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SOIL VOLUME AND DENSITY RELATIONSHIPS This cue card is based on chapt. 2 sect. 3 of Foundation Analysis and Design (5th ed) by Joseph E. Bowles (permission to quote from the book has been granted). To understand the cue card, the user should have the book. Comments or questions concerning the cue card should be directed to the developer, Helmut Schmidhofer, on 02 4862 1295 (international replace leading 0 with 61) or email engcomp@gmail.com. IMPORTANT NOTICE: soil volume and density relationships can now be processed ONLINE! Enter your custom values at lines marked ****, then process all lines. The word "process" means to select (highlight) the relevant text and click the spinning globe in the Engineers' Compendium window. To work with the cue card, you need MATHSERV, which you may download here. Given: **** moisture content in percent, W = 22.5 **** specific gravity of soil grains, GS = 2.6 **** sample mass in grams, WT = 224.0 **** sample volume in cm3, VT = 118 Then: wet unit mass in g/cm3, RHO_WET = WT/VT := 1.8983 wet unit weight in kN/m3, GAM_WET = RHO_WET*9.807 := 18.6167 dry unit weight, eq. (2-9), GAM_DRY = GAM_WET/(1+W/100) := 15.1973 unit mass of solids in g/cm3, WS = RHO_WET/(1+W/100) := 1.5496 unit volume of solids, VS = WS/GS := 0.596 unit volume of voids, VV = 1-VS := 0.404 unit mass of water WW = RHO_WET-RHO_WET/(1+W/100) := 0.3487 unit volume of water, VW = WW := 0.3487 degree of saturation in percent, S = 100*VW/VV := 86.3119 dry bulk specific gravity GB = GAM_DRY/9.807 := 1.5496 The following templates for equations 2-1 to 2-12 may be used in isolation if the required variables are given: Eq. (2-1) Void ratio E: **** volume of voids in cm3, VV = .404 **** volume of solids in cm3, VS = .596 Void ratio E = VV/VS := 0.6779 Eq. (2-2) Porosity N: **** volume of voids in cm3, VV = .404 **** total volume in cm3, VT = 1.0 Porosity N = VV/VT := 0.404 Eq. (2-3) Water content W: **** mass of water in grams, WW = .3487 **** mass of solids in grams, WS = 1.5496 Water content in percent, W = 100*WW/WS := 22.5026 Eq. (2-4) Unit weight GAMMA: **** weight of sample in g/cm3, WT = 224 **** volume of sample in cm3, VT = 118.0 Unit weight in kN/m3, GAMMA = 9.807*WT/VT := 18.6167 Eq. (2-5) Degree of saturation S: **** volume of water in cm3, VW = .3487 **** volume of voids in cm3, VV = .404 Saturation in percent, S = 100*VW/VV := 86.3119 Eq. (2-6) Specific gravity G: **** mass of solids in grams, WS = 1.5496 **** volume of solids in cm3, VS = .596 Specific gravity of soil grains, GS = WS/VS := 2.6 Eq. (2-7) Porosity N from void ratio E: **** void ratio, E = .6779 Porosity, N = E/(1+E) := 0.404 Eq. (2-8) Void ratio E from porosity N: **** porosity, N = .404 Void ratio, E = N/(1-N) := 0.6779 Eq. (2-9) Dry unit weight: **** wet unit weight in kN/m3, GAM_WET = 18.6167 **** moisture content in percent, W = 22.5 Dry unit weight, GAM_DRY = GAM_WET/(1+W/100) := 15.1973 Eq. (2-10) Void ratio E: **** moisture content in percent, W = 22.5 **** degree of saturation in percent, S = 86.3 **** specific gravity of soil grains, GS = 2.6 Void ratio, E = GS*W/S := 0.6779 Eq. (2-11) Dry unit weight: **** moisture content in percent, W = 22.5 **** degree of saturation in percent, S = 86.3 **** specific gravity of soil grains, GS = 2.6 **** unit weight of water in kN/m3, GAM_W = 9.807 Dry unit weight, GAM_DRY = GAM_W*GS/(1+GS*W/S) := 15.1968 Eq. (2-12) Wet unit weight: **** moisture content in percent, W = 22.5 **** degree of saturation in percent, S = 86.3 **** specific gravity of soil grains, GS = 2.6 **** unit weight of water in kN/m3, GAM_W = 9.807 Wet unit weight, GAM_WET = GAM_W*GS*(1+W/100)/(1+GS*W/S) := 18.6161 |