Question

Question 3: The following figure shows the soil profile at a site for a proposed building. The soil is a homogeneous, poorly graded sand. At the soil element A (as shown in the figure), if the increase in lateral effective stress is 20% of the increase in vertical effective stress, the soil element will failure. The coefficient of lateral earth pressure at rest. Ko is 0.5. Assume all stresses are principal stresses. The upper 4 m soil shares the same property: Yooil = = 30°. Unit weight of water is 10 kN/m. (a) Find the initial vertical and lateral stresses (both effective and total) at the soil element A (b) Based on the Mohr-Coulomb criterion, determine the maximum increase in vertical effective stress at the soil element A to avoid failure. (c) Plot Mohr Circle at A for both initial state and failure state. Show the Coulomb failure criterion. (Use effective stress) ground surface

Answer 1

*. The soil is Soil A- Ground surface homogeneous Im = h, i poorly goaded sand. IGWT *Y = 18 kN/m3 3 on=h₂ * O'= 30° *. Unit weight of water LOKN/m3 uppen 4m soil shares some property. a) The coefficient of Lateral earth pressure at rest le Ko = 1- Sin' = 1 - Sin 30º = 0.5 le vw = *. The *. The initial Vertical stress at 'À ) # Total vertical stress., OVCA) = Yson* (hithe) => Ovlas' = 18 (1+3) K => lo vea) = 72 Ky ng #Effective vertical stress, OveA) = OVCA) – Yws ha » Ovens = 172 - 1043) KN 412 => »lovia = 42 KN m2 *. The initial Lateral stresses at 'A', 1 #Effective Latenat stress, CCA) = kx Ovca) OTA = (0.5% 4 2 ) ko as = 21 km Cscanned with CamScanner

# Total Lateral stress, on cas = oncas + Ywha Oncas = (21 +10X3 ) kn => "nas= 51 king KN m2 more as (b) At the soil element 'A', if the increase in lateral effective stress is 20% of the increase in Vertical effective stress, the soil element will failure. As vertical (42+r) Stress increases (21+ 0.2%)KN Compare to Lateral stress. Hence the soil is in Active Condition Istress Condition at failure Coefficien, ka |- Sinop' 21+ 0.2% 42 tu Ka=1-sin 30° 1 + Sin 30° r = 52.5 KN 4 m2 50, Active earth pressure = > § = 21+0.24 It sino -IM m2 Hence, maximum increase in Vertical stress (effective) at soil element 'A' is 52.5 kN/m2 . C) Using effective stress, * Stress Condition inic initially 142 kN/m2 * Stress Condition at failure. 42+52.5 = 94.5 KN mz 21 KN m2 21 +0.2 x 52.5 = 31.5 KN csscanned with CamScanner