Study on the relationship model between P-wave velocity and strength parameters of marine sediments
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摘要: 海底沉积物具有质地松软、强度低的特点，其强度参数与海上平台插桩就位、导管架的安装等工程关系紧密，与海上作业安全息息相关。常规钻孔取芯与静力触探等强度参数获取方法成本较高、取样点少，且对沉积物扰动较大，利用易获取的声学资料预测海底沉积物的强度参数具有重要研究意义。本文基于Wood方程、Biot-Stoll模型、Dvorkin等效介质模型等声波传播理论，计算不同物性参数（密度、孔隙度）梯度下的理论纵波速度，结合室内模拟地层声学实验，对比了模型计算声速与实测声速的变化特征，建立了声速与物性参数关系模型。基于室内模拟地层土力学试验，揭示了沉积物物性与抗剪强度、黏聚力等参数之间的关系，建立了物性与强度参数关系模型。以物性参数为桥梁，建立基于声学特征的海底沉积物强度参数预测模型。此模型既避免了原位取样沉积物失水扰动的问题，又弥补了经验公式局限性的缺点，具有普适性与准确性，有效提高无法取样地区沉积物强度参数的精度，提高了经济效益，对浅层的勘探与开发起到了理论指导的作用。Abstract: Marine sediments are characterized by soft texture and low strength, and their strength parameters are closely related to offshore platform pile placement and jacket installation, and are closely related to offshore operation safety. Conventional methods for obtaining strength parameters, such as drilling and cone penetration test, have high cost, few sampling points, and great disturbance to the soil. Therefore, it is of great significance to predict the strength parameters of marine sediments with easily accessible acoustic data. Based on the acoustic propagation theories such as Wood equation, Biot-Stoll model and Dvorkin equivalent medium model, the theoretical P-wave velocity under different physical parameter (density, porosity) gradients was calculated. Combined with the indoor simulated stratum acoustic experiment, the variation characteristics of the calculated and measured sound velocity were compared, and the relationship model between sound velocity and physical parameter was established. The relationship between soil physical parameter and shear strength, cohesive force and other parameters was revealed based on laboratory geotechnical test, and the relationship model between soil physical parameter and strength parameters was established. A prediction model for strength parameters of marine sediments based on acoustic characteristics was established by using physical parameters as bridge. This model not only avoids the problem of water loss disturbance of in-situ sampled soil, but also makes up for the limitation of empirical formula. It has universality and accuracy, and can effectively improve the precision of strength parameters of soil in unsampled areas, improve economic benefits, and play a theoretical guiding role in shallow exploration and development.
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图 3 不同密度土体直接剪切试验
蓝点为实测数据
Fig. 3 Direct shear test of soil samples with different density
The blue dots represent the measured data
图 4 不同孔隙度土体直接剪切试验
蓝点为实测数据
Fig. 4 Direct shear test of soil samples with different porosity
The blue dots represent the measured data
图 5 密度、强度参数与纵波速度的关系
Fig. 5 Relationship between density, strength parameters and P-wave velocity
表 1 声波传播理论参数
Tab. 1 Parameters of the theory of acoustic propagation
序号 参数名称 Wood
模型Biot-Stoll
模型Dvorkin等效
介质模型1 孔隙流体密度ρf/（kg·m−3） 1 025 1 025 1 025 2 基质颗粒密度ρg/（kg·m−3） 2 650 2 650 2 650 3 绝对黏度η/（kg·m−3） − 0.001 − 4 密度ρ/（kg·m−3） − 实际 实际 5 孔隙度ϕ/% 实际 实际 实际 6 临界孔隙度ϕc/% − − 38 7 基质颗粒体积模量Kr/Pa 1.47×1010 1.47×1010 1.47×1010 8 基质颗粒剪切模量µr/Pa − − 1.34×1010 9 孔隙流体体积模量Kf/Pa 2.18×109 2.18×109 2.18×109 10 泊松比σ − 0.15 0.15 11 曲折度c − 1.35 − 12 渗透率κ/m2 − 公式（13） − 13 体积衰减系数δb − 0.1 − 14 剪切衰减系数δs − 0.1 − 15 颗粒平均接触次数n − − 8.5 注：“实际”代表各参数根据实际配置情况得到；“−”代表没有取值。 
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表 2 实验土样基本配置情况
Tab. 2 Basic configuration of experimental soil
序号 密度/（g·cm−3） 孔隙度/% 孔隙比 水质量/g 砂土质量/g 黏土质量/g 1 1.54 51.5 1.06 3 061 11 130 7 420 2 1.57 50.5 1.02 3 122 11 350 7 567 3 1.61 49.2 0.97 3 201 11 638 7 759 4 1.64 48.5 0.94 3 251 11 818 7 879 5 1.67 47.4 0.9 3 320 12 067 8 045 6 1.71 46.2 0.86 3 391 12 327 8 218 7 1.75 44.8 0.81 3 485 12 667 8 445 8 1.8 43.2 0.76 3 583 13 027 8 685 9 1.84 42.5 0.74 3 625 13 177 8 785 10 1.88 40.8 0.69 3 732 13 567 9 045
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表 3 纵波速度与物性参数关系
Tab. 3 Relationship between P-wave velocity and physical parameters
序号 参数 函数表达式 R2 RMSE 1 密度ρ ρ=0.669Vp2.699 0.943 1 0.029 19 2 孔隙度ϕ ϕ=1.379Vp−3.161 0.959 4 0.007 65 注：纵波速度单位为km/s，密度单位为g/cm3。
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表 4 强度与物性参数关系
Tab. 4 Relationship between strength and physical parameters
参数 函数表达式 R2 RMSE 抗剪强度τ τ=−61.22ρ2+259.2ρ−213.5 0.946 4 1.562 τ=−555.3ϕ2+351.3ϕ+6.81 0.958 0 1.383 黏聚力c c=−70.15ρ2+297.1ρ−256.2 0.924 1 2.161 c=−637.2ϕ2+403.7ϕ−3.845 0.929 1 2.089 内摩擦角φ φ=6.899ρ+7.547 0.565 1 0.740 φ=−21.92ϕ+29.47 0.550 4 0.753 注：抗剪强度、黏聚力单位为kPa，内摩擦角单位为（°）。
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表 5 强度参数预测模型
Tab. 5 Prediction model of strength parameters
序号 参数 函数表达式 R2 RMSE 1 抗剪强度τ τ=27.4Vp2.996+1.294Vp1.498−29.89 0.927 7 1.961 2 黏聚力c c=33.13Vp3.022+4.858Vp1.511−40.64 0.928 4 2.267 3 内摩擦角φ φ=−4.594×1010Vp−75.11+20 0.631 6 0.729 注：抗剪强度、黏聚力单位为kPa，内摩擦角单位为（°），纵波速度单位为km/s。
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