Experimental investigation and theoretical models on dynamic shear moduli and damping ratios for Yellow River sediment under different influence factors
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摘要: 沿黃河高速公路建設過程中，黃河泥沙作為路基填料的可行性已經得到驗證和重視，然而目前有關黃河泥沙作為路基填料的動力特性的研究較少。本文利用英國GDS動態三軸試驗系統，對取自黃河中下游鄭州段的泥沙進行應力控制的動三軸試驗，探究了圍壓、相對密實度和試驗頻率對黃河泥沙動剪應力–動剪應變關系、動剪切模量G和阻尼比D的影響，繪制了動剪應力–動剪應變關系骨干曲線和滯回曲線。結果表明，黃河泥沙的動剪切模量、阻尼比與剪應變關系可以用Hardin雙曲線模型描述，圍壓對G和D的影響較大、試驗頻率對G和D的影響較小。綜合與其他土體的動力特性對比表明，黃河泥沙動剪切模量折減曲線規律以及阻尼比D曲線規律和其他土體相符，其動力特性更接近于粉土和砂土，但與其他土體并不完全一致，具有一定的特殊性。最后，本文考慮了圍壓、相對密實度的影響，并結合現有經驗公式，建立可以較好描述黃河泥沙最大動剪切模量Gmax與圍壓、孔隙比關系的經驗公式，同時建立了動剪切模量比G/Gmax和D的數學模型，擬合結果顯示，建立的模型能較好地描述黃河泥沙的G/Gmax和D隨剪應變的變化規律。Abstract: The dynamic shear modulus and damping ratio are essential parameters for the site seismic response analysis of major projects. During highway construction along the Yellow River, the feasibility of using Yellow River sediment as a subgrade filler has been verified and valued. However, the dynamic characteristics of Yellow River sediment as subgrade filler are rarely studied. In this paper, the British GDS dynamic triaxial test system was used to perform dynamic triaxial stress control tests on the sediment taken from the Zhengzhou section of the middle and lower reaches of the Yellow River. A total of 11 groups of tests were performed to explore the effects of confining pressure, relative density, and test frequency on the dynamic shear stress–dynamic shear strain relationship, dynamic shear modulus G, and damping ratio D of Yellow River sediment. The backbone curve and hysteresis curve of the dynamic shear stress–dynamic shear strain relationship were plotted. The results show that the relationship between the dynamic shear modulus, damping ratio, and shear strain of Yellow River sediment can be described by the Hardin hyperbolic model, and confining pressure has the greatest influence on the dynamic shear modulus and damping ratio of Yellow River sediment. For a given shear strain condition, the larger the confining pressure is, the larger the dynamic shear modulus. When the strain level is large, the dynamic shear modulus increases with the relative density; the damping ratio decreases with increasing confining pressure and increasing relative density. Frequency has no obvious effect on the dynamic shear modulus and damping ratio. A comprehensive comparison with the dynamic characteristics of other soils shows that the dynamic shear modulus reduction curve law and damping ratio D curve law of Yellow River sediment are consistent with those of other soils, and their dynamic characteristics are closer to silt and sand, but not completely consistent with those of other soils, with certain particularity. Finally, considering the influence of confining pressure and relative density, combined with the existing empirical formula, an empirical formula that can better describe the relationship between the maximum dynamic shear modulus Gmax and the confining pressure and void ratio of Yellow River sediment is established. Additionally, a mathematical model of the dynamic shear modulus ratio G/Gmax and D is established. The fitting results show that the established model can better describe the variation in G/Gmax and D with the shear strain of Yellow River sediment. This capability provides an important basis for the seismic design of Yellow River sediment as subgrade filler.
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圖 3 黃河泥沙動剪應力–動剪應變關系曲線.(a) Dr=40%;(b) Dr=60%;(c) Dr=80%
Figure 3. Dynamic shear stress–dynamic shear strain curve of Yellow River sediment: (a) Dr=40%; (b) Dr=60%; (c) Dr=80%
圖 4 動剪應力–動剪應變關系曲線.(a)不同圍壓;(b)不同頻率
Figure 4. Dynamic shear stress–dynamic shear strain curve: (a) different confining pressures; (b) different frequencies
圖 5 不同影響因素下動剪切模量–剪應變關系曲線.（a）不同圍壓；（b）不同相對密實度；（c）不同頻率
Figure 5. Dynamic shear modulus–shear strain curve under different influencing factors: (a) different confining pressures; (b) different relative densities; (c) different frequencies
圖 6 不同影響因素下阻尼比–剪應變關系曲線。（a）不同圍壓；（b）不同相對密實度；（c）不同頻率
Figure 6. Different influencing factor damping ratio–shear strain curves: (a) different confining pressures; (b) different relative densities; (c) different frequencies
圖 8 (a) G–γd擬合示意圖; (b) lgGmax–lg
${\sigma'}_{ \mathrm{m}}$ 關系擬合Figure 8. (a) G–γd fitting schematic; (b) lgGmax–lg
${\sigma '}_{ \mathrm{m}}$ relationship fitting
圖 10 (a) Gmax歸一化曲線圖;(b)不同經驗模型Gmax試驗值與預測值對比
Figure 10. (a) Normalized curve of Gmax; (b) comparison of experimental and predicted Gmax values of different empirical models
圖 11 動剪切模量比–剪應變關系曲線。（a）不同圍壓；（b）不同相對密實度；（c）不同頻率
Figure 11. Dynamic shear modulus ratio–shear strain curve: (a) different confining pressures; (b) different relative densities; (c) different frequencies
圖 12 不同土的動剪切模量折減曲線
Figure 12. Dynamic shear modulus reduction curves of different soils
圖 13 G/Gmax–γd擬合圖。（a）不同圍壓；（b）不同相對密實度；（c）不同頻率
Figure 13. G/Gmax–γd fitting diagram: (a) different confining pressures; (b) different relative densities; (c) different frequencies
圖 14 阻尼比擬合曲線示意圖。（a）不同圍壓；（b）不同相對密實度；（c）不同頻率
Figure 14. Damping ratio fitting curve diagram: (a) different confining pressures; (b) different relative densities; (c) different frequencies
表 1 試驗用砂物性指標
Table 1. Physical properties of sand for testing
Sample name Coefficient of uniformity Coefficient of curvature Maximum dry density/(g·cm?3) Minimum dry density/(g·cm?3) Optimum water content/% Plasticity index Specific gravity Yellow River sediment 5.080 1.662 1.650 1.357 13.7 11.4 2.7 
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表 2 試驗方案
Table 2. Test scheme
Confining pressure/kPa Relative compaction/% Loading frequency/Hz Dynamic stress amplitude/kPa Number of cycles 50 60 1 Based on the test to determine (from 0.1 or 0.05 times the confining pressure to start the step-by-step loading until the specimen is damaged) 6 100 40/60/80 1 0.01/0.1/
0.5/1/2200 60 1 400 60 1 800 60 1
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表 3 G–γd擬合結果
Table 3. G–γd fitting results
Confining pressure/
kPaRelative compaction /
%Loading frequency/Hz m/10?3 n/10?3 R2 Gmax/MPa 50 60 1 20.45 146.13 0.997 48.90 100 40 1 10.70 98.93 0.998 93.46 60 11.54 86.08 0.997 86.66 80 10.16 71.79 0.996 98.43 100 60 0.01 10.21 104.23 0.995 97.94 0.1 10.62 111.53 0.999 94.16 0.5 10.45 89.55 0.994 95.69 1 11.54 86.08 0.997 86.66 2 10.96 71.74 0.996 91.24 200 60 1 6.81 50.41 0.997 146.84 400 4.69 23.33 0.998 213.22 800 3.36 12.03 0.995 297.62
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表 4 Gmax預測結果
Table 4. Gmax prediction results
Confining pressure/kPa Relative compaction/% Loading frequency/Hz Gmax test value This paper Liang Ke Saxena 50 60 1 48.90 63.16 52.02 39.76 100 40 1 93.46 84.23 71.47 53.27 60 86.66 93.51 80.23 59.20 80 98.43 103.76 89.94 65.88 100 60 0.01 97.94 93.51 80.23 59.20 0.1 94.16 93.51 80.23 59.20 0.5 95.69 93.51 80.23 59.20 1 86.66 93.51 80.23 59.20 2 91.24 93.51 80.23 59.20 200 60 1 146.84 138.46 123.73 88.12 400 213.22 205.02 190.81 131.18 800 297.62 303.57 294.27 195.28
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表 5 G/Gmax–γd擬合結果
Table 5. G/Gmax–γd fitting results
Confining pressure/kPa Relative compaction/% Loading frequency/Hz γ0 α β R2 50 60 1 0.137749 1.12336 0.47742 0.99756 100 40 1 0.1057 1.17527 0.51195 0.99732 60 0.1314 1.12435 0.51381 0.99745 80 0.1366 1.05175 0.509 0.99531 100 60 0.01 0.09898 1.04343 0.52563 0.996 0.1 0.09596 1.19697 0.51855 0.998 0.5 0.116152 1.11664 0.52923 0.9959 1 0.1314 1.12435 0.51381 0.99745 2 0.147542 1.1563 0.50924 0.9966 200 60 1 0.1315 0.99785 0.51681 0.99784 400 0.2032 1.17553 0.51144 0.99827 800 0.271 1.04509 0.52231 0.99571
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表 6 D–γ擬合結果
Table 6. D–γ fitting results
Confining pressure
/kPaRelative compaction/% Loading frequency/Hz Dmin γr s n R2 50 60 1 0.015 0.137749 0.26776 1.10017 0.96232 100 40 1 0.005 0.1057 0.25282 1.81916 0.9971 60 0.005 0.1314 0.25125 1.68061 0.99383 80 0.006 0.1366 0.24241 1.66633 0.99513 100 60 0.01 0.01 0.09898 0.2551 1.72492 0.99819 0.1 0.01298 0.09596 0.23819 1.71884 0.9934 0.5 0.0059 0.116152 0.24989 1.73197 0.99224 1 0.005 0.1314 0.25125 1.68061 0.99459 2 0.004 0.147542 0.23602 1.78968 0.99364 200 60 1 0.0058 0.1315 0.23385 2.08471 0.99149 400 0.00568 0.2032 0.24971 1.67225 0.9987 800 0.003 0.271 0.24124 2.09711 0.99809
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