Typically you take the total volume of the matrix including cement. Therefore it would include cement, supplementary cementitious materials such as fly ash and slag etc, water, aggregates, chemical admixtures and fiber itself. Once you know the total volume of the mix you are going to prepare, calculate the fiber volume by multiplying with given fiber volume fraction. Then convert to weight by multiplying with fiber density. You may want to use the attached simple spreadsheet for your calculations. Let me know if you have any questions.

Typically you take the total volume of the matrix including cement. Therefore it would include cement, supplementary cementitious materials such as fly ash and slag etc, water, aggregates, chemical admixtures and fiber itself. Once you know the total volume of the mix you are going to prepare, calculate the fiber volume by multiplying with given fiber volume fraction. Then convert to weight by multiplying with fiber density. You may want to use the attached simple spreadsheet for your calculations. Let me know if you have any questions.

Hi, we usually indicate the fiber content for a cubic meter of the material considered. If you need 1.5%vol of fibers per cubic meter, that means 15liters per cubic meter. If the fiber density is 2.56 that means you need to have 38.4 kg/m3 of fibers. Best wishes. Maxime.

1.5% * total volume of your mix (e.g. 1m3) * density of fiber(kg/m3)

Dear D.K Mishra

Thanks for the answer. The excel sheet is very helpful.

Regards

Saurabh

Dear D. K. Mishra

I am working on fibre reinforced earth materials and sharing the same doubt as Mr. Saurabh Khandelwal.

Here in the spreadsheet that is shared, the fibre volume fraction is not depending on the density of the fresh mix i.e., even for densities other than 2.044 g/ cc we get the same fibre weight to be used. So, I am in a doubt if we have to calculate the weight of the fibre similar to the other constituent materials and then find its volume fraction with trial and error.

Please correct me if it is wrong.

Thanking you

Yours

Bhanupratap

Please check the spreadsheet again - there was a small error in the formula for weight fraction of the fibre. Kindly note that since fiber is specified in volume fraction, weight of fibre is independent of fresh density of the material. For example, in our example for a 1 lit batch of material we have assumed 2% by volume of fiber which is 20 cc or 26 gm since fiber density is assumed to be 1.3 gm/cc. If you change the wet density the weight of the batch will change volume remaining same and hence weight fraction of fiber will change, its weight and volume remaining unchanged. Hope its helps clarify.

Dear D. K. Mishra,

Thank you for the explanation, it was very helpful. Can I please know why do authors prefer to represent fibre content in volume fraction rather than weight fraction in FRC.

Thank you.

Please see https://en.wikipedia.org/wiki/Fiber_volume_ratio for the background to why we use volume fraction instead of weight fraction. Also most polymeric fibers are low density while metallic fibers are very high density. If you used weight fraction, you will get very different volumes of fiber that would completely change the composite characteristics and make any comparison meaningless. How ever you do need the weight fraction to calculate costs as it is always given per unit weight for fibers.

Dear D K Mishra,

Thank you very much for the reply. It was a very fine explanation.

Yours

Bhanupratap

Dhanada Kanta Mishra

Respected professor,

I went through the explanation and spreadsheet calculation given above by you .it is really helpful. but in my experiment I am also trying to calculate the fiber weight (for 2%fiber volume ) in two ways: one by a spreadsheet of yours and the explanation in the 2nd time comment of yours .the result in both cases has a difference. can you please suggest me which one is better to use .i have attached the spreadsheet here. Thank you in advance