Soil Engineering

Whenever their is a movement, friction comes into action. The same is the case with earth moving equipments. We term this as rolling resistance and this has to be overcomed by vehicle engine so that it can move on that surface. This is the formula to calculate rolling resistance

R=R_fW + R_pPW
where
R = rolling resistance, lb (N)
p = tire penetration, in (mm)
R_f = rolling-resistance factor, lb/ton (N/tonne)
W = weight on wheels, ton (tonne)
R_p = tire-penetration factor, lb/ton in (N/tonne mm) penetration
R_f usually is taken as 40 lb/ton (or 2 percent lb/lb) (173 N/t) and R_p as 30 lb/ton in (1.5% lb/lb in) (3288 N/t mm).

So the above equation becomes
R=(2%+1.5 % p) W’=R’W’

where
W’ = weight on wheels, lb(N)
R’ = 2% + 1.5%p.

Case – When we have a slope
G = R_gsW
where
G = grade resistance, lb(N)
R_g­ = grade-resistance factor = 20 lb/ton (86.3 N/t) = 1%
s = percent grade which is positive for uphill motion and negative for downhill motion.

The total road resistance is calculated by adding the rolling and grade resistances and is given by:
T = (R’+R_g s )W’ =(2%b + 1.5%p + 1%s)W’

Loss due to Altitude
Generally we take 3 percent pull loss for each 1000 ft (305 m) above 2500 ft (762 m).

Soil compaction is done by Rollers. Many models of these rollers can be found in the market. Depending on the soil type and conditions, we chose rollers to work on them. For example, for soils with high % of clay we mainly use Sheepsfoot rollers and for granular soils we use vibrating rollers. The selection of roller depends on other factors like speed, desired compaction etc

The table below shows the average speeds, mi/h (km/h) under normal conditions:

To calculate compaction production use the following formula
yd³/h (m³/h) = 16WSLFE/P
where
W = width of roller, ft (m)
P = number of passes
S = roller speed, mi/h (km / h)
L = lift thickness, in (mm)
F = ratio of pay yd³ ( m³) to loose yd³ ( m³)
E = efficiency factor for excellent =0.90, average=0.80, poor= 0.75

There are many types of Soil compaction tests which are performed on soil. Some of these are :-

1) The Sand Cone Method
One of the most common test to determine the field density of soil is the sand-cone method. But it has a major limitation that this test is not suitable for saturated and soft soils

The formula used are
Volume of soil, ft³ (m³)=[weight of sand filling hole, lb (kg)] /[ Density of sand, lb/ft³ (kg/m³)]

% Moisture = 100(weight of moist soil – weight of dry soil)/weight of dry soil

Field density, lb/ft³ (kg /m³)=weight of soil, lb (kg)/volume of soil, ft³ (m³)

Dry density=field density/(1 + % moisture/100)

% Compaction=100 (dry density)/max dry density

Maximum density is found by plotting a density–moisture curve.

2) California Bearing Ratio
The California bearing ratio (CBR) is used as a determine the quality of strength of a soil under a pavement. It also measures the thickness of the pavement, its base, and other layers.
CBR = F/F_o
where
F = force per unit area required to penetrate a soil mass with a 3-in² (1935.6-mm² ) circular piston (about 2 in (50.8 mm) in diameter) at the rate of 0.05 in/min (1.27 mm/min)

F₀ = force per unit area required for corresponding penetration of a standard material.

3) Soil Permeability
Darcy’s law is applicable in determining the soil permeability. Darcy law states that
V = kiA

where
V = rate of flow, cm³ /s,
A = cross-sectional area of soil conveying flow, cm²
k = Coefficient of permeability which depends on grain-size distribution, void ratio and soil fabric. The value varies from 10 cm/s for gravel to less than 10^–7 for clays.

To check Various Lab Test On Soil see this

To calculate the approximate value of settlement the following equations is used. This establishes a relationship between loads on foundations and settlement

q/P = C₁(1+2d/b) + C₂/b
where
q = load intensity, lb/ft² (kg/m²)
P= settlement, in (mm)
d =depth of foundation below ground surface, ft (m)
b=width of foundation, ft (m)
C₁ =coefficient dependent on internal friction
C₂ = coefficient dependent on cohesion

Ultimate bearing capacity is calculated by using Prandtl equation. When the footing is below the surface the ultimate bearing capacity of the soil is modified by (1 + Cd/b) where C = 2 for cohesionless soils and C= 0.3 for cohesive soils.

The Prandtl’s equation is :-

To determine the stability of slopes, we first need to identify the type of soil. A cohesive soil behaves differently then Cohesionless Soils

Case 1 – When we have Cohesionless Soils
We consider the slope stable if it satisfies the following condition. Please note we consider no water seepage in this situation
i < f where i = slope of ground surface f = angle of internal friction of soil When seepage factor is introduced parallel to the slope and we assume that soil is totally saturated, the slope is considered stable if it fulfill this condition tan i < (Y_b/Y_sat) tan f

Case -2 When we have Cohesive Soils
The slope on a cohesive soil is considered stable if
H < (C/YN) where H = height of slope, ft (m) C = cohesion, lb/ft² or kg / m²
Y = unit weight, lb/ft³ or kg / m³
N = stability number and is dimensionless

To counter any effect of a surcharge on retaining wall on a cohesionless soil or an unsaturated cohesive soil we need to apply a uniform horizontal load of magnitude K_Ap. This load is applied over the entire wall height.

In case of saturated cohesive soil, the entire surcharge value acts on the entire wall height. This is considered to be a uniform load acting horizontally.

We know that water exerts a pressure on the wall and this thrust is calculated by using the following formula

P = ½Y_o H²
where H = height of water above bottom of wall, ft (m)
Y_o= unit weight of water.

Unit of water is 62.4 lb/ft³ 1001g/m for freshwater and 64 lb/ft³ or 1026.7 kg/m³ for saltwater.

The thrust applied by water is considered to be acting at a distance of H/3 from the bottom of the retaining wall. The pressure distribution is triangular and has the maximum pressure of 2P/H at the bottom of the wall.

The lateral pressure in cohesion less soils is given by following formula:-

Following terms are used in the formula given below

Y=unit weight of soil, lb/ft³ or kg/m³
P=total thrust of soil, lb/linear ft (kg/m) of wall
H= total height of wall, ft (m)
K_A= coefficient of active pressure

We know that The Rankine theory of lateral earth pressures is the most widely used theory to find the lateral pressure which is acting on retaining walls. But this theory has some assumptions which we need to know before hand.

Assumptions in the Rankine Theory of Lateral Earth Pressures
1) The pressure on the back of a vertical wall is the same as the pressure that would exist on a vertical plane in an infinite soil mass.
2) Their is no Friction between the wall and the soil.

What is the Lateral Pressure of Cohesive Soils?

P=1/2YH²K_A-2cH(K_A)_1/2
where
Y=unit weight of soil, lb/ft³ or kg/m³
P=total thrust of soil, lb / linear ft (kg/m) of wall
H= total height of wall, ft (m)
K_A= coefficient of active pressure
c= cohesion, lb/ft²or kPa