土壤地盤彈塑性分析之組合律建立

Construction of the Constitutive Law for Elastic-Plastic Analysis of Soil Masses

張俊陽(Jun-Yang Chang)

指導教授 ： 張達德

中原大學/工學院/土木工程學系/博士(2006年)

https://doi.org/10.6840/cycu200600524

摘要

臨界狀態理論最早是由英國劍橋大學Roscoe等人在1958年至1963間陸續提出的，稱為劍橋黏土模型。後來Burland於1965年依據能量推導提出修正，稱為修正劍橋黏土模型。目前大地工程界所慣用的有限元素或有限差分程式如ABAQUS、PLAXIS、FLAC等皆內建修正劍橋黏土組合模式，適用於正常壓密與輕度過壓密黏土地盤的深開挖或高填土穩定分析。但實務上，工程監測資料與臨界狀態模型的數值分析結果仍有差異，主要被歸因於模型的屈服函數、流動法則及硬化規律無法準確地描述土壤的塑性流動特性、剪脹性與異向性應力-應變行為，故各國學者對於臨界狀態模型提出修正的研究工作仍不斷的進行中。
本文從熱力學出發，採用連體介質熱力學定義，先辨識等溫變形條件下系統外力作功產生自由能與耗散能的互補關聯；再應用熱力學狀態變數的概念，在自由能勢函數與耗散能勢函數中導入有效應力、彈性應變、塑性應變及塑性應變增量等狀態變數，將熱力學狀態函數描述系統能量轉移軌跡的功能等效應用，據以推導臨界狀態組合模型中屈服條件、流動法則及硬化規律的函數關係。研究方向著重在土壤彈塑性組合模型參數的研選與物理性詮釋，目的是藉著熱力學詮釋的參數導入，拓展臨界狀態模型描述土壤彈塑性行為的能力，並推廣臨界狀態模型為適合於黏土、粉土與砂土的三維應力空間組合模型。
亦由於關鍵性的參數導入，使得本研究構建的組合模型更能合理地描述各類型土壤的異向性組合行為；在本文的模型驗證研究工作中，該項成果的數值模型已可精確地提供數值分析數據：
1.組合關係的數值計算結果，在應力路徑與應力-應變關係上，皆能精確反映實驗數據；透過砂土、粉土的三軸CAD試驗及黏土的三軸CAU試驗的驗證，其結果皆證明本研究導入新參數所構建的組合模型，在土壤彈塑性行為的描述上優於傳統的臨界狀態模型。
2.運用PLAXIS 8.2程式內建的user-defined soil model 功能，將本文構建的組合模型導入到PLAXIS的有限元素分析中；經比對案例工程的現地監測資料，其結果亦顯示：本文推導模型的有限元素法試算分析數據呈現優於莫爾-庫倫模型和修正劍橋黏土模型的符合性。

關鍵字

流動法則 ； 組合模型 ； 臨界狀態模型 ； 自由能函數 ； 硬化規律 ； 耗散函數 ； 遷移應力 ； 屈服函數 ； 修正劍橋黏土模型

並列摘要

Between 1958 and 1963, the concept of critical state theory was first proposed by Roscoe et al from the Cambridge University and it is generally called Cam-clay model. Later in 1965, Burland modified the model based on energy relationships and it is called Modified Cam-Clay model. Currently, all the finite-element and finite differential equation based software packages used by geotechnical engineers (such as ABAQUS, PLAXIS, and FLAC) have the Modified Cam-Clay model built in them. And they have been used in the analysis of deep excavation of normally and slightly overconsolidated clay and stability analysis of high embankments. The real situation is that there are still differences existed between the numerical analysis results and field measurements. The main reason for the situation mentioned above is the yield function, flow rule and hardening rule used in these models cannot fully describe soil’s plastic flow characteristics, expansion behavior under shearing, and anisotropic stress-strain behavior. Therefore, many researches are concentrated their efforts to modify the critical state model.
Using the definition of continuous media of thermodynamics, the complementary correlation between free energy and dissipative energy triggered by external forces was identified first under iso-thermal deformation condition. Next, the state variables including effective stress, elastic strain, plastic strain, and plastic strain increment were incorporated into both dissipative and free energy potential functions. Then, the equivalent application of the function of state on describing energy locus transfer inside the system was developed to create a more reasonable layout of yield condition, flow rule and hardening rule of critical state constitutive model. Research efforts concentrate on selecting the parameters for the soil’s elastic/plastic constitutive model and how to interpret the actual physical phenomena. The goal is to improve this model’s ability in describing constitutive behavior of soils through incorporating new parameters into the extended critical state constitutive model. Moreover, through this introduction of critical parameters, the model constructed by this research is more realistic to describe anisotropic constitutive behavior of different types of soils.
Due to the introduction of several key factors into this model, the constitutive model developed from this research can describe different soils’ anisotropic behavior more reasonable. At the model verification part of this research, the numerical model simulations did provide an accurate results comparing to field data and they include:
1. The results of numerical calculation based on this constitutive model can accurately re-establish the stress paths and stress-strain relationships observed from different laboratory tests. By examining data collected from triaxial CAD tests on sands and silts plus clays’ triaxial CAU tests, it proves that the constitutive model with new parameters developed from this research does a better job in describing soil’s plastic/elastic behavior than the traditional critical state model.
2. Using user-defined soil model function of the program PLAXIS 8.2, the constitutive model developed from this research was incorporated with the finite-element analysis of the PLAXIS. Comparing the numerical results with the field monitoring data, it also shows that this model does a better job than Mohr-Coulomb model and Modified Cam-Clay model.

並列關鍵字

constitutive model ； free energy function ； critical state model

參考文獻

【3】 Roscoe, K. H., Schofield, Thurairajah. “Yielding of clays in states wetter than critical” Géotechnique 13, London, 1963.

【8】 Collins,I.F. (2005), “The concept of stored plastic work or frozen elastic energy in soil mechanics.” Geotechnique 55, No 5, 373-382.

【9】 Collins, I.F. (2003), “A systematic procedure for constructing three dimensional critical state models.” Int. J. Solids Structures 40, 4379-4397.

【10】 Collins, I.F. and Muhunthan ,B. (2003) “On the relationship between stress-dilatancy, anisotropy and plastic dissipation for granular materials” Geotechnique 53, No 7, 611-618.

【11】 Collins, I.F. and Hilder, T. 2002 “A theoretical framework for elastic/plastic constitutive models for triaxial tests.” Int. J. Num. Anal. Meth. Geomechanics. 26, 1313-1347.