土壤液化係常見的地震衍生災害之一，1999年921地震更是在台灣中部地區造成嚴重的液化災害。有鑑於不確定性及風險是大地工程重要特徵，傳統液化與不會液化的二元表示方式並無法反映該特徵，因此，本研究基於可靠度理論，考量參數及模式的不確定性，發展一個新的土壤年液化機率評估模式。首先，本研究以Youd and Idriss（2001）建議之SPT及CPT簡易液化評估法為基本公式，利用具不變量特性之Hasofer-Lind（1974）可靠度指標進行液化機率計算。茲因在不確定性考量下，隨機變數多達7個，在滿足計算便利及大面積區域的液化評估需求下，本研究提出應用認知巢狀分割方法（knowledge nested partition method; KNPM），以1個長度L及3個角度1、2及3所組成之函數式來表示之7個隨機變數，以建立一個新的且可全搜尋的可靠度指標求解方法，進而計算出液化機率。本研究也以SPT及CPT歷史液化/不液化資料為討論案例，與蒙地卡羅模擬法（@Risk）及迭代逼近法（EXCEL規劃求解）的所得結果比較與驗證後，已顯示本文建立之KNPM所求得之結果具正確性，可達到最佳化，並具程式化之優點。
其次，基於一個嚴謹的可靠度理論架構，液化機率應能同時涵蓋模式及參數的不確定性。因此，本文透過大量歷史液化/不液化案例及現地試驗資料，分別提出模式及參數不確定性的量化方法，並將這些模式及參數的不確定性研究結果代入液化機率評估中。在模式不確定性部份，係根據搜集之SPT及CPT之歷史液化/不液化案例，進行多組不同數量之樣本隨機抽樣及分析，結果顯示Youd and Idriss修正之Seed 簡易法的模式不確定性可以c1= 1.06，COV(c1)= 0.06來表示，而Youd and Idriss修正之Robertson and Wride簡易法的模式不確定性則可以μc1= 1.16，COV(c1)= 0.12來表示，二個評估模式皆屬保守模式；在參數不確定性部份，則以員林及麥寮地區之SPT與CPT現地試驗資料為分析樣本，利用地質統計方法，來量化主要的液化評估參數（包括標準貫入試驗SPT-N值、細料含量、土壤單位重、圓錐貫入試驗CPT-qc值、圓錐貫入摩擦阻抗）之不確定性，分析結果顯示二個區域的不確定性有些許差異，但差異量不大，相當接近，本研究建議可以COV= 0.15、0.14、0.02、0.04、0.14來分別表示N、FC、Wt、qc及fs的不確定性。
綜整上述研究結果（包括可靠度指標求解、模式及參數的不確定性），本研究建立一套新的土壤液化機率評估模式。且基於台灣早期地震災害及相關資料的缺乏，地震引致的年液化機率驗證工作相當困難，本研究藉由與能量消散理論計算所得之年液化機率結果比較，已驗證本研究所建立之年液化機率模式具一定程度正確性。最後以員林地區為研究案例進行結果比較，並評估員林地區在車籠埔斷層及彰化斷層再次錯斷條件下的平均年液化機率（average annual probability of liquefaction; AAPL），車籠埔斷層錯動條件下之AAPL介於0.0007~0.0050間，彰化斷層錯動條件下之AAPL則介於0.0001~0.0021間，最後繪製液化重現期等值線分佈圖，以供區域地震液化防災參考。

Soil liquefaction is one of earthquake-induced hazards. During the 1999 Chi-Chi earthquake, the damage caused by liquefaction was most serious in the central Taiwan. The traditional binary representation, liquefied or non-liquefied, is incapable to reflect the uncertainty and risk, which are the important characters in the geotechnique engineering. Therefore, this paper develops a new evaluation model of annual probability of liquefaction (APL) in the consideration of the uncertainties of soil parameters and model based on the reliability theory. The SPT-based and CPT-based simplified methods suggested by Youd and Idriss (2001), called herein Seed method and RW method, are taken as the basic equations. The reliability index proposed by Hasofer-Lind (1974), that owns the invariable characteristic, is used to calculate the probability of liquefaction. There are seven random variables used under the uncertainty consideration in this paper. For this reason, the knowledge nested partition method (KNPM) is employed to establish a new and global-search method for determining the reliability index in the satisfaction of calculation efficiency and the need to liquefaction evaluation for large areas. Then the functions consisted of one length L and three angles 1、2 and 3 can be used to mean the foregoing seven random variables. Through the liquefied and non-liquefied case histories, analysis results of the KNPM method are compared and verified by the results of Monte Carlo simulation and iteration technique, showing that the calculating results obtained by the KNPM are correct and can reach optimal.
With a rigid framework of the reliability theory, an evaluation of probability of liquefaction has to involve the uncertainties of model and parameters at the same time. The methods to quantify the uncertainties of model and parameters are proposed by way of a great number of case histories and field data, and these quantitative results can be used in the liquefaction probability evaluation. In the model uncertainty, the random sampling and analysis of alternatives, resulted from different quantity of SPT-based and CPT-based case histories are adopted. The SPT-based results revel the uncertainty of Seed’s method can be defined by c1= 1.06 and COV(c1)= 0.06. The CPT-based results demonstrate the uncertainty of RW’s method can be expressed by c1= 1.16 and COV(c1)= 0.12. Both two methods are conservative models. In the soil parameter uncertainties, the SPT-based and CPT-based field data in the Yuanlin and Mailiao areas are taken, and geostatistic method is utilized to quantify the uncertainties of soil parameters, including the standard penetration value (N), fines content (FC), soil weight (Wt), cone tip resistance (qc) and sleeve friction (fs). These results show that the soil parameter uncertainties between two areas have some differences, which are but fairly closer. So, this paper suggests that the soil parameter uncertainties of N、FC、Wt、qc and fs are 0.15, 0.14, 0.02, 0.04 and 0.14, respectively.
To sum up the above-mentioned study results, including the reliability index and uncertainties of model and soil parameters, this paper develops a new evaluation model of probability of soil liquefaction. Owing to the lack of earthquake hazards and related data in early Taiwan, the verification of annual probability of liquefaction induced by earthquake is fairly difficult. By the comparison of the APL calculated from the energy dissipation theory, the proposed model has been proved to possess certain degree of accuracy. Finally, the APL in the Yuanlin area is evaluated subject to future re-reputure of Chelungpu fault and Changhua fault using the proposed model. The average annual probability of liquefaction (AAPL) is also calculated. Theses results show that AAPLs of Chelungpu fault and Changhua fault are 0.0007 to 0.0050 and 0.0001 to 0.0021, individually. The contour of average liquefaction return period is then drawn. In this study, these results can be a reference for regional liquefaction prevention.

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