MESO-SIMULATION ON DYNAMIC BIAXIAL COMPRESSIVE STRENGTH CRITERION OF CONCRETE
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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(10−5 s−1~10−2 s−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10−5 s−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。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 (10−5 s−1~10−2 s−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 10−5 s−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.
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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;fc,r为混凝土单轴压缩强度;αs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10−5 s−1≤$ \dot \varepsilon $≤10−2 s−1。 表 2 细观组分参数
Table 2. Meso-component parameters
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 a b 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 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 m n w 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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