TYPICAL CALCULATION FOR ACTIVE EARTH PRESSURE

 

1.         In the note, ‘Key Design Parameters’, it was indicated that for c-ø soil, calculation of active earth pressure for design of Abutment/Retaining wall should be done taking into account cohesion and angle of internal friction by modifying Coulomb’s and Rankine’s k factors, which are basically meant for cohesion less soil.  Generally soil having ø greater than 260 should for all practical purposes be treated as cohesion less and Rankine’s k factor may be safely used i.e.,

 

            ka =    1-sin  ø

                      1+sin ø

 

2.         For value of ø less than 260 and having cohesion, the earth pressure at depth z can be calculated by using the formula,

 

            Pa=γ. z. ka – 2c√ ka

 

            Sometimes resultant R and its location can be calculated by either neglecting tension zone or altering the pressure diagram for overall depth of soil.  This value is, however, on conservative side.

 

3.         A typical calculation is presented to illustrate the procedure:

 

 

           

                                                                                                            XXXXX

                                                                                                            Tension crack

 

                                                                                                              Ø =100

                                                                                             z=6m         C =10kPa

                                                                                                              γ  =17kN/m3

 

 

                                                                                            XXXXX

                                                                                                                    Given

(i)         ka = 1-sin  ø    =          1- sin100         =0.704

                   1+sin ø                1+sin100

 

            √ ka     =          √0.704 =        0.839

 

 

(ii)        At top :            z=o

 

            Pa = -2c√ka = -2 x 10 x 0.839 = 16.78 kPa

 

            For Pa=o

 

            γzka – 2c√ka = o

 

            z = 2c      = 2x10        = 1.40m

                 γ√ka   17x0.839

 

            This is the value of z for potential tension crack (-Þ), since tensile stress soil cannot carry.

 

(iii)       At base, the lateral pressure

 

            Pa        = 17 x 6 x 0.704 – 2 x10 x 0.839=71.8– 16.78 =55.02 kPa

 

1.4 m
 

 
 

1.4 m
 

9.61
 
                

 

 

 

(iv)       Neglecting tension zone

 

            Resultant R = ½ x 1 55.02 x 4.6 = 126.55 kN/m

                                     

 

            ӯ = 4.6 = 1.53m

                   3  

 

(v)        With water in the tension crack

            R =  126.55+½x (1.4) 2 x g

 

            R = 126.55 + 9.807 (1.4)2 = 126.55+9.61 = 136.16 kN/m

                                           2

 

(vi)       Overturning moment including water in the tension crack

 

            Mo = 126.55 x 1.53 + {9.807 x 1.42} (4.6 + 1.4)     = 193.62 + 46.69

                                                            2                          3

                                                                                                =246.31kN-m/m

            ӯ = 246.31 = 1.765 m

                  136.16

 

(vii)      Using alternative pressure diagram

 

            R = 55.02 x 6 = 165.06 kN/m

                                 2

            ӯ = 6 =2m

                  3

 

            Thus it is clear that the alternative method gives conservative value.

 

(viii)     For any super-imposed load or surcharge the value can be super imposed.

 

References : Foundation Analysis & Design by Joseph E.Bowels.

 

 

 

( R.R.Jaruhar )

Member Engineering

13th July, 2005