为验证该模型测试精确性,设计验证试验(图11),试验土样为砂土,其物理参数与建模土样一致,压实度95%,含水率为最佳含水率状态,试件直径5 cm,长度为14 cm。试件保持水平状态下,表面随机施加10组不同压应力fi,读取压应力数值并测试试件整体剪切波速。

图11 验证试验示意图Figure 11 Verification test

如图11所示,沿应力传播方向取一微土层厚度为dh,该土层位置距离试件表面为h,微土层剪切波速为v,计算公式为

$\begin{array}{l} v = 0.003{\left[ {{f_i}\left( {1 - {{\left( {\frac{1}{{1 + {{\left( {r/h} \right)}^2}}}} \right)}^{3/2}}} \right)} \right]^2} + \\ \quad 1.002\left[ {{f_i}\left( {1 - {{\left( {\frac{1}{{1 + {{\left( {r/h} \right)}^2}}}} \right)}^{3/2}}} \right)} \right] + 199.5 \end{array}$(6)

式中r为试件表面受力面半径。则剪切波速通过dh微土层的时间dt为

${\rm{d}}t = \frac{{{\rm{d}}h}}{v}$(7)

将式(6) 代入式(7),并对试件长度取积分可得剪切波速通过整个试件长度所需时间T,即

$\begin{array}{l} T = \int_0^H {{\rm{d}}h} /\left\{ {0.003{{\left[ {{f_{\rm{i}}}\left( {1 - {{\left( {\frac{1}{{1 + {{\left( {r/h} \right)}^2}}}} \right)}^{3/2}}} \right)} \right]}^2}} \right. + \\ \left. {\quad \quad 1.002\left[ {{f_{\rm{i}}}\left( {1 - {{\left( {\frac{1}{{1 + {{\left( {r/h} \right)}^2}}}} \right)}^{3/2}}} \right)} \right] + 199.5} \right\} \end{array}$(8)

则试件整体剪切波速计算值Vs为

${V_{\rm{s}}} = \frac{H}{T}$(9)

将式(8) 代入式(9) 可求出试件整体剪切波速理论计算值,此处H为14 cm,r为5 cm。将每个fi作用下试件整体剪切波速的理论计算值与实测值进行对比分析,结果如表1所示。

表1 数据验证对比表Table 1 Verification and contrast of data

表1中Vt为试件整体剪切波速的理论计算值,Va为试件整体剪切波速的实测值,平均相对误差指整体剪切波速的理论计算值与实测值的相对误差平均值,其值为0.04,表明模型计算精度相对较高。
4 结论
本文设计了变应力剪切波速测试仪器,对粘土、砂土两种土样分别进行变应力状态下剪切波速测试试验。在考虑土颗粒应力传播扩散及损失特点的前提下,对试验数据进行分析研究,建立土基应力与剪切波速理论模型,在此基础上设计验证实验,对比分析理论及实测数据,验证模型的有效性,得出如下结论。
(1) 土基剪切波速随应力的增大总体呈增大趋势。但因土颗粒应力传播扩散特性,应力相等条件下,土体剪切波速随测试土层厚度的增大而下降。
(2) 在外界其他条件固定的前提下,土基应力对土基剪切波速的影响显著。同密实度条件下,剪切波速随应力的变化幅度可达5倍以上,工程中必须考虑应力对剪切波速的影响。
(3) 在试验建模过程中,土中应力排除了土体自重应力对剪切波速的影响,建立的应力-剪切波速模型基于土颗粒应力扩散特点,可准确反映土层所受应力与剪切波速的相关性规律,其中应力作用方向与剪切波速传播方向相同。通过实测数据验证,模型计算相对误差为0.04,表明模型计算精度相对较高。
(4) 本文研究成果将大幅提升深层地基剪切波速测试试验及物探试验的评估准确性,对大应力、高深度地基土剪切波速特性及抗剪性能研究与分析有重要参考价值。同时也存在不足,建模及试验环节尚可继续改进,减小测试误差,模型的实用性也需要大量试验及实测数据进一步完善。
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