混凝土动态双轴压缩强度准则细观研究

李健; 金浏; 余文轩; 杜修力

doi:10.6052/j.issn.1000-4750.2022.01.0091

混凝土动态双轴压缩强度准则细观研究

doi: 10.6052/j.issn.1000-4750.2022.01.0091

北京工业大学城市减灾与防灾防护教育部重点实验室，北京 100124

基金项目: 国家自然科学基金项目(51978022)

详细信息

作者简介:
李　健(1996−)，男，天津人，硕士生，主要从事混凝土材料动态性能方面研究(E-mail: bgdlijian@126.com)

余文轩(1993−)，男，浙江人，博士生，主要从事混凝土结构尺寸效应方面研究(E-mail: ywxmailbox@163.com)

杜修力(1962−)，男，四川人，中国工程院院士，博士，博导，主要从事土木工程防灾减灾方面研究(E-mail: duxiuli@bjut.edu.cn)

通讯作者:
金　浏(1985−)，男，江苏人，教授，博士，博导，主要从事混凝土结构防灾减灾方面研究(E-mail: jinliu@bjut.edu.cn)

中图分类号: TU528.1
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出版历程
- 收稿日期: 2022-01-19
- 修回日期: 2022-04-08
- 网络出版日期: 2022-04-23
- 刊出日期: 2023-11-25

MESO-SIMULATION ON DYNAMIC BIAXIAL COMPRESSIVE STRENGTH CRITERION OF CONCRETE

Key Laboratory of Urban Security and Disaster Engineering of Ministry of Education, Beijing University of Technology, Beijing 100124, China

摘要

摘要: 由于物理试验设备和条件限制，目前对混凝土动态双轴压缩强度准则的研究仅停留在低应变率范围(10⁻⁵s⁻¹~10⁻²s⁻¹)。针对这些强度准则在更高应变率范围内是否适用，该研究建立了细观随机骨料模型，对边长100 mm的混凝土立方体试块开展了动态双轴压缩细观模拟分析。研究了应变率和侧应力比对混凝土动态双轴压缩破坏模式及压缩强度的影响，建立了适用于更高应变率的动态强度准则。研究结论：相同侧应力比下，随应变率增大，混凝土内部损伤区域增多，动态压缩强度增大；相同应变率下，随侧应力增大，混凝土破坏模式由柱状压裂变为片状劈裂，动态压缩强度先增大后减小。现有的混凝土动态双轴压缩强度准则在应变率为10⁻⁵s⁻¹~1 s⁻¹时很难适用，而该研究建议的强度准则适用于更高的应变率范围，并且得到了不同物理试验的初步验证。
- 混凝土 /
- 侧应力比 /
- 应变率 /
- 动态双轴压缩强度 /
- 双轴强度准则
Abstract: Due to the limitations of physical test equipment and conditions, the existing studies on dynamic biaxial compressive strength criteria of concrete only in the range of low strain rate (10⁻⁵s⁻¹~10⁻²s⁻¹). To investigate whether these strength criteria are applicable at higher strain rates or not, a mesoscopic random aggregate model was established. The meso-simulation analysis of concrete cubic specimens with side length of 100 mm under dynamic biaxial compressive loads were carried out. The influence of strain rate and lateral stress ratio on dynamic biaxial compressive failure modes and compressive strengths of concrete were analyzed. A dynamic biaxial compressive strength criterion applicable to higher strain rate was established. The conclusions are as follows: Under the same lateral stress ratio, a higher strain rate leads to an increase in the internal damaged area and the dynamic compressive strength of concrete. Under the same strain rate, a higher lateral stress ratio causes the failure mode of concrete changes from cylindrical fracturing to sheet splitting and the dynamic compressive strength first increases and then decreases. The existing dynamic biaxial compressive strength criterion of concrete is inapplicable in 10⁻⁵s⁻¹~1 s⁻¹, while the improved strength criterion proposed can be applied to a larger strain rate range, which has been preliminarily verified by various physical tests.
- concrete /
- lateral stress ratio /
- strain rate /
- dynamic biaxial compressive strength /
- biaxial strength criterion

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图 1 3D细观有限元模型

Figure 1. 3D Meso-Finite Element Model

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图 2 模拟结果与试验^[4]的对比

Figure 2. Comparison between simulation and test results^[4]

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图 3 不同工况下同一破坏阶段的混凝土破坏模式

Figure 3. Failure modes of concrete in the same failure stage under different loading conditions

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图 4 不同工况下混凝土双轴压缩强度

Figure 4. Concrete biaxial compressive strength under different loading conditions

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图 5 数值模拟值与物理试验值对比

Figure 5. Comparison of numerical and test results

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图 6 不同静态双轴压缩强度准则的对比

Figure 6. Comparison of different static biaxial compression strength criteria

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图 7 不同应变率下对式(15)的拟合结果

Figure 7. Fitting results of Eq. (15) under different strain rates

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图 8 低应变率下数值模拟点与式(17)的拟合结果

Figure 8. Fitting results between the numerical data and Eq. (17) under low strain rates

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图 9 不同侧应力比下对式(17)的拟合结果

Figure 9. Fitting results of Eq. (17) under different lateral stress ratios

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图 10 强度准则拟合值与文献[5]的对比结果

Figure 10. Comparison between the fitted data and Ref. [5]

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图 11 强度准则拟合值与文献[6]的对比结果

Figure 11. Comparison between the fitted data and Ref. [6]

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表 1 混凝土双轴强度准则研究现状

Table 1. Research status of concrete biaxial strength criteria

文献	工况	破坏准则
文献[1]	静态	$ \sqrt {f_1^2 + f_2^2 - {f_1}{f_2}} - {\alpha _{\text{s}}}\left( {{f_1} + {f_2}} \right) = \left( {1 - {\alpha _{\text{s}}}} \right){f_{{\text{c}},{\text{r}}}} $
文献[2-3, 8]	静态	$ {\left( {\dfrac{{{f_1}}}{{{f_{{\text{c}},{\text{r}}}}}} + \dfrac{{{f_2}}}{{{f_{{\text{c}},{\text{r}}}}}}} \right)^2} + a\dfrac{{{f_1}}}{{{f_{{\text{c}},{\text{r}}}}}} + b\dfrac{{{f_2}}}{{{f_{{\text{c}},{\text{r}}}}}} = 0 $
文献[4-7, 9]	动态	$ \dfrac{{{f_1}}}{{{f_{{\text{c}},{\text{r}}}}}} = {P_1} + {P_2}\lg \left( {\dfrac{{\dot \varepsilon }}{{{{\dot \varepsilon }_{\text{s}}}}}} \right) + \dfrac{{{P_3}}}{{{{\left( {1 + \lambda } \right)}^2}}} + \dfrac{{{P_4}\lambda }}{{{{\left( {1 + \lambda } \right)}^2}}} $
文献[10]	动态	$ \dfrac{{{f_1}}}{{{f_{{\text{c}},{\text{r}}}}}} = \left[ {1 + \left( {a + \exp \left( {b\ln \dot \varepsilon } \right)} \right)\dfrac{{{f_2}}}{{{f_{{\text{c}},{\text{r}}}}}}} \right]\Bigg/{\left( {1 + \dfrac{{{f_2}}}{{{f_{{\text{c}},{\text{r}}}}}}} \right)^2} $
文献[11]	动态	$ \dfrac{{{f_1}}}{{{f_{{\text{c}},{\text{r}}}}}} = \left[ {1 + a\lg \left( {\dfrac{{\dot \varepsilon }}{{{{\dot \varepsilon }_{\text{s}}}}}} \right)} \right]\dfrac{{b + c\lambda }}{{{{\left( {1 + \lambda } \right)}^2}}} $
注：f₁和f₂分别为双轴荷载下混凝土主轴和侧轴压缩强度；f_c,r为混凝土单轴压缩强度；α_s为受剪屈服参数，取值详见文献[1]；其余参数为各文献中不同形式强度准则的回归参数。动态工况应变率范围为10⁻⁵s⁻¹≤$ \dot \varepsilon $≤10⁻²s⁻¹。

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表 2 细观组分参数

Table 2. Meso-component parameters

组分参数	弹性模量E/GPa	泊松比ν	偏心率η/(%)	应力比	膨胀角ψ/(°)	断裂能G_c/(m²·J⁻¹)	不变量应力比K_c	抗压强度σ_c/MPa	抗拉强度σ_t/MPa
骨料颗粒	60.0^①	0.16	0.1	1.16	30	60	0.667	80.0^①	8.0^①
砂浆基质	32.5^①	0.20	0.1	1.16	18	50	0.667	40.0^①	4.0^①
界面过渡区	26.0^②	0.22	0.1	1.16	15	30	0.667	32.0^③	3.2^③
注：① 参考文献[4]；② 参考文献[14-19]；③ 通过反演方法确定。

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表 3 不同工况下式(15)的回归分析参数

Table 3. Regression parameters of Eq. (15) under different loads

应变率/s⁻¹	回归分析参数		R²
应变率/s⁻¹	a	b	R²
10⁻⁵	1.00	3.95	0.999
10⁻³	1.00	3.80	0.998
10⁻²	1.00	3.29	0.990
10⁻¹	1.00	4.00	0.997
1	1.00	4.87	0.997

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表 4 不同侧应力比下对式(18)的拟合结果

Table 4. Fitting results of Eq. (18) under different lateral stress ratios

侧应力比λ	回归参数			R²
侧应力比λ	m	n	w	R²
0.00	0.017	−0.010	1.00	0.958
0.25	0.043	−0.101	1.00	0.919
0.50	0.042	−0.089	1.00	0.970
0.75	0.041	−0.086	1.00	0.939
1.00	0.047	−0.122	1.00	0.951

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表 5 式(19)各参数拟合结果

Table 5. Fitting results of parameter in Eq. (19)

文献	拟合参数
文献	P_h	P_k	P_l	P_m	P_n
文献[5]	0.134	0.020	8.500	2.373	−1.376
文献[6]	0.276	−0.021	3.289	0.976	0.299

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