筏基變形數值分析之土壤彈簧模式應用比較

Comparisons of Alternate Soil Spring Models for Numerical Analysis on Mat Foundation Deformations

林宏諭(Hong-Yu Lin)

指導教授 ： 張德文

淡江大學/工學院/土木工程學系碩士班/碩士(2021年)

https://doi.org/10.6846/TKU.2021.00259

摘要

本研究以WERAFT之筏基變形差分程式為基礎，代入各學者所建議之土壤彈簧參數進行受力基礎沉陷量分析，並與三維有限元素分析軟體Midas-GTX-NX分析結果驗證，以了解各種彈簧之優缺點與適用條件。本研究考慮的彈簧模式除Lysmer類比模式和修正Lysmer類比模式外，尚包括雙區域土壤彈簧模式以及以Pasternak地基模型類型為主的土壤彈簧模式，Pasternak地基模型除垂直向受壓的地盤反力係數K_s外，尚以地盤剪切彈簧勁度K_s描敘基礎向外側傳遞的剪力作用。由於本研究所採用的WERAFT分析邊界條件與Pasternak地基模型有區別，為消弭誤差，本研究將K_g進行折減並納入面積比進行修正。
研究成果顯示:1. WERAFT-S1分析採Lysmer彈簧時，採用面積比n=3對均佈載重下基礎沉陷預測能力佳，在筏基尺寸增大時誤差將增加，且不適合用於集中載重條件。2. WERAFT-S2分析採改良Lysmer土壤彈簧對均佈荷重基礎沉陷的準確度優異，大尺寸筏基亦適用，惟囿於土壤彈簧條件，不適用於集中載重。3. Adhikary雙區域彈簧所得沉陷量在基礎邊緣過低，且差異沉陷較大，可進一步改良。4. Kerr and Rhines彈簧過於簡單，以致預測能力不佳。5. Vlasov彈簧有較大的調整彈性，但其參數變化大不易掌握，使用時須特別注意參數η和H的選定問題。6. Worku彈簧在筏基尺寸較小與土壤勁度較低時預測頗佳，均佈載重與集中載重均可得到合理結果；惟當筏基尺寸過大或土壤強度過高時，需藉由限制整體結構剛度值K_r以及深度影響修正因子χ進行改善。

關鍵字

筏式基礎 ； 垂直載重 ； 基礎位移 ； WERAFT分析 ； Pasternak地基模型 ； 雙區域彈簧模式

並列摘要

This study is to model the raft foundation settlements caused by vertical loads using the WERAFT finite-difference analysis. Various soil spring models are implemented into the analysis to understand their applicability. The solutions are verified by the solutions from three-dimensional finite-element analysis using Midas GTS-NX program. Soil spring models such as the Lysmer’s analog spring, modified Lysmer’s analog spring, Pastermak type spring models and two-zone spring are considered. Owing to the zero-shear boundary condition assumed in WERAFT, for any soil spring model adopted from the Pastermak foundation, a reduction factor is suggested for the shear rigidity, kg when the foundation encountered uniform load.
The results of this study find that: 1. For WERAFT-S1 analysis using Lysmer’s spring, if the uniform load was applied, the area ratio n=3 can provide satisfactory solutions to the foundation settlements. However for raft with larger dimensions or if the load is concentrated, the solution will be deteriorated. 2. WERAFT-S2 analysis can provide comparable solution to the FE analysis. However, it became vital when the load is concentrated one. 3. Adhikary’s two-zone spring model will provide excessive settlement at center of the raft and underrated settlements along the edge. Therefore it requires further calibrations. 4. Kerr and Rhines model is too simple to provide rational solution to the foundation settlements. 5. For the Vlasov’s spring model, one must be cautioned on the selection of h and H parameters. There are uncertainties involved in using such spring model. 6. The Worku’s spring model is found appropriate for the cases of smaller foundation on soft soils under all types of loadings. When the foundation became larger or the soils became stiffer, the calibration factorχshould be limited in order to obtain adequate solutions.

並列關鍵字

Raft foundation ； vertical loads ； foundation displacements ； WERAFT analysis ； Pasternak foundation model ； two-zone model

參考文獻

1.ACI Committee 336 (1988), “Suggested Analysis and Design for Combined Footings and Mats”, Report ACI 336.2R-88, American Concrete Institute, Farmington Hills, MI, USA

2.Adhikary, S.,Singh, Y., Paul, D.K. (2014) Modelling of Soil-Foundation-Structure System. Soil Dynamics and Earthquake Engineering, Vol.61, ISSN 0267-7261

3.Bowles, J. E. (1982) Foundation analysis and design, 3rd edn, McGraw-Hill, New York, 361-363

4.Breeveld, B.J.S.(2013) “Modelling the Interaction between Structure and Soil for Shallow Foundations-A Computational Modelling Approach”, Delft University of Technology, Civil Engineering and Geosciences, Master of Science Thesis

5.Chang, D.W. and Lien, H.W. (2018).“Finite Difference Analysis of Raft Foundations under Vertically Static Loads” Procds., 20th SEAGS and 3rd AGSSEA Conference, Nov. 5-8, Jakarta, Indonesia.