A MODIFIED DUNCAN-CHANG E-B MODEL WITH PARTICLE BREAKAGE FOR CALCAREOUS SAND
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摘要: 在常规应力水平下颗粒发生破碎是钙质砂有别于其他砂土的重要性质之一，且由于颗粒破碎的存在，使用传统的本构模型无法很好地模拟钙质砂的力学行为。因此本文以最为普及的本构模型之一——邓肯-张E-B模型为基础，对其进行颗粒破碎方面的修正以得到一个能用于钙质砂的本构模型。具体方法为：首先本文采用Hardin提出的相对破碎Br这一指标来度量颗粒破碎的大小。之后研究分析得出了颗粒破碎对邓肯-张模型参数(内摩擦角φ、割线模量E50及体积模量B)的影响规律。然后通过颗粒破碎与输入能量之间的关系将各状态下无法直接确定的相对破碎Br与可确定的应力-应变状态联系起来。最终得到了一个考虑颗粒破碎的钙质砂修正邓肯-张E-B模型。为验证模型的准确性及适用性，本文还使用该模型对4种不同粒径范围且试验围压不同的钙质砂的三轴排水行为进行了模拟。结果表明拟合效果较好，模型能适用于各种不同粒径范围的钙质砂，并且在颗粒破碎较大的情况下明显优于传统邓肯-张模型。Abstract: Particles breakage under normal stress levels distinguishes calcareous sand from other sands and is one of the important properties of calcareous sands. Due to particle breakage, the mechanical behavior of calcareous sands cannot be well simulated using the traditional constitutive models. Therefore, based on the Duncan-Chang E-B model, this paper proposes a constitutive model that can be used for calcareous sands by considering particle breakage. The specific method is as follows. Firstly, this paper uses the relative breakage Br proposed by Hardin to measure the degree of particle breakage. Moreover, the influence of particle breakage on Duncan-Chang model parameters including internal friction angle, secant modulus E50 and bulk modulus B is obtained. Then, the relative breakage Br, which cannot be directly determined in each state, is related to the determinable stress-strain state by the relationship between particle breakage and input energy. Finally, a modified Duncan-Chang E-B model for calcareous sand considering particle breakage is proposed in this paper. In order to verify the accuracy and applicability of the model, this model is used to simulate the triaxial drainage behavior of calcareous sands with four particle sizes. It is shown that the simulation results agree well with the experimental ones, and the modified model is significantly better than the conventional Duncan-Chang E-B model in the case of large particle breakage.
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Key words:
- Calcareous sand /
- Particle breakage /
- Input energy /
- Modified model /
- Duncan-Chang E-B model
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图 1 钙质砂1 ε1/(σ1-σ3)-ε1曲线
Figure 1. The ε1/(σ1-σ3)-ε1 relations of calcareous sand No.1
图 2 钙质砂1 E50、摩擦角、B与围压及Br关系图
Figure 2. The E50、friction angle and B-confining pressure and Br relationships of calcareous sand No.1
图 3 钙质砂1相对破碎Br与输入能量E关系曲线
Figure 3. The Br-E relationship curve of calcareous sand No.1
表 2 模型参数
Table 2. Model constants
参数名称 钙质砂1 钙质砂2 钙质砂3 钙质砂4 Kn1 155.46 189.53 155.36 91.98 n 0.185 0.560 0.315 0.233 Kn2 37 211 5.7 264 Km1 58.89 122.26 60.81 29.98 m 0.045 0.282 0.195 0.079 Km2 0.0232 0.0006 0.0011 0.2211 φ0 45.78 49.47 45.26 48.02 Δφ1 10.95 5.08 7.02 6.04 Δφ2 44.22 8.24 5.16 75.1 a 0.030 05 0.015 37 0.156 26 0.033 65 b 1.003 75 1.001 08 1.001 59 1.006 55 Rf 0.751 0.698 0.680 0.746 
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