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 k_v as

K_v ( 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 / 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);

F_v = 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.

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.

The approximate ultimate bearing capacity under a long footing at the surface of a soil is given by Prandtl’s equation.

The Prandtl’s equation is :-

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.

Cohesionless Soils

A slope in a cohesionless soil without seepage of water is stable if

i < f

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 < ( g_b /g_sat ) tan f

where

i = slope of ground surface
f = angle of internal friction of soil

g_b , g_sat = 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 - ( g_b/ g_sat ) tan f ]

When the slope is submerged, f is the angle of internal friction of the soil and g is equal to g_b. 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 ( g_b/ g_sat ) f, and g is equal to g_sat.

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 K_Ap 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. K_A is defined earlier.