IS OUR CONCRETE FAIL ?

Is concrete fail if  strength of concrete of any particular grade less than its characteristics strength ?

No, we can't directly say that concrete fail if strength is less than characteristics strength.
As per special publication SP 23 of CONCRETE we follow the following steps if strength is less than Fck.

1) Strength  of  concrete of any sample   should  not  less  than

a) characteristics strength  minus  1.35 times of standard  deviation.

b) 0.80 times of characteristics strength of concrete.

c) And average strength of concrete sample should not less than

   fck + ( 1.65 - 1.65/(root of number of samples)* standard deviation

THE ABOVE THREE   CRITERIA    MUST BE FULL FILLED  IF ANY ONE CRITERIA  IS   FAILED THAN FORTH EQUATION IS GIVEN BELOW  :

Fck + ( 1.65 - 3/( root of samples)* standard deviation


IT   IS  ELABORATED  WITH   SIMPLE  EXAMPLE   GIVEN BELOW:

Let Grade of concrete  M35

Strength of different  samples is derive during cube test is:

39, 42, 40, 43, 32 , 40 N / mm2  respectively


1 , 2 , 3 , 4 samples are directly passed more than 35 N/ mm2

But in the case of 5th sample it is 32 N / mm2

Which is less than 35 N/ mm2


Than from 1st criteria:

 35 - 1.35 × 5 = 28.25 N/ mm2

From second criteria:

0.80 × 35 = 28 N / mm2

1st and 2nd criteria full fill  hence ok



Let come on third criteria:

Average of  sample strength
39+ 42+40+43+32= 196

196/5 = 39.2 N/ mm2

According to 3rd criteria:

35 + ( 1.65 - 1.65/ 2.23) × 5
  
     ( 2.23 is root of 5)

After calculation it is   39.5 mm2 which is greater than 39.2 N/ mm2. ( Here our concrete is fail ) but we have fouth equation
If fouth criteria meet the requirement than our concrete passed with the sole discretion of designer.


Let we are going to 4th criteria

35+( 1.65- 3/ 2.23) × 5
After calculation we get 36.5 N / mm2


Average strength 39. 2 N / mm2 is greater than 36.5 N / mm2 hence our concrete 5th sample also  passed .


NOTE : STANDARD DEVIATION  IS 5 IN ABOVE EXAMPLE