Effects of Particle Shapes and Sizes on the Minimum Void Ratios of Sand

Table 5

The predicted and the measured values of (e_min)_min.

Sands	Mixtures (mm)	d (mm)	D (mm)	Equation (2)	Measured	Predicted
NS	2–5∼0.1–0.25	0.175	3.5	(emin)min = 0.54 ∗ {1 − exp(−(d/d)/0.0691)}	0.305	0.278
	2–5∼0.25–0.5	0.375			0.426	0.425
	2–5∼0.5–1	0.75			0.502	0.516
	2–5∼1-2	1.5			0.550	0.539
	1-2∼0.1–0.25	0.175	1.5		0.425	0.440
	1-2∼0.25–0.5	0.375			0.517	0.525
	1-2∼0.5–1	0.75			0.537	0.540
DS	2–5∼0.1–0.25	0.175	3.5	(emin)min = 0.54 ∗ {1 − exp(−(d/d)/0.0721)}	0.355	0.270
	2–5∼0.25–0.5	0.375			0.425	0.418
	2–5∼0.5–1	0.75			0.505	0.512
	2–5∼1-2	1.5			0.531	0.539
	1-2∼0.1–0.25	0.175	1.5		0.435	0.433
	1-2∼0.25–0.5	0.375			0.496	0.523
	1–2∼0.5–1	0.75			0.528	0.539
FS	1-2∼0.1–0.25	0.175	1.5	(emin)min = 0.54 ∗ {1 − exp(−(d/d)/0.1168)}	0.346	0.342
	1-2∼0.25–0.5	0.375			0.450	0.476
	1-2∼0.5–1	0.75			0.503	0.533
B1 & C4	3∼0.9	0.9	3	(emin)min = 0.54 ∗ {1 − exp(−(d/d)/0.2165)}	0.402	0.405
B1 & C3	3∼1.5	1.5			0.482	0.486
B1 & C2	3∼2.1	2.1			0.538	0.519
B2 & C3	2.1∼1.5	1.5	2.1		0.525	0.520
B2 & C4	2.1∼0.9	0.9			0.452	0.466
B1 & B4	3∼0.9	0.9	3	(emin)min = 0.54 ∗ {1 − exp(−(d/d)/0.2417)}	0.385	0.384
B1 & B3	3∼1.5	1.5			0.481	0.472
B1 & B2	3∼2.1	2.1			0.532	0.510
C1 & C4	3∼0.9	0.9	3	(emin)min = 0.54 ∗ {1 − exp(−(d/d)/0.1871)}	0.422	0.431
C1 & C3	3∼1.5	1.5			0.491	0.503
C1 & C2	3∼2.1	2.1			0.508	0.527
C2 & C3	2.1∼1.5	1.5	2.1		0.518	0.528
C2 & C4	2.1∼0.9	0.9			0.440	0.485
C3 & C4	1.5∼0.9	0.9	1.5		0.482	0.518