地球構造

公式總表

公式總表

閱讀時間 // 約 2 分鐘

主題公式
應變e=(l−l0)/l0e = (l-l_0)/l_0；s=1+es = 1+e；λ=s2\lambda = s^2；γ=tan⁡ψ\gamma = \tan\psi；R=X/YR = X/Y
Flinnk=X/Y−1Y/Z−1k = \dfrac{X/Y - 1}{Y/Z - 1}
體積變化Δ=(V−V0)/V0\Delta = (V - V_0)/V_0
靜岩壓σV=ρgz\sigma_V = \rho g z（約 26–30 MPa/km）
Mohr 圓σn=σ1+σ32+σ1−σ32cos⁡2θ\sigma_n = \frac{\sigma_1+\sigma_3}{2} + \frac{\sigma_1-\sigma_3}{2}\cos 2\theta；σs=σ1−σ32sin⁡2θ\sigma_s = \frac{\sigma_1-\sigma_3}{2}\sin 2\theta
平均應力σm=(σ1+σ2+σ3)/3\sigma_m = (\sigma_1+\sigma_2+\sigma_3)/3
單軸應變σH=ν1−νσV\sigma_H = \frac{\nu}{1-\nu}\sigma_V；σdiff=1−2ν1−νσV\sigma_{\text{diff}} = \frac{1-2\nu}{1-\nu}\sigma_V
熱應力ΔσH=EαΔT1−ν\Delta\sigma_H = \dfrac{E\alpha\Delta T}{1-\nu}
彈性σ=Ee\sigma = Ee；σs=μγ\sigma_s = \mu\gamma；μ=E2(1+ν)\mu = \frac{E}{2(1+\nu)}；K=E3(1−2ν)K = \frac{E}{3(1-2\nu)}；Vs=G/ρV_s = \sqrt{G/\rho}
黏性σs=ηγ˙\sigma_s = \eta\dot\gamma；Maxwell tM=η/Gt_M = \eta/G
Maxwell／Kelvine˙=σ˙/E+σ/η\dot e = \dot\sigma/E + \sigma/\eta；σ=Eε+η dε/dt\sigma = E\varepsilon + \eta\,d\varepsilon/dt
Bingham／Prandtlτ=τy+ηγ˙\tau = \tau_y + \eta\dot\gamma；ε=σ/E+εp\varepsilon = \sigma/E + \varepsilon_p
冪律潛變e˙=Aσnexp⁡(−Q/RT)\dot e = A\sigma^n\exp(-Q/RT)
褶皺主導波長L=2πt(ηL6ηM)1/3L = 2\pi t\left(\dfrac{\eta_L}{6\eta_M}\right)^{1/3}
Byerleeσs=0.85σn\sigma_s = 0.85\sigma_n；σs=50+0.6σn\sigma_s = 50 + 0.6\sigma_n（MPa）
摩擦強度σ1−σ3≥βρgz(1−λ)\sigma_1 - \sigma_3 \ge \beta\rho g z(1-\lambda)；β=3, 1.2, 0.75\beta = 3,\ 1.2,\ 0.75
Coulombσs=C+μσn\sigma_s = C + \mu\sigma_n；θ=45∘+φ/2\theta = 45^\circ + \varphi/2；有效 σs=C+μ(σn−pf)\sigma_s = C + \mu(\sigma_n - p_f)
Griffithσs2=4T(σn+T)\sigma_s^2 = 4T(\sigma_n + T)（壓為正）；C=2TC = 2T；UCS =8T= 8T
應力集中σtip=σr(1+2a/c)\sigma_{\text{tip}} = \sigma_r(1 + 2a/c)
水力破裂Pf>σ3+TP_f > \sigma_3 + T
節理流量Q=−ρg b312μHΔPQ = -\dfrac{\rho g\,b^3}{12\mu}H\Delta P
位移–長度Dmax⁡=γLnD_{\max} = \gamma L^n
Coulomb 應力變化ΔCFS=Δτs−μ(Δσn−Δp)\Delta\mathrm{CFS} = \Delta\tau_s - \mu(\Delta\sigma_n - \Delta p)
應力形狀比Φ=σ2−σ3σ1−σ3\Phi = \dfrac{\sigma_2-\sigma_3}{\sigma_1-\sigma_3}
InSARΔϕ=4πλ(R1−R2)\Delta\phi = \dfrac{4\pi}{\lambda}(R_1 - R_2)（一環 = λ/2\lambda/2）
單位1 kbar = 100 MPa；1 GPa = 10 kbar；1 bar = 10⁵ Pa

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