<i>K</i><sub>0</sub>固结珊瑚砂的应力-应变模型及变形参数研究

张季如; 彭伟珂; 郑颜军

doi:10.11779/CJGE20211558

K₀固结珊瑚砂的应力-应变模型及变形参数研究 English Version

武汉理工大学土木工程与建筑学院, 湖北武汉 430070

基金项目:

国家自然科学基金项目 42172295

详细信息

作者简介:
张季如(1964—)，男，博士，教授，博士生导师，主要从事岩土工程方面的教学和科研工作。E-mail: zhangjr@whut.edu.cn

中图分类号: TU431
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出版历程
- 收稿日期: 2021-12-26
- 网络出版日期: 2023-03-15
- 刊出日期: 2023-02-28

Stress-strain model and deformation parameters of K₀-consolidated coral sand

School of Civil Engineering and Architecture, Wuhan University of Technology, Wuhan 430070, China

摘要

摘要: 珊瑚砂作为岛礁吹填地基的填料，在填筑期的应力路径具有K₀固结的特点。利用三轴试验系统对不同初始相对密度的珊瑚砂进行了一系列的K₀固结试验，研究了珊瑚砂的应力–应变特性，测试了珊瑚砂的K₀系数和颗粒破碎率。基于广义虎克定律，建立了幂函数形式的非线性弹性模型来描述K₀固结珊瑚砂的应力–应变关系，提出了变形参数的函数表达式，并将模型计算结果与试验曲线进行了对比。结果表明：K₀固结珊瑚砂的应力-应变关系可用幂函数表示。随着轴向有效应力的增加，K₀减小，颗粒破碎率增大。在相同的轴向有效应力条件下，珊瑚砂的初始相对密度越小，K₀越大，颗粒破碎率越高。在K₀状态下，随着轴向有效应力的增加，珊瑚砂的切线模量增加，切线泊松比减小。珊瑚砂的初始相对密度越大，相同轴向有效应力下的切线模量越大，切线泊松比越小。幂函数模型合理地预测了一定应力范围内K₀固结珊瑚砂的应力–应变关系，模型及变形参数反映了K₀固结的应力路径对应力–应变关系的影响。
- 应力-应变模型 /
- 变形参数 /
- 珊瑚砂 /
- K₀固结 /
- 静止土压力系数
Abstract: The stress path followed by soil consolidation in the hydraulic filling site where the coral sand is used as the filling materials is characterized by K₀-consolidation. In order to investigate the stress-strain behaviors of the K₀-consolidated coral sand, a series of K₀-consolidation tests in a triaxial cell are carried out for the coral sands with different initial relative densities. The K₀-values of the coral sands are measured and their particle breakage indexes are evaluated. Based on the generalized Hooke's law, a nonlinear elastic model in the form of a power function is proposed to describe the stress-strain relationship of the K₀-consolidated coral sand. The functional expressions for the deformation parameters are presented, and the calculated results of the model are compared with the test curves. The results show that the stress-strain relationship of the K₀-consolidated coral sand may be expressed by a power function. With the increase of the axial effective stress, the K₀-value decreases, and the particle breakage index increases. Under the same axial effective stress, a small initial relative density corresponds to a large K₀-value and a large particle breakage index. As the increase of the axial effective stress in the K₀-state, the tangent modulus of the coral sand increases, and the tangent Poisson's ratio decreases. Under the same axial effective stress, the larger the initial relative density, the larger the tangent modulus, and the smaller the tangent Poisson's ratio. The stress-strain relationship of the K₀-consolidated coral sand with different initial relative densities within a certain stress range is reasonably predicted by the power function model. The model and deformation parameters reflect the influence of the stress path of K₀-consolidation on the stress-strain relationship.
- stress-strain model /
- deformation parameter /
- coral sand /
- K₀-consolidation /
- coefficient of earth pressure at rest

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图 1 珊瑚砂的粒径分布曲线

Figure 1. Grain-size distribution curves of coral sand

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图 2 试验设备

Figure 2. Test apparatus

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q- $p'$ 平面内的应力路径

Stress paths in q- $p'$ plane

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图 4 轴向有效应力与轴向应变的关系曲线

Figure 4. Curves of axial effective stress versus axial strain

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图 5 K₀与轴向有效应力的关系曲线

Figure 5. Curves of K₀ versus axial effective stress

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图 6 K₀与 $\lg ({\sigma '_1}/{p_{\text{a}}})$ 的关系曲线

Figure 6. Curves of K₀ versus $\lg ({\sigma '_1}/{p_{\text{a}}})$

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图 7 K₀试验结束时q- $p'$ 平面内的有效应力和颗粒破碎率

Effective stresses in q- $p'$ plane and particle breakage indexes at end of K₀-tests

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图 8 参数A，K₁的试验回归值与D_r的关系曲线

Figure 8. Curves of test regression values A, K₁ versus D_r values

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图 9 K₀的计算与试验结果的比较

Figure 9. Comparison between calculated and measured K₀-values

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图 10 切线泊松比的计算与试验结果的比较

Figure 10. Comparison between calculated and measured tangent Poisson's ratio

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图 11 切线模量的计算与试验结果的比较

Figure 11. Comparison between calculated and measured tangent moduli

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图 12 应力-应变曲线的预测与试验结果的比较

Figure 12. Comparison between predicted and measured stress-strain curves

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表 1 珊瑚砂的基本物理指标

Table 1 Physical parameters of coral sand

土粒相对质量密度G_s	平均粒径d₅₀/mm	不均匀系数C_u	最大孔隙比e_max	最小孔隙比e_min
2.78	0.50	1.93	1.196	0.829

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表 2 式（1）参数A，B的试验回归值

Table 2 Test regression values for parameters A and B of Eq. (1)

D_r	A	B	R²
0.5	718.94	1.281	0.9960
0.6	732.40	1.242	0.9961
0.7	779.94	1.245	0.9969
0.8	870.28	1.261	0.9976
0.9	906.65	1.237	0.9965

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表 3 式（2）参数K₁，ΔK的试验回归值

Table 3 Test regression values for parameters K₁ and ΔK of Eq. (2)

D_r	K₁	ΔK	R²
0.5	0.434	0.087	0.9777
0.6	0.426	0.093	0.9739
0.7	0.420	0.097	0.9800
0.8	0.403	0.090	0.9903
0.9	0.383	0.087	0.9589

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表 4 试验参数回归值的计算公式

Table 4 Formulas for test parameter regression value

试验参数	回归值计算公式	相关参数	R²
A	$A = {a_1} + {b_1}{D_{\text{r}}}$	a₁ =442.33, b₁=513.30	0.9284
B	$B = {c_1}$	c₁= 1.253
K₁	${K_1} = {a_2} - {b_2}{D_{\text{r}}}$	a₂ =0.501, b₂=0.125	0.9226
$\Delta K$	$\Delta K = {c_2}$	c₂=0.091

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表 5 试验参数的计算回归值

Table 5 Calculated regression values of test parameters

D_r	A	B	K₁	ΔK
0.5	698.98	1.253	0.439	0.091
0.6	750.31	1.253	0.426	0.091
0.7	801.64	1.253	0.414	0.091
0.8	852.97	1.253	0.401	0.091
0.9	904.30	1.253	0.389	0.091

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