INTRODUCTION
Geotechnical engineering is the branch of the civil engineering that concerns the application of the principle of mechanics ,hydraulics and to some extent chemistry ,it involves few really complicated solution of various problems in terms of equations but more important then that it consist some graphical solutions of various problems which are just based on the pure geometry and some of them are as ,,,,



CULMANN'S GRAPHICAL METHOD

• This method is convenient for determining the active earth pressure of the soil having no cohesion.
•  Morever it can be used for backfill surfaces of any shape,different types of surcharge load and even for a layered backfill.
• It consist of constructing the force triangle for the number of assumed trial failure plane.

Procedure

1. A line AF is drawn at an angle φ to the horizontal,this line is called as the slope line or weight line.
2. Trial planes AC1,AC2 etc are drawn and weight of trial wedges are calculated  this is as follows .

• When a back surface is planar then each triangular wedge has its base on the ground surface and a constant perpendicular distance L from a Common vertex A . 
• The area and hence the weight of each sliding wedge is thus proportional to its base length measured from B.
• The weight of the wedge can therefore be represented as the base length,so the weight of the wedge can be represented the (AD1=BC1).

     3) A second line AG (earth pressure line) is drawn at an angle Ψ=(90-θ-δ) to the slope line AF.

     4) Lines are drawn through D1,D2 etc ,,, parallel to the earth pressure line AG to intersect the                 corresponding slip planes at E1,E2 etc... AD1E1 ,AD2E2 etc.....

     5)Points E1,E2 etc... are joined to obtain the earth pressure locus .This curve is called as the culmann curve.

     6)To obtain the max value of P, which is the active earth pressure ,a tangent parallel to AF is drawn to the culmann curve. Then the line DE is drawn parallel to line AG through point of tangency E.

7)DE will be calculated from the drawn figure and so the vertical length also...

8)Finally TOTAL MAX PRESSURE (P)=(1/2)*Υ*L*DE.

DETERMINATION OF PRE-CONSOLIDATION PRESSURE(Cassagrande method)

1. Plot the graph b/w void ratio and log(σ').
2. Draw the horizontal line ab from this point.
3. Draw the line ac tangent to a.
4. Draw the line ad bisector of the angle between ab and ac.
5. Plot the straight line portion of the e-log(σ'),plot to intersect ad at f .
6. The abcissa of F is the pre-consolidation pressure σ'c.

Logrithm of time method (to find Cv)

Plot the graph b/w deformation and logt......

1. Extend the straight line portion of the primary and secondary consolidation curve to intersect at A .
2. The ordinate of it is represented by d100(ie...deformation at the end of 100% primary consolidation)
3. Select the times t1&t2 on the curved portion such that (t2=4t1),let the difference of specimen deformation during time (t2-t1) be equal to x.
4. Draw the horizontal line DE such that ,the vertical distance BD is equal to x then the deformation corresponding to line DE is d0.(ie..deformation at the zero consolidation)
5. Obtain d50=((d100-d0)/2),the ordinate of point f on the consolidation curve represent the deformation at 50% and the abscissa represent the t50.
6. Now use T50=Cv(t50)/(Hdr^2)

where T50=time factor at 50% average degree of consolidation.

Hdr=average longest drainage path during consolidation

SQUARE ROOT OF TIME METHOD

plot the graph b/w deformation and t^(1/2)

1. Draw AB through the early portions of the curve .
2. Draw the line AC such that OC=1.15OB.
3. The abscissa of the point D will give you the square root of the time for 90% consolidation(ie..(t90)^(1/2).
4. Again use T50=Cv(t50)/(Hdr^2).