Shear strength is a factor that affects and influences soil stability as well as the soil's load bearing ability. Cohesion, internal friction, and angle of internal friction are the forces that define shear strength. The stretched material is assumed to suffer principal stress (1), minor principle stress (3), and intermediate principal stress (2) in the calculation.
Shea strength can be expressed using the linear function using Mohr-strength Coulomb's theory:
S = C + σ tan φ
Where: S = Shear strength, C= cohesion, σ = normal stress and φ = angle of internal friction . In the calculation the assumption is that the strained material experiences principal stress ( σ1), Minor principle stress (σ3) and the intermediate Principal stress (σ2).
Using Mohr –Coulomb’s strength theory then Shea strength and be expressed using the linear function:
S = C + σ tan φ
Where: S = Shear strength, C= cohesion, σ = normal stress and φ = angle of internal friction.
Considering the site has normal consolidated silty clay then the soil is cohesive frictional soil, it is assumed that c= φ and the soil have both C and φ forces .
Using the Coulomb equation then the plot is shown.
S = C + σ tan φ
σ
C
µ
φ
S = C + σ tan φ
The silo will be 0.6m underground, with un-drained sear strength value of 13.7 Cµ (KN/m2) based on the strength values from the shear vane testing.
Using the BS EN 1997 design approach 1 determine the initial height to which the silo can be filled with grain such that AGeo = 100 percent
If AGeo = 100 is the maximum stress applied to cause silo failure
Then it should be equivalent to the resisting moments of the shear forces on the silo . When using Design approach 1 there are two possible combinations
Combination 1 : A1 + M1 + R1
Combination 2: A2 + M2 + R2
For maximum: Ageo = 100 then we use combination 2
Whereby A2 is shear force on the surface of the silo
M2 and R2 is the resisting moment of the shear force at two different ends
The resisting moments by the equation can be given by:
A1= (π d h) Cµ (d/2)
Where (π d h) Cµ is the surface area of the silo
(d/2) is the moment arm
Surface area of the silo = πr2h + 2/3πr3+ d/2
Not we use the internal dimensions therefore: d = 5.8m and height = 9.7m found by subtracting 200mm or 0.2 meters from the diameter and 300mm of 0.3meters from the height
Surface Area = (3.14 x 2.92 * 9.7)+ (2/3 * 3.14 * 2.93 )
Surface Area = 307.192 m2
A1 = 307.192 *5.8/2
A1 = 860.14 Kg/m2
For calculation of (M2 and R2) we assume several types of shear strength distribution on the silo:
Triangular: Shear strength mobilization is Cµ at periphery decreases linearly to Zero
Uniform: shear strength mobilization is constant that is Cµ that is from periphery to center
Parabolic: the shear strength mobilization Cµ decreases parabolically to the zero at the centre.
Based on above assumptions then the maximum shear at failure is at R2 equivalent to Ageo = 100:
R2= π Cµ{ r2 h /2 + β(d3/3)}
In this equation β is ½ the triangular mobilization of the undrained shear strength
Given Ageo = 100, π = 3.14, d =6 meters r = 6/2, β = 13.7/2 from the shear table, Height = 10 For internal dimensions the silo r= 5.8/2 and height = 9.7 meters
R2 = 307.192/2 + 6.85 (24.839/2)
R2 = 238.669 Kg/M2
R2 is the maximum force that can be exerted on the silo before failure. Using the pressure formula we can find the height. (Assuming gravity g = 9.8 m/s2 ) The density of concrete 2450 Kg/m3 and Density of grain = 850 kg/m3
h= R2 /d*g (d= density, g=gravity, h= height)
h = (2450/238.669 * 9.8)
h= 1.04 meters
Undrained shear height is subtracted from the total height
Therefore
Maximum height = 9.7- 1.04
Maximum loading height so that Ageo is at 100 = 8.66 meters
Estimate the consolidation settlement of the silo , assuming it has been filled to capacity
Note that the strain for the silo
S1 = C1 C2 qnet ∑ Iz/E
For this S1 is settlement settlement
C1= 1-0.5 σ/d which is the correctional factor
σ = overburden pressure exerted on the foundation
C2 = 1 + 0.2 log t/0.1
t-is the time in months
σ = 9.7 * 238.669 = 2315. 0893 kPa
C1 = 2315.0893/2450
C1= 0.944
C2 = 2315.0893/850
C2 = 2.723
S1 = 0.944*2.723/13.7
S1 = 0.1876 m which is equivalent to 1.876mm which is the consolidation settlement for the silo when filled to maximum.
References
Lehtonen, Ville. "Modelling undrained shear strenth and pore pressure based on an effective stress soil model limit." Tampere University of technology (2015).
Mayne, Paul and Mathew Coop. "Geometrical behavior and testing." Seventeenth international conference (2009).
Powrie, William. "Soil mechanics: concepts and application." Taylor and francis (2004).
