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Civil Engineering Department of Shanghai University Soil Mechanics Chapter 2 §3 permeability in soil 土的渗透性 •土的渗透性 Permeability •有效应力 Effective stress 3.1 土的渗透性 Permeability 1 达西定律Darcy Law This states that discharge velocity, v of water is proportional to the hydraulic gradient, i . v=q/A= k i H1 H 2 i L where : K=Darcy coefficient of permeability ,m/s The hydraulic gradient i is the ratio of the head loss h over a distance L The discharge velocity v is defined as the quantity of water , q percolating through a cross-sectional area A in unit time .This is not the sane as the velocity of the water percolating through the soil which is known as the seepage velocity . n Vv V , As nA q v 1 e v0 v As n e Constant head permeameter Falling head permeameter Civil Engineering Department of Shanghai University Soil Mechanics Chapter 2 2 粘性土的渗透性 Permeability of Clay (C la y) v= k( i-i b' ) v= ki (s an d) v i ib ib' 3 渗透性力 Force of permeability w h1 F w LF cos w h2 F TLF 0 Z1 Z 2 cos L wh1 w Z1 w Z 2 wh2 TL 0 w h1 Z1 Z 2 h2 TL 0 h1 Z1 h2 Z 2 H1 H 2 H1 H 2 i L T wi j T wi j wi d s 1 1 e w 1 nd s 1 w 4 流砂与管涌 Running Sand, Heaving or Piping 解 水头差:h=1.5+2.5=4m 流径长L=2.5+2d 细砂的浮容重: s 26.8 10 9.6 KN / m3 1 e 1 0.75 ' 临界水力梯度 考虑安全系数后,实有的水力梯度为: h ' K1 2.5 2d 4 9.6 1.5 2.5 2d 10 d 1.88m ' icr h i K1 2.5 2d 5 临界水力梯度 Critical hydraulic gradient ' s w icr w w (1 e) Civil Engineering Department of Shanghai University Soil Mechanics Chapter 2 • Calculate the Force of permeability applied on sand γs=26.8kN/m3, e=0.72, Determine whether will running sand occur? • If • If the running sand occurs, calculate the necessary water head difference. L=25cm For the seepage situations shown in Fig below, the length of the sand sample L=25cm and water head difference h=20cm. h=20cm Exercise 3-1 Civil Engineering Department of Shanghai University Soil Mechanics Chapter 2 3.2 有效应力Effective stress 1.The Principle of Effective Stress ♦ The importance of the forces transmitted through the soil skeleton from particle to particle was recognized in 1923 when Terzaghi presented the principle of effective stress, an intuitive relationship based on experimental data. The principle applies only to fully saturated soils and relates the following three stresses: (1) 总应力 the total normal stress (σ) (2) 孔隙水压力 the pore water pressure (u) (3) 有效应力 the effective normal stress (σ’ ) 总应力 the total normal stress (σ) on a plane within the soil mass, being the force per unit area transmitted in a normal direction across the plane, imaging the soil to be a solid (single-phase) material. 孔隙水压力 the pore water pressure (u), being the pressure of the water filling the void space between the solid particles. 有效应力 the effective normal stress (σ’ ) on the plane, representing the stress transmitted through the soil skeleton only. Civil Engineering Department of Shanghai University Soil Mechanics Chapter 2 A A Ns uAw Ns Aw u ' 1 u A A ♦ The relationship is : σ = σ’ +u The Principle of Effective Stress -Un-Saturated soil Bishop,1959 ua xua uw ' x Aw A For Saturated soil: x=1 For completely dried soil x=0 ' uw ' ua Civil Engineering Department of Shanghai University Soil Mechanics Chapter 2 Skempton A W, 1961 a tg u uw ' 1 tg ' a tg u S xuw ' 1 tg ' (For Completely Saturated soil) (For Partly Saturated soil) Civil Engineering Department of Shanghai University Soil Mechanics Chapter 2 -静水条件下的有效应力 hydrostatic Total stress at a-a plane w h1 sat h2 pore water pressure u w hw w h1 h2 effective normal stress at a-a plane ’ =-u w h1 sat h2 w h1 h2 'h2 Civil Engineering Department of Shanghai University Soil Mechanics Chapter 2 -自上而下的稳定渗流 Seepage to the down Total stress at a-a plane w h1 sat h2 pore water pressure u w h1 h2 h w hw effective normal stress at a-a plane ' u w h1 sat h2 w h1 h2 h ' h2 w h ' w i h2 i=h/h2 Civil Engineering Department of Shanghai University Soil Mechanics Chapter 2 -自下而上的稳定渗流 Seepage to the upper Total stress at a-a plane w h1 sat h2 h h1 hw b pore water pressure u w h1 h2 h whw b h2 a a u effective normal stress at a-a plane ' u w h1 sat h2 w h1 h2 h ' h2 w h ' wi h2 i=h/h2 γwh σ' Civil Engineering Department of Shanghai University Example For sand, e=0.6, Sr=35% (above water table) γs=27kN/m3, For clay, γsat=21kN/m3 Calculate the total stress, pore water pressure and the effective stress in 9m depth. Plot the distribution. Soil Mechanics Chapter 2