The Law of Combined Effect of Rate and Temperature on Compressive Strength of Concrete Materials
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摘要: 混凝土材料的动态压缩强度不仅具有明显的应变率强化（硬化）效应，同时还具有明显的温度弱化（软化）效应。在应变率和温度联合条件下，压缩强度随应变率和温度变化过程中不仅存在清晰的应变率拐折点，拐折点前后压缩强度随应变率变化速率明显不同，而且在不同温度下发生拐折时，其拐折点对应的应变率也存在明显差异。参考近年来相关文献中混凝土材料在率温联合条件下的压缩实验数据，结合理论分析，探讨了在不同温度、不同应变率条件下混凝土材料压缩强度联合效应因子K的变化规律；并对实验数据进行拟合，得到了不同应变率、不同温度下K(T)-
$\dot{\varepsilon} $ 的预测表达式，确定了应变率强化和温度弱化对压缩强度的耦合影响；通过分析应变率拐折点与温度的关系，确定了应变率和温度联合条件下应变率敏感区和不敏感区的率温联合条件界限；建立了率温效应相当（K = 1）时的率温等效方程，并确定了混凝土材料的率温等效参数。Abstract: The dynamic compressive strength of concrete material not only has obvious strain rate strengthening (hardening) effect, but also has obvious temperature weakening (softening) effect. Under the combined condition of strain rate and temperature, there are not only clear strain rate inflection point in the process of compression strength changing with strain rate and temperature, the change of compression strength with strain rate is obviously different before and after the inflection point. Under the same condition, there also are significant differences in the strain rate values corresponding to the inflection points which are existed when the curve bends at different temperatures. Combined with theoretical analysis and references to the compression experimental data of concrete materials under the combined temperature and strain rate condition in recent years, the variation law of the joint effect factor K of concrete compressive strength under different temperatures (T) and different strain rates ($\dot {\varepsilon} $ ) is discussed. By fitting the experimental data, the prediction expressions of K(T)-$\dot{\varepsilon} $ at different strain rates and different temperatures were obtained, and the coupling effects of strain rate hardening and temperature softening on compression strength were determined. The relationship between the inflection point of strain rate and temperature is analyzed, and the combined rate-temperature boundary for strain rate sensitive and strain rate insensitive region is determined. The rate-temperature equivalent equation is established when the rate-temperature effect is equivalent (namely, K=1) and the rate-temperature equivalent parameters of concrete materials are determined. -
图 1 在不同温度和不同应变率下混凝土材料压缩强度的率温联合效应
Figure 1. Joint effect of rate-temperature on compressive strength of concrete at different temperatures and strain rates
图 2 混凝土材料在不同温度和不同应变率下的K-
$ \dot{\varepsilon} $ 关系Figure 2. Relationship of K-
$ \dot{\varepsilon} $ of concrete at different temperatures and strain rates
图 3 高应变率部分以及拐折点处K随应变率的变化规律
Figure 3. Variation of K with strain rate at high strain rate and the turning point
图 4 混凝土材料在准静态条件下的温度弱化效应
Figure 4. Temperature weakening effect of concrete under quasi-static condition
图 5 温度弱化因子随温度的变化曲线
Figure 5. Curve of temperature weakening factorvarying with temperature
图 6 温度T与拐折应变率
$ \dot{\varepsilon} $ in之间的拟合关系曲线Figure 6. Fitting curve between temperature and inflection strain rate
$ \dot{\varepsilon}_{\rm{in}}$ 
图 7 当
$\dot{\varepsilon} $ >$\dot{\varepsilon} $ in时率温联合效应因子变化速率与温度的关系Figure 7. Relationship between temperature and change rate of combined effect factor of strain rate and temperature when
$\dot{\varepsilon} $ >$\dot{\varepsilon} $ in
图 8 各温度下的K-
$\dot{\varepsilon} $ 曲线和$\delta $ ·KsT-$\dot{\varepsilon} $ 曲线的对比Figure 8. Comparison of K-
$\dot{\varepsilon} $ curves and$\delta $ ·KsT-$\dot{\varepsilon} $ curves at different temperatures
图 9 K=1时温度和应变率的关系曲线
Figure 9. Relation curve between the temperature and the strain rate when K=1
表 1
$ K\text{-}\dot{\varepsilon} $ 拟合方程中的相关参数Table 1. Relevant parameters in
$K\text{-}\ \dot{\varepsilon} $ fitting equationT/℃ Ls $ \dot{\varepsilon} $in/s−1 Kin LT 20 0.034 14.0 1.22 0.79 200 0.031 33.6 1.11 1.12 400 0.021 51.0 0.88 1.53 600 0.030 55.5 0.68 1.17 800 0.013 60.0 0.34 0.72 
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表 2
$K=1$ 时各温度下的应变率Table 2. Strain rates at different temperatures when
$K=1$ Temperature/℃ Strain rate/s−1 20 10−5 200 0.008 400 61.1 600 104.2 800 495.2
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