根據圓錐貫入試驗資料判識土壤層面與分析工址的機率特性

Stratigraphic profiling and probabilistic site characterization based on cone penetration test

王俊翔(Jiun-Shiang Wang)

指導教授 ： 卿建業

國立臺灣大學/工學院/土木工程學研究所/碩士(2016年)

https://doi.org/10.6342/NTU201601155

摘要

在大地工程也逐漸步入可靠度分析與設計 (Reliability Analysis & Reliability-based Design) 後，如何估計土壤設計參數的隨機場參數便成為不可忽視的議題。然而，對於不同種類的土壤所需考慮的工程設計參數並不相同，必須先進行土壤分層，再估計各層土壤所需的工程參數的隨機場參數，才能進行設計。本研究提出以圓錐貫入試驗 (CPTu) 資料為基準進行土壤分層的方法，並與文獻中的方法比較，再討論各種估計方法對於土壤設計參數隨機場的適用性及使用上的穩健性與方便性。
首先將CPTu資料轉換成土壤行為指數Ic (Soil Behavior type, SBTn, index) (Robertson 1990)，再利用小波轉換 (wavelet transform) 來辨識層面位置；現行分層的方法如群法 (clustering; Liao & Mayne 2007)、模糊方法 (fuzzy approach; Zhang & Tumay 1999)、學生檢定統計量法 (T ratio method; Wickremesinghe & Campanella 1991) 與貝氏分析法 (Bayesian method; Wang et al. 2013) 等都有其弱點，如群法的群數需要人為判斷，分層結果會受到人為主觀因素影響；貝氏分析法則是運算量過大、理論較抽象，於工程實務中不易於實際操作。本研究為提升分層演算法之可行性及實用性，選用Wavelet Transform Modulus Maxima (WTMM) 作為演算法。小波轉換利用一連串大小不同的尺度 (scale) 之基底函數 (basis function) 計算出的轉換頻譜 (spectrum)，能夠有效偵測Ic函數中的不連續點，也就是土層的交界面的高程位置。WTMM法的演算過程，不需要太多的人為主觀判斷，計算量也較貝氏分析小許多，其分層解析度也能依照工程師的需求調整，在工程使用上有更高的實用性；本研究也以Texas A&M的黏土工址和臺灣鹿港鎮的砂-黏土互層工址為分析案例，比較上述分析法與WTMM法的優劣與討論它們之間的差異。
相較於土壤分層的議題，估計隨機場參數所能用的資料往往非常稀少，使得分析工址的機率特性 (probabilistic site characterization) 變得十分困難。本研究旨在於現有的理論方法中找出一個以圓錐貫入試驗資料為基底，估計工址中砂土有效摩擦角，與黏土不排水剪力強度之隨機場參數的最有效方法。統計估計理論主要分成兩個學派：相對頻率派 (relative frequency; frequentist) 與相信程度派 (degree of belief; Bayesian)，Ching 等人 (Ching et al. 2015) 從兩派中各選擇兩種估計法，檢驗在不同的資料量之下，估計行為是否仍保持一致性的數值實驗：最大概似法 (maximum likelihood) 與自助取樣法 (bootstrap) 屬於相對頻率派；最大事後機率法 (maximum a posteriori) 與馬可夫鏈蒙地卡羅法 (Markov chain Monte Carlo method, MCMC) 則歸屬相信程度派；研究結果顯示：相信程度派的一致性較相對頻率派高，而馬可夫鏈蒙地卡羅法在四種方法中一致性最高，即使在少量資料的情況下也不例外。而在馬可夫鏈蒙地卡羅法的架構中，有許多不同實作技術的演算法，本研究選擇最常為人使用的Metropolis - Hasting algorithm (MH algorithm)，與Ching and Chen (Ching and Chen 2007) 提出的漸進式馬可夫鏈蒙地卡羅法 (transitional MCMC, TMCMC) 比較，發現TMCMC於實際應用上較為方便，也能維持估計的一致性，還能估計資料對不同的模型的配適度，進而進行模型選擇 (model class selection)，於實務上有較高的使用性。
而後，Betz 等人 (Betz et al. 2016) 於2016年提出一系列對TMCMC演算法改進的措施，將新的演算法稱為iTMCMC。本研究參考其提出的修改措施，討論採用不同組合的方案修改的演算法在雙峰議題、高維度問題，及土壤參數的隨機場估計議題的表現進行比較與討論，進一步提出改善過的TMCMC演算法，於本研究中稱其為wTMCMC。
本研究透過上述一連串的研究整理出下述利用CPTu結果估計可靠度設計所需的參數之流程：首先將CPTu資料轉成Ic值，利用WTMM法分離出土壤層面，進而判斷土壤種類；而後利用wTMCMC估計相對應土壤種類之設計參數的隨機場，便可依照CPTu資料完成可靠度設計所需估計參數。

關鍵字

圓錐貫入試驗 ； 工址調查 ； 土壤分層 ； 小波轉換 ； 統計不確定性 ； 漸進式馬可夫鏈蒙地卡羅法

並列摘要

As the reliability analysis and reliability-based design become more popular in geotechnical engineering, it attracts much attention and can not be ignored that how to estimate the random field parameters of specific geotechnical parameters in geotechnical design. In practice, the design parameters for sands and for clays are totally different. Thus, we should get the information about the underground profiling and the distribution of soil layers before we start to estimate the random field parameters for the design parameters we need. In this study, a stratigraphic profiling approach is proposed with some comparison with others appearing in the previous literatures, and a robust and convenient algorithm for probabilistic site characterization in geotechnical design parameters is introduced.
In the afore part of this study, one stratigraphic profiling approach is proposed based on the soil behavior type index, Ic, obtained from cone penetration tests (CPT). Different from other methods’ in the literature, the basic idea of this approach is simple: the layer boundaries can be identified as the points at which a change occurs in the Ic profile. It is shown that these change points can be easily identified using the wavelet transform modulus maxima (WTMM) method. This method is able to accurately pinpoint the locations of change points in the Ic profile and to produce graphs and plots that fit well with engineers’ methods of visualization and intuition. Moreover, by virtue of the fast Fourier transform, the computation is very fast. Case studies show that the WTMM method is effective for the detection of change points in the Ic profile. It is also capable of detecting thin soil layers.
Another, this study applies the transitional Markov chain Monte Carlo (TMCMC) algorithm to probabilistic site characterization problems. The purpose is to characterize the statistical uncertainties in the spatial variability parameters based on the cone penetration test (CPT) dataset. The spatial variability parameters of interest include the trend function, standard deviation and scale of fluctuation for the spatial variability, and so on. In contrast to the Metropolis–Hastings (MH) algorithm, the TMCMC algorithm is a tune-free algorithm: it does not require the specification of the proposal probability density function (PDF), hence there is no need to tune the proposal PDF. Also, there is no burn-in period to worry about, and the convergence issue is mild for TMCMC because the samples spread widely. Moreover, it can estimate the model evidence, a quantity essential for Bayesian model comparison, without extra computation cost. The effectiveness for the TMCMC algorithm in probabilistic site characterization for geotechnical design parameters is demonstrated through simulated examples and a real case study.
Besides, Betz et al. (Betz et al. 2016) have proposed several possible modifications to the original transitional Markov chain Monte Carlo method. The modifications are applied on original TMCMC method respectively to investigate which ones are really helpful; also, the performance of each modified TMCMC method, including iTMCMC, on probabilistic site characterization is surveyed.
In conclusion, this study proposed one characterized process based on CPTu dataset, including stratigraphic profiling and probabilistic site characterization. With these underground information and random field parameter of geotechnical design parameters, the reliability analysis and the reliability-based design can be done.

並列關鍵字

site investigation ； cone penetration test ； stratigraphic profiling ； wavelet transform ； probabilistic site characterization ； transitional Markov chain Monte Carlo algorithm

參考文獻

Ahmadi, M. M., and Robertson, P. K. (2005). “Thin-layer effects on the CPT q c measurement.” Canadian Geotechnical Journal, 42(5), 1302–1317.

Ahmed, A., and Soubra, A. H. (2014). “Probabilistic analysis at the serviceability limit state of two neighboring strip footings resting on a spatially random soil.” Structural Safety, 49(1), 2–9.

Betz, W., Papaioannou, I., and Straub, D. (2016). “Transitional Markov Chain Monte Carlo : Observations and Improvements.” Journal of Engineering Mechanics, 142(15), in press.

Bleistein, N., and Handelsman, R. A. (1975). Asymptotic expansions of integrals. Courier Corporation.

Briaud, J. (2000). “The National Geotechnical Experimentation Sites at Texas A&M University: Clay and Sand, A Summary.” National Geotechnical Experimentation Sites, 26–51.