Question

h(m) sand 13 1 04 3.3 use total Sand stresses to deter mine . rave rave Depth u

Answer 1

Solution:

a) Vertical Stress ($\sigma _{v}$):

For the active case,

at 1m depth: = 17 * 1 = 17 kN/m²

(dry-sand) 1

at 3m depth: = 17 * 3 = 51 kN/m²

(dry-sand) *

at 6m depth: = 17 * 3 +23 * 3 = 120 kN/m²

(dry-sand) *3sat-gravel

For the passive case,

at 3m depth: 0

at 6m depth: = 23 * 3 = 69 kN/m²

sat-gravel

b) Pore pressure (u):

For the active case,

at 1m depth: = 0 kN/m²

W *

at 3m depth: = 0 kN/m²

W *

at 6m depth: = 9.81 * 3 = 29.43 kN/m²

W *

For the passive case,

at 3m depth: 0

at 6m depth: = 9.81 * 3 = 29.43 kN/m²

W *

c) Effective vertical Stress ($\sigma _{v}$'):

For the active case,

at 1m depth: $\sigma _{v}-u$   = 17 - 0 = 17 kN/m²

at 3m depth: $\sigma _{v}-u$ = 51 - 0 = 51 kN/m²

at 6m depth: $\sigma _{v}-u$ = 120 - 29.43 = 90.57 kN/m²

For the passive case,

at 3m depth: $\sigma _{v}-u$ = 0

at 6m depth: $\sigma _{v}-u$   = 69 - 29.43 = 39.57 kN/m²

d) Effective horizontal Stress ($\sigma _{H}$'):

For the active case,

at 1m depth: $\sigma _{v}*K_{a}$   = 17 * 0.4 = 6.8 kN/m²

at 3m depth (just above the junction): $\sigma _{v}*K_{a}$ = 51 * 0.4 = 20.40 kN/m²

at 3m depth (just below the junction): $\sigma _{v}*K_{a}$   = 51 * 0.3 = 15.30 kN/m²

at 6m depth: $\sigma _{v}*K_{a}$ = 90.57 * 0.3 = 27.17 kN/m²

For the passive case,

at 3m depth: $\sigma _{v}*K_{p}$ = 0

at 6m depth: $\sigma _{v}*K_{p}$   = 3.6 * 39.57 = 142.45 kN/m²

e) Horizontal Stress ($\sigma _{H}$):

For the active case,

at 1m depth: $\sigma _{v}'*K_{a}$   = 17 * 0.4 = 6.8 kN/m²

at 3m depth (just above the junction): $\sigma _{v}'*K_{a}$ = 51 * 0.4 = 20.40 kN/m²

at 3m depth (just below the junction): $\sigma _{v}'*K_{a}$ = 51 * 0.3 = 15.30 kN/m²

at 6m depth: $\sigma _{v}'*K_{a}+\gamma _{w}*H$ = 90.57 * 0.3 + 9.81 * 3 = 57.14 kN/m²

For the passive case,

at 3m depth: $\sigma _{v}'*K_{p}$ = 0

at 6m depth: $\sigma _{v}'*K_{p}+\gamma _{w}*H$   = 3.6 * 39.57 + 9.81 * 3 = 171.88 kN/m²