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Soil Engineering

Is force and moment equilibrium satisfied by Janbu’s method, Bishop’s method and Morgenstern-Price method?

Janbu’s method and Morgenstern-Price method are non-circular analytical method and they are frequently used for soil slopes while Bishop’s method is circular analytical method. Bishop’s Simplified method and Janbu’s Simplified method assume that the inter-slice forces are horizontal and inter-slice shear forces are neglected.


Equilibrium Method



Force Equilibrium
Horizontal Vertical
Janbu’s Simplified No Yes Yes
Bishop’s Simplified Yes No Yes
Morgenstern-Price Yes Yes Yes

This question is taken from book named – A Self Learning Manual – Mastering Different Fields of Civil Engineering Works (VC-Q-A-Method) by Vincent T. H. CHU.

How to Control Vibration In Blasting?

When ever explosive substances are used to blast, a large amount of vibration occurs. This vibration is not only dangerous for people working their but also to the neighboring structures. Therefore proper care must be taken to keep vibration in check.

The vibrations caused by blasting are related to velocity (V), wavelength (L) and frequency (f) as
L= V/f

Now Velocity V depends on the amplitude of the vibrations A and is given by
Where p – pie = 3.14

Case – When we know velocity velocity v1 at a distance D1 from the explosion and wish to find velocity v2 at a distance D2 from the explosion
v2=(approx) v1(D1/D2)1.5

The scaled-distance formula is used for vibration control

b and H are constants and depend on site.

Earth Quantities Hauled

Many people wonder that why the soil looks bulkier after excavation. The answer is that with increase in voids, the volume of soil increases and thus the soil pile looks bulkier. Here is a mathematical formula for this change in soil volume

Vb = VbL = (100/(100 + % swell))VL
Vb = original volume, yd3 (m3),
VL = loaded volume, yd3 (m3),
L = load factor

Similarly when we compact the soil, its volume decrease as voids are now filled.
Vc = VbS
Vc = compacted volume, yd3 (m3)
S = shrinkage factor.

What are the formulas For Earth Moving?

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=RfW + RpPW
R = rolling resistance, lb (N)
p = tire penetration, in (mm)
Rf = rolling-resistance factor, lb/ton (N/tonne)
W = weight on wheels, ton (tonne)
Rp = tire-penetration factor, lb/ton in (N/tonne mm) penetration
Rf usually is taken as 40 lb/ton (or 2 percent lb/lb) (173 N/t) and Rp 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’

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

Case – When we have a slope
G = RgsW
G = grade resistance, lb(N)
Rg­ = 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’+Rg 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).

Describe Compaction Equipment Rollers

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:

Type mi/h km/h
Grid rollers 12 19.3
Sheepsfoot rollers 3 4.8
Tamping rollers 10 16.1
Pneumatic rollers 8 12.8

To calculate compaction production use the following formula
yd3/h (m3/h) = 16WSLFE/P
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

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