effect along the potential slip curves, and (b) uncertain failure path, It is shown that the slip curve is associated with the minimum line averaged strength of potential slip curves, and the critical scale of fluctuation is the result of the tradeoff between these two factors.

Topic Category 工學院 > 土木工程學研究所
工程學 > 土木與建築工程
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Times Cited
  1. 林群詔(2013)。探討空間變異性下Φ=0°土壤的整體剪力強度分佈形式。臺灣大學土木工程學研究所學位論文。2013。1-98。