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[subha_mukherjee]

We know the vertical subgrade reaction of soil formula: 40xFOSxBearing Capacity of Soil. Now, please let me know if there is any formula for calculating the horizontal subgrade reaction of soil?

[vikram.jeet]

MODULUS OF SUBGRADE REACTION as per NBC

EMPIRICAL FORMULA FOR CALCULATING MODULUS K

K= 0.65 {(Es*B^4)/(E I)}^(1/12) *  Es/(1 - u^2)  * 1/B

Approximately K can be taken as
K = 0.65 * Es/(1 - u^2)  * 1/B
(1/12 the power term taken as nearly unity)

Es - Modulus of Elasticity of soil
E - Young's modulus of foundation material
u - Poisson ratio of soil
B - Foundations width

Kindly Refer National Building Code of India,  Chspter on Soil Foundations,  Appendix is given at end of this chapter

[vikram.jeet]

Modulus of subgrade reaction  is =( Load/area )/ settlement.

Bowels formula  K = 40*SBC*FOS

The formula considers 25mm settlement of foundation

At ultimate Bearing capacity , settlement of 25 mm is taken
K value in Tonne/m3 or KN/m3 ( based on  SBC in T/m2 or KN/m2)

Thus   K = Ultimate BC / 0.025 = 40*Ultimate BC = 40*(SBC*FOS)

The other formula for working out  modulus of subgrade reaction is given in National Building Code of India at its appendix of Soil Chapter

[vikram.jeet]

MODULUS OF SUBGRADE REACTION


MODULUS K = (LOAD/AREA) /( CORRESPONDING SETTLEMENT)

Generally for field tests on 75cm  circular plate , pressure for 1.25mm Settlement is taken .
Then  K = p/0.125  MPA/cm =  10p / 0.125   kg/cm2/cm
P is the pressure for a settlement of 1.25mm on plate

REFER IS 9214 FOR DETERMINATION OF K VALUE


USEFUL SOIL DATA (AS PER SP-7, NBC OF INDIA)

COHESION LESS SOIL

LOOSE SOIL
RELATIVE DENSITY  < 20%
SPT N VALUE (BLOWS/30CM)   < 10
MODULUS OF SUBGRADE REACTION K   15000KN/m3(DRY,MOIST)
MOD OF SUBGRADE REACTION K   9000 kN/m3 (Submerged state)

MEDIUM SOILS
RD 20% TO 70%
SPT N VALUE    10 TO 30
K (DRY/MOIST) -  15000  - 47000 KN/m3
K (Submerged state) -  9000 - 29000 kN/m3

DENSE SOILS
RD> 70%
SPT N VALUE >30
K (DRY/MOIST) -  47000 - 180000 kN/m3
K (Submerged)  29000 - 108000  kN/m3

ALL ABOVE DATA IS FOR COHESION LESS SOILS



USEFUL SOIL DATA (AS PER SP-7 )

COHESIVE SOILS

SOFT TO VERY SOFT SOILS
SPT N VALUE  < 4

UNCONFINED COMPRESSIVE STRENGTH - NOT GIVEN , MUST BE SMALL
MODULUS OF SUBGRADE REACTION K - NOT GIVEN



MEDIUM SOILS
SPT N VALUE   4  TO  8

UNCONFINED COMPRESSIVE STRENGTH  Not given , but seems < 100 kN/m2 , since stiff values are given in range 100 - 200 kN/m2.

K  value - not given , but seem  < 27000 kN/m3 looking at range of stiff values


STIFF SOILS
SPT N VALUE  8  TO  15
UCS  100  -  200 KN/m2
Modulus of subgrade reaction K value    27000 kN/m3


VERY STIFF SOILS
SPT N VALUE  >  15
UCS   200 - 400 KN/m2
Mod of subgrade reaction K value  27000 to 54000 kN/m3


HARD SOILS
SPT N VALUE  > 15
UCS  > 400 KN/m2
Mod of subgrade reaction K   54000 to 108000 kN/m3

UCS VALUES AND K VALUES ARE ON SQ PLATE 300X300MM
AV LOAD INTENSITY TO BE LESS THAN (ULTIMATE BC/2)


FOR MORE INFO REFER SP7 CHAPTER 6 ANNEXURE B