基于3D细观模型的混凝土动态压缩行为分析

张湘茹; 程月华; 吴昊

doi:10.11883/bzycj-2022-0541

基于3D细观模型的混凝土动态压缩行为分析

doi: 10.11883/bzycj-2022-0541

同济大学土木工程学院，上海 200092

基金项目: 国家自然科学基金（52078379）

详细信息

作者简介:
张湘茹（1999－　），女，硕士研究生，2032542@tongji.edu.cn

通讯作者:
程月华（1994－　），女，博士，yhcheng@tongji.edu.cn

中图分类号: O347.3
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- 被引次数: 0
出版历程
- 收稿日期: 2022-12-01
- 修回日期: 2023-04-17
- 网络出版日期: 2023-04-26
- 刊出日期: 2024-02-06

Analysis on dynamic compressive behavior of concrete based on a 3D mesoscale model

College of Civil Engineering, Tongji University, Shanghai 200092, China

摘要

摘要: 通过建立混凝土的3D细观模型，在细观尺度上分析动态压缩荷载作用下混凝土材料内部裂缝的产生和发展、损伤演化和动态强度及其影响因素。首先，基于传统的“生成-投放”法生成粒径、形状和空间分布均随机的凸多面体粗骨料模型，并通过骨料沉降和粒径缩放实现粗骨料的大体积率（达50%）和可调控；使用四面体网格划分骨料和砂浆表征其真实物理形状；使用界面粘结接触表征界面过渡区（ITZ）提升计算效率。进一步通过对比不同粗骨料粒径混凝土的分离式霍普金森压杆（SHPB）试验数据与模拟结果，如杆上应变时程、试件动态应力-应变曲线和试件损伤破坏模式，验证了建立的混凝土3D细观有限元模型、参数确定方法和数值仿真方法的准确性。最后，分析了30~100 s⁻¹应变率范围内骨料粒径（4~8、10~14和22~26 mm）、体积率（20%、30%和40%）和类型（石灰岩、花岗岩和玄武岩）对混凝土动态压缩强度的影响。结果表明：粗骨料粒径增大，混凝土动态压缩强度先增大后减小；粗骨料体积率越高，混凝土动态压缩强度越大；混凝土动态压缩强度随粗骨料强度的增加而提高。
- 混凝土 /
- 3D细观模型 /
- 动态力学行为 /
- 粘结接触 /
- 应变率效应
Abstract: As the most widely used construction material, concrete is common in military protection and civil transportation infrastructures. During its services life, concrete may bear dynamic loads such as high-speed penetration, blast and impact of vehicle, ship, rockfall and so on. On the mesoscale, concrete is three-phase material composed of mortar, coarse aggregates and interface transition zone (ITZ). The concrete 3D mesoscale model was established to analyze the crack generation and development, damage evolution, dynamic strength and its influencing factors of concrete. Firstly, randomly distributed convex polyhedron aggregates of random shapes and sizes were modeled based on the conventional “take-and-place” method and Monte Carlo algorithm, and drop of aggregates under gravity were simulated in finite element software LS-DYNA to make aggregates more dense, improving aggregate volume fraction to 50%. After that, aggregate size was reduced by a trial value to control aggregate volume fraction conveniently. Then, aggregates and mortar were meshed with tetrahedral elements to display their actual physical shapes. Besides, ITZ was represented by interface cohesive contact which equals zero-thickness bonding elements to improve computational efficiency. Furthermore, SHPB simulations of different coarse aggregates sizes concrete were conducted and the accuracy of finite element model, parameter determination method and numerical simulation methods were proved by comparing test and simulated bar strain-time history, dynamic stress-strain curves and failure patterns of specimens. Finally, influences of the aggregate size (4−8, 10−14 and 22−26 mm), volume fraction (20%, 30% and 40%) and type (limestone, granite and basalt) on concrete dynamic compressive strength under the strain rate within 30−100 s⁻¹ were analyzed. It shows that the dynamic compressive strength of concrete increases first and then decreases with the increase of aggregate size; the dynamic compressive strength of concrete increases with the increase of volume fraction; the dynamic compressive strength of concrete increases with the increase of aggregate strength.
- concrete /
- 3D mesoscale model /
- dynamic mechanical behavior /
- cohesive contact /
- strain rate effect

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图 1 随机多面体粗骨料生成与沉降

Figure 1. Generation and drop of random polyhedral aggregates

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图 2 骨料缩放示意图及不同骨料体积率混凝土剖面

Figure 2. Schematic diagram of aggregates reductions and cross sections of concrete with different aggregate volume fractions

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图 3 布尔运算与网格划分

Figure 3. Boolean operation and mesh generation

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图 4 准静态单轴压缩与SHPB试验有限元模型

Figure 4. Finite element models of quasi-static uniaxial compression and SHPB tests

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图 5 杆上反射和透射波的网格敏感性

Figure 5. Convergence of mesh sizes on incident and transmitted stress waves

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图 6 RHT模型^[21]

Figure 6. RHT model^[21]

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图 7 砂浆的RHT压缩应变率效应参数修正

Figure 7. Modification of RHT compressive strain rate parameters for mortar

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图 8 牵引-分离关系曲线

Figure 8. Traction-separation law

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图 9 试验与模拟得到样品M的准静态应力-应变曲线对比

Figure 9. Comparison of quasi-static stress-strain curve between test and simulation of sample M

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图 10 试验与模拟得到样品G6的准静态应力-应变曲线对比

Figure 10. Comparison of quasi-static stress-strain curve between test and simulation of sample G6

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图 11 试验与模拟得到样品G12的准静态应力-应变曲线对比

Figure 11. Comparisons of quasi-static stress-strain curve between test and simulation of sample G12

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图 12 试验与模拟得到样品G24的准静态应力-应变曲线对比

Figure 12. Comparisons of quasi-static stress-strain curve between test and simulation of sample G24

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图 13 SHPB有限元模型应力平衡校核

Figure 13. Stress equilibrium check of SHPB finite element model

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图 14 平均应变率计算方法

Figure 14. Calculation method of average strain rate

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图 15 试验与模拟波形曲线对比（工况M-65 s⁻¹）

Figure 15. Comparison of test and simulated waveforms of case M-65 s⁻¹

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图 16 试验与模拟波形曲线对比（工况G6-85 s⁻¹）

Figure 16. Comparison of test and simulated waveforms of case G6-85 s⁻¹

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图 17 试验与模拟波形曲线对比（工况G12-60 s⁻¹）

Figure 17. Comparison of test and simulated waveforms of case G12-60 s⁻¹

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图 18 试验与模拟波形曲线对比（工况G24-80 s⁻¹）

Figure 18. Comparison of test and simulated waveforms of case G24-80 s⁻¹

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图 19 试验与模拟得到样品M的动态应力-应变曲线对比

Figure 19. Comparison of test and simulated dynamic stress-strain curves of sample M

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图 20 试验与模拟得到样品G6的动态应力-应变曲线对比

Figure 20. Comparison of test and simulated dynamic stress-strain curves of sample G6

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图 21 试验与模拟得到样品G12的动态应力-应变曲线对比

Figure 21. Comparison of test and simulated dynamic stress-strain curves of sample G12

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图 22 试验与模拟得到样品G24的动态应力-应变曲线对比

Figure 22. Comparison of test and simulated dynamic stress-strain curves of sample G24

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图 23 砂浆试件破坏模式

Figure 23. Failure patterns of mortar specimens

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图 24 不同骨料粒径混凝土试件破坏模式

Figure 24. Failure patterns for concrete specimens of different coarse aggregate sizes

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图 25 试件G24-50 s⁻¹破坏过程

Figure 25. Damage process of specimen G24-50 s⁻¹

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图 26 不同粒径骨料混凝土试件动态应力-应变曲线

Figure 26. Dynamic stress-strain curves for concrete specimens with different aggregate sizes

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图 27 不同骨料体积率混凝土试件动态应力-应变曲线

Figure 27. Dynamic stress-strain curves for concrete specimens of different aggregate volume fractions

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图 28 不同类型骨料混凝土试件动态应力-应变曲线

Figure 28. Dynamic stress-strain curves for concrete specimens of different aggregate types

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表 1 砂浆的RHT模型参数

Table 1. RHT model parameters of mortar

参数类型	参数	符号	取值	参数类型	参数	符号	取值
基本强度参数	拉压强度比	$ f_{{\mathrm{t}}} ^{\text{*}} $	0.18	失效面参数	失效面参数	A_f	1.6
基本强度参数	剪压强度比	$ f_{\mathrm{s}}^* $	0.1		失效面指数	N	0.61
弹性屈服面参数	压缩屈服面参数	$ g_{\mathrm{c}}^* $	0.53		拉压子午比	Q₀	0.6805
弹性屈服面参数	拉伸屈服面参数	$ g_{\mathrm{t}}^* $	0.7		罗德角相关系数	B_L	0.0105
残余强度面参数	残余强度参数	A_r	1.4		压缩应变率指数	$ {\beta _{\mathrm{c}}} $	5.64×10⁻³
残余强度面参数	残余强度指数	n_r	0.61		拉伸应变率指数	$ {\beta _{{\mathrm{t}}} } $	0.02
硬化段参数	剪切模量缩减系数	$ \xi $	0.9		参考压缩应变率	$ \dot \varepsilon _0^{\mathrm{c}} $	3×10⁻⁵ s⁻¹
软化段参数	损伤参数	D₁	0.02		参考拉伸应变率	$ \dot \varepsilon _0^{\mathrm{t}} $	3×10⁻⁶ s⁻¹
	损伤指数	D₂	1		过渡压缩应变率	$ \dot \varepsilon _{\mathrm{p}}^{\mathrm{c}} $	30 s⁻¹
	最小失效应变	$ \varepsilon _{\text{p}}^{\text{m}} $	0.01		过渡拉伸应变率	$ \dot \varepsilon _{\mathrm{p}}^{\mathrm{t}} $	30 s⁻¹

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表 2 不同类型骨料HJC材料参数^[31-32]

Table 2. HJC model parameters of different aggregate types^[31-32]

岩石	ρ₀/(kg·m⁻³)	f_c/MPa	G/GPa	T/MPa	A₀	B₀
石灰石^[31]	2300	60	10.1	4	0.55	1.23
花岗岩^[31]	2660	154	28.7	12.2	0.3	2.5
玄武岩^[32]	2800	200	25.2	14.65	0.79	2.5

N	$ \sigma _{\max }^ * $	C₀	$ {\dot \varepsilon _0} $	D₁	D₂	e_f,min
0.89	20	0.0097	1×10⁻⁶	0.04	1	0.01
0.79	15	0.0097	1×10⁻⁶	0.04	1	0.01
0.7	15	0.007	1×10⁻⁶	0.04	1	0.01

P_c/MPa	P_l/GPa	K₁/GPa	K₂/GPa	K_3/GPa	μ_c	μ_l
20	2	39	−223	550	0.00125	0.174
51	1.2	12	25	42	0.00162	0.012
67.7	1.2	12	25	42	0.0012	0.012
注：ρ₀为密度，f_c为压缩强度，G为剪切模量，T为最大拉伸静水压力，A₀、B₀、N、$ \sigma _{\max }^ * $、C₀为强度面参数，$ {\dot \varepsilon _0} $为应变率效应参数，D₁、D₂、e_f,min为损伤参数，P_c、P_l、K₁、K₂、K₃、μ_c、μ_l为状态方程参数。

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