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摘要:
本文从土体的导电性和Archie公式着手介绍了电阻率基本理论，调查了目前土体电阻率的主要测定方法以及常见的仪器设备，深入分析了土体电阻率的主要影响因素，对多种土体的电阻率模型及其应用现状进行归纳总结.结果表明，国内外区域性特殊土类电阻率模型构建研究较少，已有的不同土类电阻率模型使用参数存在较大差异，缺乏统一的电阻率测试方法，基于电阻率测试的土体物理力学性质的定量化评价研究不够深入，旨在为土体电阻率模型构建相关研究提供参考.
Abstract:This study introduces the basic theory of resistivity based on the soil conductivity and Archie's formula, investigates the current main measuring resistivity methods and common instruments, and the main influencing factors of soil resistivity are analyzed. The multiple soil resistivity models and applications were reviewed. The results show that there are less research on the construction of regional specific soil resistivity models, the parameters used in the existing resistivity models are quite different, and lack of unified resistivity testing method.The quantitative evaluation of soil physical mechanical properties is insufficient, aims to provide a reference for other related research work on soil resistivity model.
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Key words:
- Soil /
- Resistivity model /
- Archie's formula /
- Advance in future
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图 1
在孔隙率为50%时三种土的含水率与电阻率的关系(刘国华等，2004)
Figure 1.
The relationship between water content and resistivity of the three soils when the porosity is 50% (Liu et al., 2004)
图 2
三种土的含水率与电阻的关系(孙旭等，2019)
Figure 2.
The relationship between moisture content and electrical resistance othree types of soils (Sun et al., 2019)
图 3
饱和度对标准砂电阻率的影响(孙旭等，2019)
Figure 3.
The influence of saturation on the resistivity of standard sand (Sun et al., 2019)
图 4
饱和度对砂土、淤泥和黏土电阻率的影响(Rhoades et al., 1977)
Figure 4.
The effect of saturation on the resistivity of sand, silt and clay (Rhoades et al., 1977)
图 6
不同结构类型土的结构因子比较
Figure 6.
Comparison of structural factors of different structural types of soil(Fukue et al., 1999)
图 7
黏性土中电流的三种流通路径示意图(查甫生等，2007)
Figure 7.
Schematic diagram of three flow paths of current in cohesive soil(Zha et al., 2007)
表 1
三种常见的电阻率测试仪器
Table 1.
Three common resistivity test instruments
设备名称 示意图 优点 来源 固结仪电阻率测试装置 
在固结仪的基础上，分别在试样的顶部和底部安装电极，从而可在固结过程中测得两电极间的电势差. Fukue等(1999) Miller Soil Box优化装置 
对Miller Soil Box进行改进，不需要对测试得到的视电阻率进行换算，可直接测定土体电阻率. 刘国华等(2004) ESEU-1型土电阻率测试仪 
具备交流、低频、二项电极，能够与土工测试仪器较好搭配使用. 刘松玉等(2006) 
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表 2
砂土电阻率模型
Table 2.
Sandy soil resistivity model
模型类别 电阻率模型 应用条件及研究结论 来源 多参数模型 
适用于饱和无黏性土，最简化的电阻率模型 Archie (1942) 
适用于非饱和无黏性砂土 Keller和Frischknecht (1966) 
其中，ρ′0为污染土电阻率，F为地层结构因子，S0为混合孔液饱和度，n为饱和度指数，ρr为渗滤液电阻率，A、B为土体初始饱和度，C、D为渗滤液稀释公式系数，N为渗滤液稀释倍数在Archie公式基础上，建立的污染砂土电阻率模型 马媛媛等(2010) 
考虑了孔隙水电阻率、孔隙率以及饱和度的电阻率模型 王炳辉等(2017) 区域统计模型 原状砂土： 
相对电阻率：P=ρ′w/ρr=CN+D=0.79N+0.29
其中，ρ0为土体电阻率，Sw为含水饱和度，P为相对电阻率(混合液电阻率和初始渗滤液电阻率比值)，N为稀释后混合液体积.将电阻率与饱和度和孔隙水建立的关系式 郭秀军等(2012) ρ′0=φ－mρw=φ0.25Ln(N)－2.05(0.57N+2.77)ρr
其中，ρ′0为砂土体电阻率，ϕ为孔隙度，m为胶结指数，N为稀释倍数，ρr为原始渗滤液电阻率.城市生活垃圾渗滤液污染砂土的电阻率模型 吴水娟(2012) F=(1.028+0.096lgf)×n·exp(－1.57+1.028lgf)其中，f为电流频率. 描述了结构因子、电流频率和孔隙率的电阻率模型 刘晓凤等(2014) 多项混合模型 
其中，a1=γg－γw，a2=γg，a3=γgγw，γs为土颗粒均质材料的电阻率，γg为气相电阻率，γw为液相电阻率，Dr为密实度.考虑了饱和度和密实度的耦合关系所建立的电阻率模型 贺瑞等(2019)
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表 3
黏土电阻率模型
Table 3.
Resistivity model of cohesive soil
模型类别 电阻率模型 应用条件及研究结论 来源 多参数模型 
非饱和黏性土的电阻率模型 Waxman和Smits (1968) 
其中，ρswa为两极间土体的电阻率，ds为土粒体积质量黏性土三相电阻率模型 龚晓南等(2011) 串并联模型 
其中，θ为土水并联部分的水-土体积比.在三种电流传播路径基础上，建立的非饱和黏性土的电阻率模型 查甫生等(2007) 区域统计模型 qu=0.004e(ρ0/75.65)+36.65，R2=0.98768
qu=1.1e(ρ1/9.3)+36.785, R2=0.96614
其中，qu为无侧限抗压强度，ρ0为初始电阻率，ρ1为破坏电阻率，R2为相关系数不同干湿循环下红黏土无侧限抗压强度与初始电阻率和破坏电阻率的关系式 陈议城等(2020a) ρ=158114.79N－1.17w－3.32n1.83
其中，N为土体受污染程度.电阻率与含水率、孔隙率以及污染程度的拟合公式 陈议城等(2020b)
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表 4
黄土电阻率模型
Table 4.
Loess resistivity model
模型类别 电阻率模型 应用条件及研究结论 来源 区域统计模型 
其中，ρ为土在非饱和状态下的电阻率，ρsat为饱和状态下的电阻率，B为经验参数.含水率不变的情况下，电阻率与饱和度之间的关系式 刘志彬等(2013) 
其中，ρ/ρw为结构因子.非饱和黄土的电阻率模型 董晓强等(2015a) 多参数模型 
其中，ρdmax为最大干密度，G为相对密度，k为压实度.含水率和密实度与电阻率之间的关系式 朱才辉和李宁(2013)
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表 5
膨胀土电阻率模型
Table 5.
Resistivity model of expansive soil
模型类别 电阻率模型 应用条件及研究结论 来源 多参数模型 饱和土： 
非饱和土：
其中，ρsat为饱和土的电阻率，ρs为土骨架的电阻率，ρunsat为非饱和土的电阻率.饱和、非饱和土的电阻率模型 缪林昌等(2007) 
其中，Er为综合电阻率指标，A为各向异性系数，F为平均归一化电阻率，ϕ-m为土体电阻率的孔隙率指标.综合电阻率指标用于膨胀土的结构分析 储亚等(2017) 区域统计模型 
电阻率与孔隙度和饱和度的关系式 Yan等(2012) 
其中，ρ初始为初始电阻率.不同含水率下，无限抗压强度与电阻率之间的关系 吴道祥等(2016)
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表 6
冻土电阻率模型
Table 6.
Resistivity model of frozen soil
模型类别 电阻率模型 应用条件及研究结论 来源 区域统计模型 未冻水含量: 
未冻冰含量:
其中, ρuw0为未冻水的电阻率, ρi0为冰的电阻率, 为冰含量wuw为未冻水含量, wi为冰含量, a为电阻率与含冰量幂律的指数.未扰动冻土的电阻率与未冻水含量和未冻冰含量关系式 Fortier等(2008) 
不同温度下冻土单轴抗压强度与初始电阻率的拟合式 付伟等 (2009) 
其中, Ki、bi为与土壤颗粒、未冻水或冰晶电导率有关的系数, θu为冻土未冻水含量.冻土在整个冻结阶段的电阻率模型 Tang等(2018) 多相混合模型 
其中, A、B、C、D为系数相关的冻土的结构特性和电阻率的每个组件的冻土, w为冻土的含水量, aθ-b为冻土的未冻水水含量, θ为冻土温度的绝对值, ρd为冻土的干密度.考虑了冻土各部分电阻率系数的冻土电阻率模型 Shan等(2015)
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表 7
水泥土电阻率模型
Table 7.
Resistivity model of cement-soil
模型类别 电阻率模型 应用条件及研究结论 来源 多参数模型 
其中，δ为收缩度，m为常数.将水泥土的电阻率与孔隙率和收缩度相结合 Tumidajski等(1996) 
其中，a、b为经验参数，wpb为铅含量.水泥固化重金属铅污染土的电阻率模型 章定文等(2015) 区域统计模型 
其中，ρs(y)D、ρs(x)1分别为龄期D和龄期1 d的水泥土电阻率值，(x)1、(y)D分别为龄期1 d和D的NaOH溶液浓度，A、B、C为常数，D为龄期.受NaOH浸泡的水泥土电阻率预测公式 董晓强等(2007) 
该模型考虑了水泥掺入量、龄期对电阻率的影响 Zhang等(2012) 普通硅酸盐水泥土： 
矿渣硅酸盐水泥土：
两种水泥土电阻率与无限抗压强度关系 董晓强等(2015b) 
预测固化污染土的无限抗压强度 查甫生等(2019) 串并联模型 串联： 
并联：
其中，dsgs、dsgp分别为串联和并联模型的水泥土的电阻率，dg为水泥的电阻率，dw为孔隙水的电阻率，ds为土颗粒电阻率，λ为水泥掺合比.通过电阻率与无线抗压强度的测试，建立水泥土电阻率串、并联模型 缪林昌等(2001a，b)
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表 8
盐渍土电阻率模型
Table 8.
Resistivity model of saline soil
模型类别 电阻率模型 应用条件及研究结论 来源 区域统计模型 
盐渍土的电阻率关于含水率的拟合公式 李玲等(2012) 
测出电阻率值根据拟合公式，进而反算土体含盐量 王乐凡等(2014) 
其中，P为钠盐含量.钠盐盐渍土的电阻率模型 罗述伟(2019)
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