Vibration Control In Blasting
Explosive users should take steps to minimize vibration and noise from blasting and protect themselves against damage claims.
Vibrations caused by blasting are propagated with a velocity V, ft/s (m /s), frequency f, Hz, and wavelength L, ft (m), related by
L = V / f
Velocity v, in/s (mm/s), of the particles disturbed by the vibrations depends on the amplitude of the vibrations A, in (mm):
v = 2 p f A
If the velocity v1 at a distance D1 from the explosion is known, the velocity v2 at a distance D2 from the explosion may be estimated from
v2 ? v1 ( D1 / D2 ) 1.5
The acceleration a, in/s2 (mm/s2), of the particles is given by
a = 4 p2 f2 A
For a charge exploded on the ground surface, the overpressure P, lb/in2 (kPa), may be computed from
P = 226.62 (W1/3 / D ) 1.407
Where
W = maximum weight of explosives, lb (kg) per delay
D = distance, ft (m), from explosion to exposure.
The sound pressure level, decibels, may be computed from
dB = ( P / ( 6.95 X 10-28) )0.084
For vibration control, blasting should be controlled with the scaled-distance formula:
V = H ( D / Ö W )-b
Where
b = constant (varies for each site)
H = constant (varies for each site).
Distance to exposure, ft (m), divided by the square root of maximum pounds (kg) per delay is known as scaled distance.
Most courts have accepted the fact that a particle velocity not exceeding 2 in/s (50.8 mm/s) does not damage any part of any structure. This implies that, for this velocity, vibration damage is unlikely at scaled distances larger than 8
Scraper Production
Production is measured in terms of tons or bank cubic yards (cubic meters) of material a machine excavates and discharges, under given job conditions, in 1 h.
Production, bank yd3/h (m3/h) = load, yd3 (m3) X trips per hour
Trips per hour = working time, min/h / cycle time, min
The load, or amount of material a machine carries, can be determined by weighing or estimating the volume. Payload estimating involves determination of the bank cubic yards (cubic meters) being carried, whereas the excavated material expands when loaded into the machine. For determination of bank cubic yards (cubic meters) from loose volume, the amount of swell or the load factor must be known.
Weighing is the most accurate method of determining the actual load. This is normally done by weighing one wheel or axle at a time with portable scales, adding the wheel or axle weights, and subtracting the weight empty. To reduce error, the machine should be relatively level. Enough loads should be weighed to provide a good average:
Bank yd3 = weight of load, lb(kg) / density of material, lb/bank yd3 (kg/m3)
Equipment Required
To determine the number of scrapers needed on a job, required production must first be computed:
Production required, yd3 /h (m3/h) = quantity, bank yd3 (m3) / working time, h
No. of scrapers needed= production required, yd3/h (m3/h) / production per unit, yd3/h (m3/h)
No. of scrapers a pusher can load= scraper cycle time, min / pusher cycle time, min
Because speeds and distances may vary on haul and return, haul and return times are estimated separately.
Variable time, min= (haul distance, ft /88Xspeed, mi/ h) + (return distance, ft/88Xspeed, mi/h)
Or
= (haul distance,m/ 16.7Xspeed,km/ h) + (return distance, m/16.7Xspeed,km/ h)
Haul speed may be obtained from the equipment specification sheet when the drawbar pull required is known.
Earth Quantities Hauled
When soils are excavated, they increase in volume, or swell, because of an increase in voids:
Vb = Vb L = ( 100 / ( 100 + % swell ) ) VL
where
Vb = original volume, yd3 (m3), or bank yards
VL = loaded volume, yd3 (m3), or loose yards
L = load factor
When soils are compacted, they decrease in volume:
Vc = Vb S
where
Vc = compacted volume, yd3 (m3)
S = shrinkage factor.
Bank yards moved by a hauling unit equals weight of load, lb (kg), divided by density of the material in place, lb (kg), per bank yard (m3).
Formulas For Earth Moving
External forces offer rolling resistance to the motion of wheeled vehicles, such as tractors and scrapers. The engine has to supply power to overcome this resistance; the greater the resistance is, the more power needed to move a load. Rolling resistance depends on the weight on the wheels and the tire penetration into the ground:
R = Rf W + Rp PW
where
R = rolling resistance, lb (N)
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
p = tire penetration, in (mm)
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).
Hence,the above equation can be written as
R = (2% + 1.5 % p ) W’ = R’ W’
where
W’ = weight on wheels, lb(N)
R’ = 2% + 1.5%p.
Additional power is required to overcome rolling resistance on a slope. Grade resistance also is proportional to weight:
G = Rg s W
where
G = grade resistance, lb(N)
Rg = grade-resistance factor = 20 lb/ton (86.3 N/t) = 1% lb/lb (N/N)
s = percent grade, positive for uphill motion. Negative for downhill
Thus, the total road resistance is the algebraic sum of the rolling and grade resistances, or the total pull, lb ( N ), required:
T = (R’ + Rg s ) W’ = (2% + 1.5%p + 1%s)W’
In addition, an allowance may have to be made for loss of power with altitude. If so, allow 3 percent pull loss for each 1000 ft (305 m) above 2500 ft (762 m).
Usable pull P depends on the weight W on the drivers:
P = f W
where
f = coefficient of traction.
Compaction Equipment : Rollers
A wide variety of equipment is used to obtain compaction in the field. Sheepsfoot rollers generally are used on soils that contain high percentages of clay. Vibrating rollers are used on more granular soils.
To determine maximum depth of lift, make a test fill. In the process, the most suitable equipment and pressure to be applied, lb/in2 (kPa), for ground contact also can be determined. Equipment selected should be able to produce desired compaction with four to eight passes. Desirable speed of rolling also can be determined.
Average speeds, mi/h (km/h), under normal conditions are given in Table below
| 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 |
Compaction production can be computed from
yd3/h (m3/h) = 16WSLFE / P
where
W = width of roller, ft (m)
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 ( allows for time losses, such as those due to turns); 0.90, excellent; 0.80, average; 0.75, poor
P = number of passes
Soil Compaction Tests
1) The Sand Cone Method
The sand-cone method is used to determine in the field the density of compacted soils in earth embankments, road fill, and structure backfill, as well as the density of natural soil deposits, aggregates, soil mixtures, or other similar materials. It is not suitable, however, for soils that are saturated, soft, or friable (crumble easily).
Characteristics of the soil are computed from
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) Load-Bearing Test
One of the earliest methods for evaluating the in situ deformability of coarse-grained soils is the small-scale load-bearing test. Data developed from these tests have been used to provide a scaling factor to express the settlement r of a full-size footing from the settlement r1 of a 1-ft2(0.0929-m2) plate. This factor r /r1 is given as a function of the width B of the full-size bearing plate as
r/r1 = ( 2B / 1 + B )2
From an elastic half-space solution, E’s can be expressed from results of a plate load test in terms of the ratio of bearing pressure to plate settlement kv as
Kv ( 1 - m2 ) p / 4
E’s = ___________________
4B / ( 1 + B )2
where m represents Poisson’s ratio, usually considered to range between 0.30 and 0.40. The E’s equation assumes that r1 is derived from a rigid, 1-ft(0.3048-m)-diameter circular plate and that B is the equivalent diameter of the bearing area of a full-scale footing. Empirical formulations, such as the r /r1 equation, may be significantly in error because of the limited footing-size range used and the large scatter of the database. Furthermore, consideration is not given to variations in the characteristics and stress history of the bearing soils.
3) California Bearing Ratio
The California bearing ratio (CBR) is often used as a measure of the quality of strength of a soil that underlies a pavement, for determining the thickness of the pavement, its base, and other layers.
CBR = F / Fo
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);
Fv = force per unit area required for corresponding penetration of a standard material.
Typically, the ratio is determined at 0.10-in (2.54-mm) penetration, although other penetrations sometimes are used. An excellent base course has a CBR of 100 percent. A compacted soil may have a CBR of 50 percent, whereas a weaker soil may have a CBR of 10.
4) Soil Permeability
The coefficient of permeability k is a measure of the rate of flow of water through saturated soil under a given hydraulic gradient i, cm/cm, and is defined in accordance with Darcy’s law as
V = kiA
where V = rate of flow, cm3 /s, and A = cross-sectional area of soil conveying flow, cm2 .
Coefficient k is dependent on the grain-size distribution, void ratio, and soil fabric and typically may vary from as much as 10 cm /s for gravel to less than 10–7 for clays. For typical soil deposits, k for horizontal flow is greater than k for vertical flow, often by an order of magnitude.
Settlement Under Foundations
The approximate relationship between loads on foundations and settlement is
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
The coefficients C1 and C2 are usually determined by bearing plate loading tests.
Bearing Capacity Of Soils
The approximate ultimate bearing capacity under a long footing at the surface of a soil is given by Prandtl’s equation as
qu=(c/tan f) +1/2gdrybOKp[Kpeptan f-1]
where
qu = ultimate bearing capacity of soil, lb/ft2 (kg / m2)
c = cohesion, lb/ft2 (kg / m2)
f = angle of internal friction, degree
gdry = unit weight of dry soil, lb/ft3 (kg / m3)
b = width of footing, ft (m)
d = depth of footing below surface, ft (m)
Kp = coefficient of passive pressure
= [ tan ( 45 + f / 2 ) ]2
e = 2.718
For footings below the surface, the ultimate bearing capacity of the soil may be modified by the factor 1 + Cd / b. The coefficient C is about 2 for cohesionless soils and about 0.3 for cohesive soils. The increase in bearing capacity with depth for cohesive soils is often neglected.
Stability Of Slopes
Cohesionless Soils
A slope in a cohesionless soil without seepage of water is stable if
i <>
With seepage of water parallel to the slope, and assuming the soil to be saturated, an infinite slope in a cohesionless soil is stable if
tan i < ( gb /gsat ) tan f
where
i = slope of ground surface
f = angle of internal friction of soil
gb , gsat = unit weights, Ib/ft3 (kg/m3)
Cohesive Soils
A slope in a cohesive soil is stable if
H < (C/gN)
where
H = height of slope, ft (m)
C = cohesion, lb/ft2 (kg / m2 )
g = unit weight, lb/ft3 (kg / m3 )
N = stability number, dimensionless
For failure on the slope itself, without seepage water,
N =(cos i)2 (tan i - tan f )
Similarly, with seepage of water,
N = (cos i)2[ tan i - ( gb/ gsat ) tan f ]
When the slope is submerged, f is the angle of internal friction of the soil and g is equal to gb. When the surrounding water is removed from a submerged slope in a short time (sudden drawdown), f is the weighted angle of internal friction, equal to ( gb/ gsat ) f, and g is equal to gsat.
Lateral Pressure From Surcharge
The effect of a surcharge on a wall retaining a cohesionless soil or an unsaturated cohesive soil can be accounted for by applying a uniform horizontal load of magnitude KAp over the entire height of the wall, where p is the surcharge in pound per square foot (kilopascal). For saturated cohesive soils, the full value of the surcharge p should be considered as acting over the entire height of the wall as a uniform horizontal load. KA is defined earlier.
Water Pressure
The total thrust from water retained behind a wall is
P = ½ go H2
where H = height of water above bottom of wall, ft (m); and
go= unit weight of water, lb/ft3 (62.4 lb/ft3 (1001g/m
The thrust is applied at a point H/3 above the bottom of the wall, and the pressure distribution is triangular, with the maximum pressure of 2P / H occurring at the bottom of the wall. Regardless of the slope of the surface behind the wall, the thrust from water is always horizontal.
Lateral Pressrues In Cohesive Soils
For walls that retain cohesive soils and are free to move a considerable
amount over a long period of time, the total thrust from the soil (assuming a
level surface) is
P = ½ g H2KA – 2 c H KA1/2
or, because highly cohesive soils generally have small angles of internal
friction,
P = ½ g H2- 2 c H
The thrust is applied at a point somewhat below H /3 from the bottom of the
wall, and the pressure distribution is approximately triangular.
For walls that retain cohesive soils and are free to move only a small amount
or not at all, the total thrust from the soil is
P = ½ g H2KP
because the cohesion would be lost through plastic flow.
Lateral Pressures In Cohesionless Soils
For walls that retain cohesionless soils and are free to move an appreciable amount, the total thrust from the soil is
Lateral Pressrues In Soils
LATERAL PRESSURES IN SOILS, FORCES ON RETAINING WALLS
The Rankine theory of lateral earth pressures, used for estimating approximate values for lateral pressures on retaining walls, assumes that 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. Friction between the wall and the soil is neglected. The pressure on a wall consists of (1) the lateral pressure of the soil held by the wall, (2) the pressure of the water (if any) behind the wall,
and (3) the lateral pressure from any surcharge on the soil behind the wall.
Physical Properties Of Soils
The soil properties and parameters can be broadly classified as
1)Physical
2)Engineering
3)Index
Physical soil properties include density, particle size and distribution, specific gravity, and water content.
The water content w of a soil sample represents the weight of free water contained in the sample expressed as a percentage of its dry weight.
The degree of saturation S of the sample is the ratio, expressed as percentage, of the volume of free water contained in a sample to its total volume of voids Vv
Porosity n, which is a measure of the relative amount of voids, is the ratio of void volume to the total volume V of soil:
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