低矮型鋼筋混凝土剪力牆往復載重行為之高仿真非線性分析

High-Fidelity Nonlinear Cyclic Response Simulations of Squat RC Shear Walls

温子漢(Tzu-Han Wen) ； 洪崇展(Chung-Chan Hung) ； Hexin Zhang ； Phu Anh Huy Pham ； 袁宇秉(Terry Y.P. Yuen)

《結構工程》 37卷2期 (2022/06) Pp. 99-112

https://doi.org/10.6849/SE.202206_37(2).0005

摘要

國內外耐震設計規範對特殊鋼筋混凝土（RC）結構設計要求進行高仿真、非線性之地震歷時動力分析。非線性結構模擬的核心技術是材料的組成律模型，特別是混凝土材料。然而，許多現有的混凝土組成律模型無法解決一些關鍵問題，包括開裂引起的異向性、非比例載荷下應力傳遞機制的變化、剪切滑移和開裂後再接觸行為、網格尺寸敏感性以及計算效率和細部精準度兩者之間的平衡。為此，本文介紹一個穩定且經過實驗驗證的組成律模型（Yuen等人2022），用於混凝土結構的高仿真非線性反應分析。該組成律模型的主要特徵包括（一）基於總應變的數學模型，其中包含與加載歷史相關的內部參數，（二）開裂面上的往復法向和切向應力－應變反應，（三）利用新穎的開裂平面搜索算法求得符合唯一性之固定三維開裂平面坐標，（四）以等效單軸應變－變換方法模擬多軸應變的相互作用，（五）改進的剪切滑移和開裂重新接觸模擬，以及（六）透過模型參數正規化減輕網格尺寸敏感性。該組成律模型透過使用者副程式在ABAQUS中建立，並已於前文（Yuen等人2022）證明能成功應用於模擬剪切板實驗（shear panel tests）與受剪切控制之實尺寸RC柱的反覆載重行為。本文進一步展示該組成律模型應用於模擬小剪跨比且高強度RC牆的反覆載重實驗，模擬結果成功吻合RC牆的損傷演變和遲滯迴圈。因此，所提出的混凝土組成律模型具優異性能，可以用於特殊混凝土結構的高仿真非線性分析。

關鍵字

組成律模型 ； 異向性 ； 剪切與開裂行為 ； 網格敏感性 ； 非比例載荷 ； 有限元素分析

並列摘要

As stipulated by most of the prevailing structural design standards, nonlinear response analysis with high-fidelity numerical models would be inevitable for designing unconventional reinforced concrete structures under extreme seismic loading. The core of nonlinear numerical models is the constitutive modelling of materials, particularly for concrete materials. Nevertheless, many of the existing concrete constitutive models could not resolve some critical issues that involve crack-induced anisotropy, change of stress transfer mechanisms under non-proportional loading, shear-slip and re-contact behaviour, mesh-size sensitivity, and balance between computational efficiency and modelling the detailed responses. To this end, this paper presents a robust and experimentally validated constitutive model that was developed recently (Yuen et al., 2022) for high-fidelity nonlinear response analysis of reinforced concrete elements. The key features include (1) the total-strain based formulation with loading-history dependent internal variables, (2) cyclic normal and tangential stress-strain responses prescribed on crack planes, (3) fixed 3D crack plane coordinate that is uniquely determined by a novel crack plane searching algorithm, (4) multi-axial strain interaction modelled by the equivalent uniaxial-strains transformation method, (5) shear-slip and re-contact of the crack planes modelled by the modified shear retention model, and (6) mesh-size sensitivity mitigation through the model parameter regularisation. The proposed model was already implemented into ABAQUS through the user-subroutine and successfully applied to simulate reserved-cyclic loading tests on shear panels and a full-scale shear-controlled column (Yuen et al., 2022). This paper presents a further validation study of the proposed model on a high-strength squat RC wall. The high-fidelity model can again well capture the damage evolutions and complete load-deflection hysteresis response of the tested wall. Hence, with the demonstrated performances, the proposed model could be a competent candidate for the high-fidelity nonlinear analysis of next generations of concrete structures that feature unconventional design.

並列關鍵字

Constitutive model ； anisotropy ； shear-slip and re-contact ； mesh-sensitivity ； non-proportional loading ； concrete ； finite element

參考文獻

ABAQUS Inc. (2020). “Abaqus/Explicit User Subroutines: VUMAT.” Abaqus User Subroutines Reference Guide.

ASCE. (2017). ASCE/SEI 41-17 Seismic Evaluation and Retrofit of Existing Buildings. American Society of Civil Engineers, Reston, Virginia, USA.

Bažant, Z. P., and Oh, B. H. (1983). “Crack band theory for fracture of concrete.” Matériaux et Constructions, 16(3), 155-177.

British Standard (BSI). (2004). Eurocode 8: Design of Structures for Earthquake Resistance — Part 1: General Rules, Seismic Actions and Rules for buildings.

CEB-FIP. (2012). Model Code 2010 - Final version, Vol. 1. fib Bulletin 65.Federation Internationale du Beton, Lausanne., fédération internationale du béton, Bulletin 66, Lausanne, Switzerland.