02 Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay 3 – Phase system Soil composition Volume Weight V AIR a Wa = 0 VV Vw WATER Ww = SOLIDS Vs Ws V = VS+VW+Va W = WS + WW Partially Saturated Soil Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Volumetric ratios Volumetric ratios commonly used in soil mechanics are: -Void ratio e -Porosity n -Degree of Saturation Sr -Air content ac -Air void ratio or Percentage air voids na Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Void ratio e is defined as the ratio of volume of voids to the volume of solids e = Vv/Vs Volume of voids Vv refers to that portion of the volume of the soil not occupied by solid grains Since the relationship between Volume of air Va and Volume of water Vw usually changes with ground water conditions as well as imposed loads, it is convenient to designate all the volume not occupied by solid grains as void space Volume of voids Vv Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay e = 0 ⇒ absence of voids (solid material) e > 1 ⇒ Vv >> VS in the soil mass Soil type void ratio e Uniform sand, loose 0.85 Mixed-grain sand, dense 0.43 Soft glacial clay 1.20 Soft highly organic clay 3.00 Soft Bentonite 5.20 Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay In nature, even though the individual void spaces are larger in coarse-grained soils, the void ratios of fine-grained soils are generally higher than those of coarse-grained soils. The ratio of volume of voids Vv to total volume V is defined as Porosity n. n = Vv/V But V = Vv + Vs = (1+Vv/VS) VS = (1+e) VS ⇒ n = e/(1+e) The porosity provides a measure of the permeability of a soil Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Porosity n of soil cannot exceed 100 % 0 < n < 100 Porosity n of a natural deposit = f ( Shape of grains, uniformity of grain size, and the conditions of sedimentation. n = 25 – 50 % (natural sands) n = 30 – 60 % (soft natural clays) Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Out of void ratio e and Porosity n, void ratio is used frequently in soil engineering because: e = Vv/Vs n = Vv/V Any change in V is a direct consequence of a similar changes in VV and while VS remains the same. Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Water content The water content w is given as WW/WS, expressed as a percentage. - where WW = Weight of water WS = Weight of solids (dry) Natural water content of fine-grained soils > coarse-grained soils. [No upper limit to w] Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Degree of saturation Sr For a fully saturated soil-water system, since all the voids will be completely filled with water: VVγW = WW where γW = unit weight of water For partial saturation: (VV - Va)γW = WW Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Hence the relationship for Sr the degree of saturation is given as: Sr = [(VV - Va)γW] / VV γW = VW /VV Sr is the ratio of the volume of water to the volume of void space (Generally expressed as a Percentage) 0 < Sr < 100 - For completely dry soil Sr = 0; - For fully saturated soil Sr = 1 or (100 %) Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Soil can be partially saturated [ 0 < Sr < 100] Sr ≈ 100 Thus, at a Sr of 100 % all the voids are filled with water. Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Degree of Saturation of Sand in various states Condition of Sand Sr [%] Dry 0 Humid 1-25 Damp 26-50 Moist 51-75 Wet 76-99 Saturated 100 - Valid only for sands Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Degree of saturation Sr Fine or silty sands are moist, wet or saturated. Clays are always completely or nearly saturated except in the layer of soil subjected to seasonal variation of temperature and moisture. Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Air content ac = Va/VV = [Va + VW – VW] /VV = [VV-VW]/VV = 1- Sr ac = 0 for saturated soil ac = 1 for dry soil Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Air void ratio or Percentage air voids na = Va/V By writing as Va Vv/(V Vv) = n ac Using n = Vv/V and ac = Va/Vv = n (1- Sr) Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Unit weight γ = (W/V) is one of the most important physical properties of the soil. -The unit weight must be expressed with due regard to the state of soil. γ = f (unit weight of solid constituents, n, and Sr) Earth Vertical stress ? pressure ? Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay (for a partially saturated soil) Bulk unit weight γb = Total weight of soil mass / Total Volume = (WW + WS)/ (VW + VS + Va) For a saturated soil γb = γsat ⇒ Va = 0 = (WW + WS)/ (VW + VS) Where γsat = Saturated unit weight of the soil Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Dry unit weight γd ⇒ Vw = 0 For a dry soil γd = (WS)/ (Va + VS) γd = Ws/V = (W – WW)/V = [W/V – wWS/V] = γbulk – w γd γd = γb/(1+w) Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Typical values of Unit Weight for Soils 3 3 Soil type γsat (kN/m ) γd (kN/m ) Gravel 20 - 22 15 - 17 Sand 18 - 20 13 - 16 Silt 18 - 20 14 - 18 Clay 16 - 22 14 - 21 Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Specific Gravity Specific Gravity is the ratio of the unit weight of a substance to the unit weight of water γw at 4˚C. In soil mechanics, specific gravity generally refers to the specific gravity of solid particles Gs, and is defined as the unit weight of solid particles to the unit weight of water. Gs = γS / γW Unit weight of solid constituents γS = WS/VS = WS/VSγW Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay The value of the specific gravity can be determined from laboratory tests. W2 W3 W1 W4 Where W1 = Wt. of empty sp. gravity bottle W2 = W1 + dry soil W3 = W2+ water (without any entrapped air) W4 = W1 + water Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Specific Gravity Gs = Weight of soil solids / Weight of water volume equivalent to that of water = (W2 – W1) / [(W4-W1) – (W3-W2) ] For most of soils Gs ranges from 2.5 – 2.9 Mineral G Gs = 2.65 for sands s Kaolinite 2.62-2.66 G = 2.2 – 2.4 for Pond ash s Illite 2.60 – 2.86 Gs = 4.4 – 5.2 for Iron ore Montmorillonite 2.75-2.78 Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay For a partially saturated soil: Mass Specific Gravity Gm = γb / γw Gm (dry) = γd / γw – for dry soil Gm (saturated) = γsat / γw – for saturated soil Gm (dry) = Mass Specific gravity (dry state) Gm (sat.) = Mass Specific gravity (saturated state) Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Submerged (Buoyant unit weight) γ' = Weight of soil inside the water / Total volume Treating whole soil mass as one unit = [ (WS + WW) - VγW] /V = (WS + WW)/V - γW = γsat - γW VW WW γ′ = γsat - γW VS WS Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Phase relations Two approaches: I. Specific Volume approach (VS = 1) II. Unit Volume approach (V = 1) Using specific volume approach, VS is put as unit volume. Specific Volume ν = 1 + e = V/VS (which is nothing but Total volume per unit Volume of solids) Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay For dry soil – 2 phase system VV = Air e Wa = 0 Va V W Solids VS 1 WS = GSVSγW Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Soil is dry: From the definition of void ratio e = VV/VS VV = e VS = 1 Gs = γS / γW = WS/VSγW WS = GSγW γd = WS/V = GSγW/(1+e) γd = GSγW/ (1 + e) Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Basic relationships VV = Water e WW = eγW Vw V W Solids VS 1 WS = GSγW For Saturated soil – 2 phase system Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Soil is fully saturated: From the definition of water content W = WW/WS = eγW / GSγW e = W GS For fully saturated case γsat = W/V = (GSγW + eγW)/(1+e) γsat = (GS + e)γW/(1 + e) Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Basic relationships Va AIR Wa = 0 VV = e Vw = wGS WATER Ww = wGSγW SOLIDS 1 Ws = GSγW For Partially Sat. soil – 3 phase system Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay From the definition of degree of saturation Sr = VW/VV = wGS/e e = wGS/Sr For Sr = 1, e = wGS γd = WS/V = GSγW/(1+wGS/Sr) -Valid for a partially saturated soil Prof. B V S Viswanadham, Department of Civil Engineering, IIT Bombay Relationship between γd, Gs, w and na Using VS = WS/GSγW V = VS + VW + Va VW = WW/γW 1 = VS/V + VW/V + na & by writing Ww = w Ws 1 – na = VS/V + VW/V = γd/γW (w + 1/GS) γd = (1-na) GSγW / (1 + wGS) When soil becomes completely saturated na = 0 Prof.