• Optics and Precision Engineering
  • Vol. 31, Issue 5, 565 (2023)
Ou ZOU1,2, Jian XUE3, Na LI2, Xin WANG2..., Rong YANG3 and Yuqiong LI2,*|Show fewer author(s)
Author Affiliations
  • 1College of Engineering Science, University of Chinese Academy of Sciences, Beijing00049, China
  • 2Key Laboratory for Mechanics in Fluid Solid Coupling Systems, Institute of Mechanics, Chinese Academy of Sciences, Beijing100190, China
  • 3State Key Laboratory of Nonlinear Mechanics, Institute of Mechanics, Chinese Academy of Sciences, Beijing100190, China
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    DOI: 10.37188/OPE.20233105.0565 Cite this Article
    Ou ZOU, Jian XUE, Na LI, Xin WANG, Rong YANG, Yuqiong LI. Inversion method of soil Mohr-Coulomb parameters based on dynamic cavity expansion model[J]. Optics and Precision Engineering, 2023, 31(5): 565 Copy Citation Text show less

    Abstract

    To achieve accurate and rapid interpretation of in-situ soil mechanical parameters and quantitatively evaluate military equipment mobility, an inversion method for soil Mohr-Coulomb parameters is established based on the dynamic cavity expansion model using the resistance-velocity relationship, acceleration and velocity curves, and the relationship between depth and initial velocity measured during the impact penetration process. It indicates that accurate fitting of the resistance coefficients is critical for interpreting Mohr-Coulomb parameters. Precise results could be derived using the measured velocity curve. Based on the experimental results reported by Forrestal et al. using the proposed method, the relative errors of soil cohesion and internal friction angle interpretation are 2.14% and 9.77%, respectively. Furthermore, the solution domain of the Mohr-Coulomb parameters under the dynamic cavity expansion model is revealed, and parameter sensitivity is investigated. The proposed inversion method resolves the problems of unclear physical images and strong parameter dependency in traditional semi-empirical interpretation methods. It could provide a new approach for rapidly determining soil Mohr-Coulomb parameters and assessing soil bearing capacity in complex geological environments.
    η*=1-ρ0/ρ*(1)

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    σr-σθ=τ0+λp(2)

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    τ0=6Ccosφ3-sinφλ=6sinφ3-sinφ(3)

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    13r(r+u)3=ρ0ρ*r2(4)

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    (r+u)2σrr+21+ur(r+u)(σr-σθ)+ρ0r22ut2=0,(5)

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    u(r=0,t)=Vt(6)

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    ρ*v2-c=ρ0v1-c(7)

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    σr2+ρ*v2v2-c=σr1+ρ0v1v1-c(8)

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    σn=τ0A+ρ0BVzcosϕ2(9)

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    A=1αγ2α1+τ02E2α-1λ(10)

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    B=31-η*1-2α2-α+1γ2α+21+τ02E2α3τ0E+η*1-3τ02E2-γ321-η*2-α+3γ31-η*1-2α2-α1+τ0/2E4,(11)

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    α=3λ3+2λγ=Vc=1+τ02E3-1-η*1/3(12)

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    A=2γ1+τ02E-43(13)

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    B=-2lnγ1-η*+1γ31+τ02E3τ0E+η*1-3τ02E2-          231+τ02E-3-3ln1+τ0/2E1-η*.          (14)(14)

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    A=23-2lnγ1+τ0/2E-1(15)

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    B=321-η*+1γ23τ0E+η*1-3τ02E2-γ21+τ0/2E41+31+τ0/2E31-η*.(16)

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    Fz=αs+βsVz2(17)

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    αs=πr2τ0A1+4μψ2π/2-θ0-μ2ψ-14ψ-11/2,(18)

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    βs=πr2ρ0B8ψ-124ψ2+μψ2π/2-θ0-μ2ψ-16ψ2+4ψ-14ψ-11/224ψ2.(19)

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    Φ=8ψ-124ψ2(20)

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    αs=πa2τ0A(21)

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    βs=πa2Φρ0B(22)

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    mdVzdt=-(αs+βsVz2)(23)

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    Vz=αsβs1/2tanarctanβsαs1/2V0-αsβs1/2tm(24)

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    az=αs/mcos2arctanβsαs1/2V0-αsβs1/2tm(25)

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    P=m2βsln1+βsV02αs(26)

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    C=3τ023+2λ3-λφ=arcsin3λ6+λ(27)

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    Π1τ0,λ=τ0EA-αsπa2E(28)

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    Π2τ0,λ=B-βsπa2Φρ0(29)

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    L1τ0=τ0EA-αsπa2E(30)

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    L2τ0=B-βsπa2Φρ0(31)

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    Q1=i=1NFz,i-αs-βsVz,i22(32)

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    Q1αs=0,Q1βs=0(33)

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    αs=i=1NFz,ii=1NVz,i4-i=1NFz,iVz,i2i=1NVz,i2Ni=1NVz,i4-i=1NVz,i22(34)

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    βs=Ni=1NFz,iVz,i2-i=1NFz,ii=1NVz,i2Ni=1NVz,i4-i=1NVz,i22(35)

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    C=2.61 MPa,φ=15.33°(36)

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    τ=6sinφ3-sinφp+6Ccosφ3-sinφ(37)

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    C=2.64 MPa,φ=18.75°(38)

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    C=3.81 MPa,φ=3.14°(39)

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    Q2=i=1NPi-m2βsln(1+βs'V0,i2)2(40)

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    βs'=βs/αs(41)

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    Q2βs=0,Q2βs'=0(42)

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    i=1NPi-m2βsln(1+βs'V0,i2)V0,i21+βs'V0,i2=0(43)

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    βs=m2i=1Nln2(1+βs'V0,i2)i=1NPiln(1+βs'V0,i2)(44)

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    fβs'=i=1NPi-i=1NPiln(1+βs'V0,i2)i=1Nln2(1+βs'V0,i2)ln(1+βs'V0,i2)V0,i21+βs'V0,i2(45)

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    C=25.17 kPa,φ=29.08°(46)

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    Ou ZOU, Jian XUE, Na LI, Xin WANG, Rong YANG, Yuqiong LI. Inversion method of soil Mohr-Coulomb parameters based on dynamic cavity expansion model[J]. Optics and Precision Engineering, 2023, 31(5): 565
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