Water absorption of sand is about 1%. Hence additional water is added in the mix according to the percentage weight of sand i.e 16.76 kg for saturated surface dry condition of aggregate and same amount of mass is subtracted from the initial amount of aggregate for maintaining 1m3 of concrete.

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I absolutely agree with you, Shashikant Kumar! However, there must be a parcel of the water content that is not absorbed by the aggregate but adsorbed by the aggregate (and which improves workability). Thanks a lot for taking the time to answer my question and thanks for the recommendations!

When we design a mix the water absorption of aggregate is calculated in comparison to their bone-dry conditions and then how much water must be added to have the aggregate of Saturated Surface Dry (SSD) conditions. This is what we call water absorption of the aggregate. If the aggregate currently used already have some moisture, then we must find out the existing percentage of moisture and make necessary additions or subtraction in water quantity to be added.

Agreed, Prof. Om Prakash Chhangani ! But, if we design a mixture based on a given consistency level, we are adding a parcel of water that is only responsible for workability (it will neither hydrate cement nor be absorbed by the aggregate). Do you think it is reasonable to define this extra water as the total water content minus the water content for hydration (based on Bogue's compounds) and minus the water absorbed by the aggregate?

Agreed, Mr. Guilherme S. Munhoz ,Lot of work has been done on what is minimum water cement ratio required for hydration of cement and it is around (w/c)0.21 and we need additional water for making aggregates corresponding to Saturated Surface Dry conditions. Over and above, this is required for workability of concrete. However, too much extra water can lead to large capillaries and air voids on drying which will increase permeability of the concrete. Thus, excess water will decrease the strength of the concrete. If the quantity is just sufficient then capillaries water will self-desiccate to hydrate un-hydrated cement particles which will increase the strength of the concrete and the size of capillaries will also be much smaller.

The water/cement ratio (w/c) determines mortar mixtures' strength, durability, and workability. The w/c ratio determines how much water will be available to hydrate the cement and how much paste (cement and water) will fill the voids between the sand particles and create a strong bond. Determining the proper w/c ratio for mortar mixtures is crucial, as more water can lead to better-quality mortar. When choosing the w/c ratio for a mortar mixture, it is essential to consider the desired properties of the cannon. For example, if the mortar needs to be highly workable, such as for a stucco application, a higher w/c ratio may be necessary. Conversely, a lower w/c ratio may be required if a more durable mortar is desired. The desired properties will dictate the target w/c percentage, which can be determined by determining the water needed to hydrate the cement. The sand's initial moisture content must be considered to determine the water required to hydrate the cement. This is because the sand will absorb some water in the mix, reducing the water available to hydrate the cement. Generally speaking, a 1:1 ratio of sand to water is recommended to ensure adequate moisture content in the sand. Once the initial moisture content of the sand is determined, the amount of water needed to hydrate the cement can be calculated using the following formula: Volume of water = (Cement weight/Cement density) × (Water/Cement ratio). Once the volume of water needed to hydrate the cement has been determined, the amount required for the paste mix can be calculated. The formula for this is Volume of water for paste mix = (Cement weight/Cement density) + (Water/Cement ratio). The w/c ratio can be determined for a given mortar mixture using these two formulas. For example, suppose 10 pounds of cement and a w/c ratio of 0.5 is desired. In that case, the volume of water needed for the paste mix can be calculated as follows: Volume of water for paste mix = (10 lbs/94 lbs/ft3) + (0.5) The volume of water for paste mix = 0.106 ft3 This calculation shows that 0.106 ft3 of water is needed for the paste mix to achieve the desired w/c ratio of 0.5. In summary, the w/c ratio of a mortar mixture can be determined by considering the selected properties of the mortar, determining the initial moisture content of the sand, and then calculating the amount of water needed to hydrate the cement and create the paste mix. The two formulas above can calculate the water/cement ratio required for a paste mixture based on a mortar mixture. References: 1. National Ready Mixed Concrete Association. (2019). Mortar Mixes. Retrieved from https://www.nrmca.org/aboutconcrete/mortarmixes.html 2. The Portland Cement Association. (2015). Estimating the Amount of Water Needed for a Concrete Mix. Retrieved from https://www.cement.org/cement-concrete-applications/commercial-construction/estimating-amount-of-water-needed-for-a-concrete-mix

Second part:

When determining the water/cement (w/c) ratio needed for a paste mixture based on a mortar mixture, it is crucial to understand the properties of the mortar mixture, the consumptions in question, and the desired paste mixture. In this case, we have a given mortar mixture with a w/c ratio of 0.74, consumed materials are 339.8 kg/m3 of cement, 1676.7 kg/m3 of sand, and 251.8 kg/m3 of water, and the sand is siliceous with water absorption of 0.1%. To calculate the w/c ratio of the paste mixture, we first need to calculate the w/c ratio of the mortar mixture. To do this, we must calculate the mass of water and cement per unit volume of the mortar mixture. The group of water per unit volume of the mortar mixture equals the water consumption divided by the total volume of the mortar mixture (251.8/2m3). Similarly, the mass of cement per unit volume of the mortar mixture equals the cement consumption divided by the total volume of the mortar mixture (339.8/2m3). Then, we can calculate the w/c ratio of the mortar mixture by dividing the water mass by the cement mass (251.8/339.8 = 0.74). Next, we need to calculate the w/c ratio of the paste mixture. To do this, we must calculate the mass of water and cement per unit volume of the paste mixture. The mass of water per unit volume of the paste mixture is equal to the water consumption divided by the total volume of the paste mixture (251.8/1m3). Similarly, the mass of cement per unit volume of the paste mixture equals the cement consumption divided by the total volume of the paste mixture (339.8/1m3). Then, we can calculate the w/c ratio of the paste mixture by dividing the water mass by the cement mass (251.8/339.8 = 0.74). Finally, we can calculate the w/c ratio of the paste mixture by considering the sand's water absorption. The water absorption of the sand is 0.1%, which means that 1% of the total mass of the sand is considered “dead,” – meaning it cannot be used to form mortar. Therefore, we need to adjust the water consumption in the paste mixture by subtracting the mass of water absorbed by the sand from the total water consumption. In this case, the water absorbed by the sand is equal to the water absorption times the sand consumption (0.1% x 1676.7 kg/m3 = 167.7 kg/m3). Therefore, the adjusted water consumption in the paste mixture is equal to the actual water consumption minus the mass of water absorbed by the sand (251.8 - 167.7 = 84.1). Then, we can calculate the w/c ratio of the paste mixture by dividing the adjusted water mass by the cement mass (84.1/339.8 = 0.25). In conclusion, to determine the water/cement ratio needed for a paste mixture based on a mortar mixture, it is essential to understand the properties of the mortar mixture, the consumptions in question, and the desired paste mixture. Then, it is necessary to calculate the w/c ratio of the mortar mixture and the w/c ratio of the paste mixture and to take into account the water absorption of the sand when calculating the adjusted mass of water for the paste mixture. References 1. American Society for Testing and Materials. (2016). Cement and Concrete Terminology. ASTM International. 2. Brown, B. (2018). How to Calculate the Water/Cement Ratio of a Concrete Mixture. The Constructor. 3. Bureau of Indian Standards. (2017). Water/Cement Ratio of Concrete. BIS. 4. National Ready Mixed Concrete Association. (2017). Understanding W/C Ratios. NRMCA.

Thanks a lot for your significant contribution, Prof. Felix M. Delmonte

What do you mean by "cement paste with the water content proportional to the amount of water in the mortar mixture"? Do you need to design the paste of the same consistency or strength? Because each needs other approach to the task.