CE3701 GEOTECHNICAL ENGINEERING ssignment 1: Weight-Volume Relations Problem 1 O Example 4.4 in the Coduto textbook is a Type II weight-volume problem. In these types of problems, you're allowed to assume any quantity-not just volume. For this exercise, redo Example 4.4 by assuming a weight of solids of 10 kN instead of assuming a total volume of 1 cubic meter. Once you've completed your solution, compare your results with the author's to see how the different assumption affects the outcome. Example 4.4 A certain soil has the following properties: G, = 2.71 n = 41.9% w = 21.3% Find the degree of saturation, S, and the unit weight, y. Solution: Although this problem could be solved using Equations 4.17 and 4.26-4.28, we will use the phase diagram method to illustrate Step 2 of the procedure described above. Step 1: Draw and annotate phase diagram (see Figure 4.5) Weight (kN) Volume (m') Air 0.084 O | 0.419 18.74 3.29 Water 1.335 1.000 FIGURE 4.5 Phase diagram 15.45 Solids 0.581 for Example 4.4. Step 2: Assume one weight or volume. No weights or volumes were stated, so all of the given data applies to the entire soil strata. Therefore, we will develop a phase diagram for an assumed total volume V of 1 m. Step 3: Determine weights and volumes in phase diagram. n = V Y x 100% - 0.419 = = VY_> Vy = 0.419 m3 V, = V - Vv = 1.000 m3 - 0.419 m3 = 0.581 m3 GS = V Ws - 2 2.71 = W , (0.581 m')(9.81 kN/m3) -W, = 15.45 kN Ww W = TI Ww x 100% - 0.213 = W S 15.45 kN -Ww = 3.29 KN W = W, + Ww = 15.45 kN + 3.29 kN = 18.74 kN W w yw = V W _ 9.81 kN/m3 = 3.29 KN Vw -Vw = 0.335 m3 V. = Vv - Vw = 0.419 m3 - 0.335 m3 = 0.084 m3 O Step 4: Compute parameters. S = W x 100% = 0.335 m3 0.335 m + 0.084 m3 3X 100% = 80.0% W y = " 18.74 kN = 18.7 kN/m3 1 m3CE3701 GEOTECHNICAL ENGINEERING 5S - Sample diameter 3 inches | ao Sample length 6 inches i : Wt. before drying in oven 2.95 Ib ' Wt. after drying in oven 2.54 |b | a | a a) Find its total, dry, and saturated unit weights. Assume specific gravity of solids as 2.65. B) Calculate its void ratio, porosity, and degree of saturation. As a geotechnical engineer, you are tasked with an earth-fill project requiring 15,000 m? of compacted fill with a void ratio of 0.70. The soil at the borrow pit has a void ratio of 1.10. Calculate the total volume of natural soil that must be excavated from he borrow pit for this project