BEARING CAPACITY OF SOIL AND CALCULATION OF BEARING CAPACITY

BEARING CAPACITY OF SOIL AND CALCULATION OF BEARING CAPACITY

What is bearing capacity of Soil?

The bearing capacity of soil is defined as the capacity of the soil to bear the loads coming from the foundation. The pressure which the soil can easily withstand against load is called allowable bearing pressure.

Following are some types of bearing capacity of soil:

Ultimate bearing capacity of soil (qu)

The gross pressure at the base of the foundation at which soil fails is called ultimate bearing capacity.

Net ultimate bearing capacity (qnu)

By neglecting the overburden pressure from ultimate bearing capacity we will get net ultimate bearing capacity.

Where = unit weight of soil, D_f = depth of foundation

Net safe bearing capacity of soil (qns)

By considering only shear failure, net ultimate bearing capacity is divided by certain factor of safety will give the net safe bearing capacity.

q_ns = q_nu/ F

Where F = factor of safety = 3 (usual value)

Gross safe bearing capacity (qs)

When ultimate bearing capacity is divided by factor of safety it will give gross safe bearing capacity.

q_s = q_u/F

Net safe settlement pressure (qnp)

The pressure with which the soil can carry without exceeding the allowable settlement is called net safe settlement pressure.

Net allowable bearing pressure (qna)

This is the pressure we can used for the design of foundations. This is equal to net safe bearing pressure if q_np > q_ns. In the reverse case it is equal to net safe settlement pressure.

How to Calculate Bearing Capacity of Soil?

Calculation of bearing capacity of soil:

For the calculation of bearing capacity of soil, there are so many theories. But all the theories are superseded by Terzaghi’s bearing capacity theory.

Terzaghi’s bearing capacity theory

Terzaghi’s bearing capacity theory is useful to determine the bearing capacity of soils under a strip footing. This theory is only applicable to shallow foundations. He considered some assumptions which are as follows.

1.   The base of the strip footing is rough.

2.   The depth of footing is less than or equal to its breadth i.e., shallow footing.

3.   He neglected the shear strength of soil above the base of footing and replaced it with uniform surcharge. ( D_f)

4.   The load acting on the footing is uniformly distributed and is acting in vertical direction.

5.   He assumed that the length of the footing is infinite.

6.   He considered Mohr-coulomb equation as a governing factor for the shear strength of soil.

As shown in above figure, AB is base of the footing. He divided the shear zones into 3 categories. Zone -1 (ABC) which is under the base is acts as if it were a part of the footing itself. Zone -2 (CAF and CBD) acts as radial shear zones which is bear by the sloping edges AC and BC. Zone -3 (AFG and BDE) is named as Rankine’s passive zones which are taking surcharge (y D_f) coming from its top layer of soil.

From the equation of equilibrium,

Downward forces = upward forces

Load from footing x weight of wedge = passive pressure + cohesion x CB sin

Where P_p = resultant passive pressure = (P_p)_y + (P_p)_c + (P_p)_q

(P_p)_{y is} derived by considering weight of wedge BCDE and by making cohesion and surcharge zero.

(P_p)_{c is} derived by considering cohesion and by neglecting weight and surcharge.

(P_p)_q is derived by considering surcharge and by neglecting weight and cohesion.

Therefore,

By substituting,



So, finally we get q_u = c’N_c + y D_f N_q + 0.5 y B N_y

The above equation is called as Terzaghi’s bearing capacity equation. Where q_u is the ultimate bearing capacity and N_c, N_q, N_y are the Terzaghi’s bearing capacity factors. These dimensionless factors are dependents of angle of shearing resistance ().

Equations to find the bearing capacity factors are:

Where

Kp = coefficient of passive earth pressure.

For different values of , bearing capacity factors under general shear failure are arranged in the below table.

ø	Nc	Nq	Ny
0	5.7	1	0
5	7.3	1.6	0.5
10	9.6	2.7	1.2
15	12.9	4.4	2.5
20	17.7	7.4	5
25	25.1	12.7	9.7
30	37.2	22.5	19.7
35	57.8	41.4	42.4
40	95.7	81.3	100.4
45	172.3	173.3	297.5
50	347.5	415.1	1153.2

Finally, to determine bearing capacity under strip footing we can use

q_u = c’N_c + D_f N_q + 0.5  B N_y

By the modification of above equation, equations for square and circular footings are also given and they are.

For square footing

q_u = 1.2 c’N_c +  D_f N_q + 0.4  B N_y

For circular footing

q_u = 1.2 c’N_c +D_f N_q + 0.3 B N_y

Hansen’s bearing capacity theory

For cohesive soils, Values obtained by Terzaghi’s bearing capacity theory are more than the experimental values. But however it is showing same values for cohesion less soils. So Hansen modified the equation by considering shape, depth and inclination factors.

According to Hansen’s

q_u = c’N_c Sc dc ic +  D_f N_q Sq dq iq + 0.5  B N_y Sy dy iy

Where Nc, Nq, Ny = Hansen’s bearing capacity factors

Sc, Sq, Sy = shape factors

dc, dq, dy = depth factors

ic, iq, iy = inclination factors

Bearing capacity factors are calculated by following equations.

For different values of  Hansen bearing capacity factors are calculated in the below table.

ø	Nc	Nq	Ny
0	5.14	1	0
5	6.48	1.57	0.09
10	8.34	2.47	0.09
15	10.97	3.94	1.42
20	14.83	6.4	3.54
25	20.72	10.66	8.11
30	30.14	18.40	18.08
35	46.13	33.29	40.69
40	75.32	64.18	95.41
45	133.89	134.85	240.85
50	266.89	318.96	681.84

Shape factors for different shapes of footing are given in below table.

Shape of footing	Sc	Sq	Sy
Continuous	1	1	1
Rectangular	1+0.2B/L	1+0.2B/L	1-0.4B/L
Square	1.3	1.2	0.8
Circular	1.3	1.2	0.6

Depth factors are considered according to the following table.

Depth factors	Values
dc	1+0.35(D/B)
dq	1+0.35(D/B)
dy	1.0

Similarly inclination factors are considered from below table.

Inclination factors	Values
ic	1 – [H/(2 c B L)]
iq	1 – 1.5 (H/V)
iy	(iq)2

Where H = horizontal component of inclined load

B = width of footing

L = length of footing.

CONTOUR MAPS & THEIR USES

CONTOUR MAPS & THEIR USES

A contour line is a imaginary line which connects points of equal elevation. Such lines are drawn on the plan of an area after establishing reduced levels of several points in the area. The contour lines in an area are drawn keeping difference in elevation of between two consecutive lines constant. For example, Fig. 1 shows contours in an area with contour interval of 1 m. On contour lines the level of lines is also written.

Fig. 1: Contours

1. Characteristics of Contours

The contours have the following characteristics:

1. Contour lines must close, not necessarily in the limits of the plan.

2. Widely spaced contour indicates flat surface.

3. Closely spaced contour indicates steep ground.

4. Equally spaced contour indicates uniform slope.

5. Irregular contours indicate uneven surface.

6. Approximately concentric closed contours with decreasing values towards centre (Fig. 1) indicate a pond.

7. Approximately concentric closed contours with increasing values towards centre indicate hills.

8. Contour lines with U-shape with convexity towards lower ground indicate ridge (Fig. 2).

Fig. 3

9. Contour lines with V-shaped with convexity towards higher ground indicate valley (Fig.3).

10. Contour lines generally do not meet or intersect each other.

11. If contour lines are meeting in some portion, it shows existence of a vertical cliff (Fig. 4).

12. If contour lines cross each other, it shows existence of overhanging cliffs or a cave (Fig. 5).

2. Uses of Contour Maps

Contour maps are extremely useful for various engineering works:

1.   A civil engineer studies the contours and finds out the nature of the ground to identify. Suitable site for the project works to be taken up.

2.   By drawing the section in the plan, it is possible to find out profile of the ground along that line. It helps in finding out depth of cutting and filling, if formation level of road/railway is decided.

3.   Intervisibility of any two points can be found by drawing profile of the ground along that line.

4.   The routes of the railway, road, canal or sewer lines can be decided so as to minimize and balance earthworks.

5.   Catchment area and hence quantity of water flow at any point of nalla or river can be found. This study is very important in locating bunds, dams and also to find out flood levels.

6.   From the contours, it is possible to determine the capacity of a reservoir.

PLANE TABLE SURVEY AND ITS ACCESSORIES

PLANE TABLE SURVEY AND ITS ACCESSORIES

In plane table surveying a table top, similar to drawing board fitted on to a tripod is the main instrument. A drawing sheet is fixed on to the table top, the observations are made to the objects, distances are scaled down and the objects are plotted in the field itself. Since the plotting is made in the field itself, there is no chance of omitting any necessary measurement in this surveying. However the accuracy achieved in this type ofsurveying is less. Hence this type of surveying is used for filling up details between the survey stations previously fixed by other methods.

The most commonly used plane table is shown in Fig. 1. It consists of a well seasoned wooden table top mounted on a tripod. The table top can rotate about vertical axis freely. Whenever necessary table can be clamped in the desired orientation. The table can be levelled by adjusting tripod legs.

Fig: Plane table with tripod stand

The following accessories are required to carry out plane table survey:

1. Alidade

2. Plumbing fork with plumb bob.

3. Spirit level

4. Trough compass

5. Drawing sheets and accessories for drawing.

1. Alidade

It is a straight edge ruler having some form of sighting device. One edge of the ruler is bevelled and is graduated. Always this edge is used for drawing line of sight. Depending on the type of line of sight there are two types of alidade:

(a) Plain alidade

(b) Telescopic alidade

Plain Alidade: Figure 2 shows a typical plain alidade. A sight vane is provided at each end of the ruler. The vane with narrow slit serves as eye vane and the other with wide slit and having a thin wire at its centre serves as object vane. The two vanes are provided with hinges at the ends of ruler so that when not in use they can be folded on the ruler. Plain alidade is not suitable in surveying hilly areas as the inclination of line of sight in this case is limited.

Fig: 2 – Plane Alidade

Telescopic Alidade: It consists of a telescope mounted on a column fixed to the ruler [Fig. 3]. The line of sight through the telescope is kept parallel to the bevelled edge of the ruler. The telescope is provided with a level tube and vertical graduation arc. If horizontal sight is required bubble in the level tube is kept at the centre. If inclined sights are required vertical graduation helps in noting the inclination of the line of sight. By providing telescope the range and the accuracy of line of sight is increased.

Fig. 3: Telescopic alidade

2. Plumbing Fork and Plumb Bob

Figure 4 shows a typical plumbing fork with a plum bob. Plumbing fork is a U-shaped metal frame with a upper horizontal arm and a lower inclined arm. The upper arm is provided with a pointer at the end while the lower arm is provided with a hook to suspend plumb bob. When the plumbing fork is kept on the plane table the vertical line (line of plumb bob) passes through the pointed edge of upper arm. The plumb bob helps in transferring the ground point to the drawing sheet and vice versa also.

Fig. 4: Plumbing fork and plumb bob

3. Spirit Level

A flat based spirit level is used to level the plane table during surveying (Fig.5). To get perfect level, spirit level should show central position for bubble tube when checked with its positions in any two mutually perpendicular directions.

Fig. 5: Spirit level

4. Trough Compass

It consists of a 80 to 150 mm long and 30 mm wide box carrying a freely suspended needle at its centre (Ref. Fig. 6). At the ends of the needle graduations are marked on the box to indicate zero to five degrees on either side of the centre. The box is provided with glass top to prevent oscillation of the needle by wind. When needle is centred (reading 0–0), the line of needle is parallel to the edge of the box. Hence marking on the edges in this state indicates magnetic north–south direction.

Fig. 6: Trough compass

5. Drawing Sheet and Accessories for Drawing

A good quality, seasoned drawing sheet should be used for plane table surveying. The drawing sheet may be rolled when not in use, but should never is folded. For important works fibre glass sheets or paper backed with thin aluminium sheets are used.

Clips clamps, adhesive tapes may be used for fixing drawing sheet to the plane table. Sharp hard pencil, good quality eraser, pencil cutter and sand paper to keep pencil point sharp are other accessories required for the drawing work. If necessary, plastic sheet should be carried to cover the drawing sheet from rain and dust.