IS method mix design for fck 30 N/mm2 (numerical)

Method: IS 10262 with IS 456:2000.

Data: M30; 20 mm angular aggregate; compaction factor 0.85 (low-medium workability, about 50 mm slump); fair quality control; severe exposure.

Assumptions: OPC 43 grade ($G = 3.15$); sand Zone II, $G_{FA} = 2.65$; $G_{CA} = 2.74$; no admixture; aggregates in SSD condition; entrapped air 2%.

Step 1: Target strength. IS 10262 Table 1 (and IS 456 Table 8) gives $s = 5.0$ N/mm$^2$ for M30 with good site control; for fair control the value is increased by 1 N/mm$^2$, so $s = 6.0$ N/mm$^2$.

$$f'_{ck} = 30 + 1.65 \times 6 = 39.9\ \text{N/mm}^2$$

(this is higher than $f_{ck} + X = 30 + 6.5 = 36.5$ required by the 2019 revision).

Step 2: w/c ratio. The strength-w/c curve for OPC 43 (IS 10262:2019 Fig 1) gives about 0.42 for 39.9 N/mm$^2$. For severe exposure (IS 456 Table 5, RCC): maximum w/c = 0.45, minimum cement 320 kg/m$^3$. Adopt the lower value, w/c = 0.42.

Step 3: Water (IS 10262 Table 2): for 20 mm angular aggregate at 50 mm slump, no correction needed. Water = 186 kg/m$^3$.

Step 4: Cement = $186/0.42 = 443$ kg/m$^3$; this is $> 320$ (minimum) and $< 450$ (maximum).

Step 5: Coarse aggregate volume (Table 3: 20 mm, Zone II, w/c 0.50 gives 0.62). For w/c 0.42 (0.08 lower): $+0.016$, so the volume of CA = 0.636 and FA = 0.364 of the total aggregate.

Step 6: Mix calculation per m$^3$ (absolute volume)

$$\begin{aligned} CA &= 0.6534 \times 0.636 \times 2.74 \times 1000 = 1139\ \text{kg} \\ FA &= 0.6534 \times 0.364 \times 2.65 \times 1000 = 630\ \text{kg} \end{aligned}$$

Answer (per m$^3$): cement 443 kg, water 186 kg, FA 630 kg, CA 1139 kg; w/c = 0.42; ratio 1 : 1.42 : 2.57 (about 2398 kg/m$^3$). Corrections for moisture and absorption, and trial mixes, follow.