Concrete Materials Testing, ASTM C136 / C33 Sieve Gradation & ACI 211.1 Mix Design
ASTM C136 Sand Sieve Analysis & Fineness Modulus Formula
Calculate Cumulative Percentage Retained Sum Across the 6 Standard ASTM Sieves (#4 to #100), Fine-Aggregate Fineness Modulus FM, ACI 211.1 Coarseness Shift vs 2.70 Baseline, and ASTM C33 Spec Status.
Summing INDIVIDUAL sieve percentages—or accidentally including the #200 pan sieve—ruins ACI 211.1 concrete coarse-aggregate batching!
Under ASTM C136 and ACI 211.1 concrete proportioning, Fine-Aggregate Fineness Modulus (`FM`) is an empirical index of logarithmic mean sand particle size defined STRICTLY as the sum of CUMULATIVE percentages retained on the six standard halving-aperture sieves—`#4` (4.75 mm), `#8` (2.36 mm), `#16` (1.18 mm), `#30` (600 um), `#50` (300 um), and `#100` (150 um)—divided by `100`: `FM = (CumRet_#4 + CumRet_#8 + CumRet_#16 + CumRet_#30 + CumRet_#50 + CumRet_#100) / 100`! Lab technicians frequently make two costly mistakes: summing individual-sieve retained weights instead of monotonically increasing CUMULATIVE retained percentages, or adding `#200` (75 um) and pan fines into the numerator! ASTM C33 requires concrete sand `FM` between `2.30` and `3.10` (`FM < 2.30` fine dune/masonry sand spikes mixing-water demand and shrinkage; `FM > 3.10` coarse sand produces harsh, bleeding mixes), and ACI 211.1 shifts coarse-aggregate bulk volume fraction `b / b_0` by `-0.01` for every `+0.10` rise in `FM` (`Delta_FM = FM - 2.70`)!
Verify on a Washed Natural River Sand Gradation—Cumulative_%_Retained on `#4` = 2.0% (B2), `#8` = 14.0% (B3), `#16` = 33.0% (B4), `#30` = 56.0% (B5), `#50` = 81.0% (B6), and `#100` = 95.0% (B7): Six-Sieve Cumulative Sum equals `281.0` (E2), Fineness Modulus hits `FM = 2.81` (E3), Coarseness Shift vs `2.70` Reference equals `+0.11` (E4), and Specification Gate confirms `"ASTM C33 SPEC SAND (2.3-3.1)"` (E5)!
| ASTM C136 / C33 Sand KPI (Cum Retained: 2, 14, 33, 56, 81, 95%) | Formula | Verified Output |
|---|---|---|
| 6-Sieve Cumulative Retained Sum | B2 + B3 + B4 + B5 + B6 + B7 | 281.0 (221.0 @ fine pit sand) |
| Fineness Modulus FM | Cum_Retained_Sum / 100 | 2.81 (2.21 < 2.30 @ fine pit sand!) |
| ACI 211.1 Reference Shift (dFM) | Fineness_Modulus_FM - 2.70 | +0.11 (-0.49 @ fine pit sand) |
| ASTM C33 Concrete Sand Gate | 2.30 <= FM <= 3.10 | ASTM C33 SPEC SAND (2.3-3.1) |
Monotonic Cumulative Sieve Validation & ASTM C136 Fineness Modulus Formula
Enforce monotonically non-decreasing cumulative percentages `0 <= #4 <= #8 <= #16 <= #30 <= #50 <= #100 <= 100` right on `E2` (and `ISTEXT(E2)` on `E3..E4`)—immediately catching anyone who accidentally pastes non-cumulative individual-sieve percentages where `#50` or `#100` drops below `#30`!
=LET(s_a, B2, s_b, B3, s_c, B4, s_d, B5, s_e, B6, s_f, B7, IF(OR(s_a < 0, s_b < s_a, s_c < s_b, s_d < s_c, s_e < s_d, s_f < s_e, s_f > 100), "Invalid Sieve Input", LET(fm_v, (s_a + s_b + s_c + s_d + s_e + s_f) / 100, IF(fm_v < 2.3, "TOO FINE (HIGH WATER DEMAND)", IF(fm_v > 3.1, "TOO COARSE (HARSH BLEEDING)", "ASTM C33 SPEC SAND (2.3-3.1)")))))Fine Windblown Pit Sand Water-Demand Reject Check (Set Cum Retained = 0, 4, 15, 38, 72, 92%)
Test a fine pit sand shipment (`B2=0, B3=4, B4=15, B5=38, B6=72, B7=92`): Cumulative Sum E2 drops to `221.0`, Fineness Modulus E3 falls to `2.21` (`Delta_FM = -0.49` in E4), and E5 flags `"TOO FINE (HIGH WATER DEMAND)"` unless blended with coarse manufactured crusher sand!
=IF(ISTEXT(E2), E2, ROUND((B2 + B3 + B4 + B5 + B6 + B7) / 100, 2))Try the example
Use the original values or change them to test your understanding.