Modelling the permanent deformation of unbound granular materials in pavements

Figures & data

Figure 1. Typical PD behaviour of UGMs in different SDR classes, depending on the stress level.

Table 1. Stress levels for MS RLT tests, prescribed by the European Standard (HSL).

High stress level
Sequence 1			Sequence 2			Sequence 3			Sequence 4			Sequence 5
Confining	Deviator		Confining	Deviator		Confining	Deviator		Confining	Deviator		Confining	Deviator
stress, σ3	stress, σd		stress, σ3	stress, σd		stress, σ3	stress, σd		stress, σ3	stress, σd		stress, σ3	stress, σd
kPa	kPa		kPa	kPa		kPa	kPa		kPa	kPa		kPa	kPa
Constant	Min	Max	Constant	Min	Max	Constant	Min	Max	Constant	Min	Max	Constant	Min	Max
20	0	50	45	0	100	70	0	120	100	0	200	150	0	200
20	0	80	45	0	180	70	0	240	100	0	300	150	0	300
20	0	110	45	0	240	70	0	320	100	0	400	150	0	400
20	0	140	45	0	300	70	0	400	100	0	500	150	0	500
20	0	170	45	0	360	70	0	480	100	0	600	150	0	600
20	0	200	45	0	420	70	0	560

Table 2. Stress levels for MS RLT tests, prescribed by the European Standard (LSL).

Low stress level
Sequence 1			Sequence 2			Sequence 3			Sequence 4			Sequence 5
Confining	Deviator		Confining	Deviator		Confining	Deviator		Confining	Deviator		Confining	Deviator
stress, σ3	stress, σd		stress, σ3	stress, σd		stress, σ3	stress, σd		stress, σ3	stress, d		stress, σ3	stress, σd
kPa	kPa		kPa	kPa		kPa	kPa		kPa	kPa		kPa	kPa
Constant	Min	Max	Constant	Min	Max	Constant	Min	Max	Constant	Min	Max	Constant	Min	Max
20	0	20	45	0	60	70	0	80	100	0	100	150	0	100
20	0	40	45	0	90	70	0	120	100	0	150	150	0	200
20	0	60	45	0	120	70	0	160	100	0	200	150	0	300
20	0	80	45	0	150	70	0	200	100	0	250	150	0	400
20	0	100	45	0	180	70	0	240	100	0	300	150	0	500
20	0	120	45	0	210	70	0	280	100	0	350	150	0	600

Figure 2. PSDs of the UGMs used for this study.

Table 3. Material properties.

Material	Type	D10 (mm)	Cu (–)	Cc (–)	Fc (%)	Gs (–)	ρdmax (ton/m^3)	wopt (%)
M1	Crushed rock	6.00	2.0	0.2	2.4	2.64	2.11	5.5
M2	Crushed rock	0.13	69.2	5.3	6.5	2.64	2.26	6.0
M3	Crushed rock	0.06	128.0	2.0	12.0	2.64	2.22	6.5
M4	Crushed rock	0.65	20.0	2.4	2.2	2.63	2.08	5.5
M5	Crushed rock	0.06	208.0	0.6	10.2	2.54	2.21	6.0
M6	Crushed rock	0.70	10.0	0.2	8.6	2.68	2.35	6.9
M7	Crushed natural gravel	0.33	25.8	0.9	3.8	2.49	2.13	7.5
M8	Crushed natural gravel	0.43	37.2	5.2	1.4	2.61	2.16	5.0

Notes: D₁₀ is the effective particle size (10% of the particles are finer than D₁₀); C_u is the uniformity coefficient; C_c is the gradation coefficient; F_c is the fine content (< 0.075mm); G_s is the specific gravity.

Table 4. Test conditions.

Material	ρd (Ton/m^3)	e (–)	w (%)	S (%)	Stress level	Samples tested
M1	2.05	0.29	1.0	9.1	HSL	2
			3.0	27.3	LSL	2
			3.0	27.3	HSL	2
			5.0	45.5	HSL	2
			7.0	63.8	HSL	2
M2	2.19	0.20	1.0	12.9	HSL	2
			3.0	38.8	HSL	2
			5.0	64.6	HSL	2
			6.5	84.0	HSL	2
M3	2.15	0.23	1.0	11.7	LSL	2
			1.0	11.7	HSL	2
			2.0	23.4	HSL	3
			3.5	40.9	HSL	2
			5.0	58.4	HSL	2
			6.0	70.1	HSL	2
M4	2.01	0.31	1.0	8.6	LSL	1
			3.5	30.0	LSL	2
			5.5	47.2	LSL	2
			6.5	55.7	LSL	2
M5	2.19	0.16	2.0	31.6	LSL	2
			4.5	71.0	LSL	3
			6.0	94.7	LSL	2
M6	2.23	0.20	2.0	26.7	LSL	2
			4.0	53.5	LSL	2
			7.0	93.6	LSL	2
M7	2.02	0.23	3.5	37.8	HSL	2
			5.5	59.4	LSL	1
			5.5	59.4	HSL	2
			7.5	81.0	HSL	2
			8.5	91.8	HSL	2
			9.2	99.4	HSL	2
M8	2.10	0.25	1.0	10.6	LSL	2
			3.5	37.2	LSL	2
			5.0	53.1	LSL	2
			7.0	74.4	LSL	2

Figure 3. Accumulation of permanent strain with the number of load cycles for M7 with w = 5.5% during MS RLT test with LSL.

Figure 4. Typical model fitting and SDR matching.

Figure 5. Measured and modelled accumulation of permanent strains for different w’s.

Table 5. Calibrated material parameters of the model.

			Model parameters (–)
Material	W (%)	S (%)	(b = 250)	R^2 (–)	SDR matching (%)
			a
M1	1.0	9	3.8	0.88	61
	3.0	27	5.2	0.94	71
	5.0	46	7.8	0.91	86
	7.0	64	8.9	0.84	89
M2	1.0	13	2.6	0.99	93
	3.0	39	4.4	0.99	89
	5.0	65	4.8	0.98	75
	6.5	84	7.6	0.84	93
M3	1.0	12	6.7	0.98	93
	2.0	23	10.7	0.93	79
	3.5	41	17.7	−1.15	86
	5.0	58	23.2	0.98	100
	6.0	70	29.0	0.90	100
M4	1.0	9	2.6	0.99	89
	3.5	30	2.6	0.93	89
	5.5	47	2.8	0.99	93
	6.5	56	3.1	0.98	71
M5	2.0	32	4.2	0.73	68
	4.5	71	4.7	0.95	82
	6.0	95	9.7	0.90	82
M6	2.0	27	4.1	0.99	82
	4.0	53	7.1	0.95	68
	7.0	94	12.6	0.97	79
M7	3.5	38	1.6	0.88	82
	5.5	59	3.8	0.97	75
	7.5	81	6.7	0.97	89
	8.5	92	7.8	0.98	75
	9.2	99	8.1	0.87	100
M8	1.0	11	1.4	0.99	93
	3.5	37	1.9	0.94	89
	5.0	53	2.9	0.97	93
	7.0	74	3.9	0.92	71

Figure 6. Parameter a as a function of w for the different materials.

Table 6. Parameters of Equation (9(9) $a=c_1(S)+c_2$(9) ).

Material		M1	M2	M3	M4	M5	M6	M7	M8
Parameters	c1	0.098	0.063	0.375	0.010	0.080	0.127	0.079	0.039
	c2	2.8	1.7	2.1	2.4	0.9	0.6	0.0	0.8
R^2		0.98	0.89	0.99	0.76	0.69	0.99	0.98	0.94

Figure 7. Measured versus predicted accumulation of permanent strain using the fitted models.

Table 7. Statistical evaluation of the quality of prediction by the models.

				R^2			SDR matching [%]
					Proposed			Proposed
			Stress level		model			model
	w	S	used for	Proposed	(moisture	MEPDG	Proposed	(moisture	MEPDG
Material	(%)	(%)	validation	model	based)	model	model	based)	model
M1	3	27	LSL	0.98	0.96	0.97	82	82	61
M3	1	12	LSL	0.98	0.97	0.89	96	96	64
M7	5.5	59	LSL	0.98	0.96	0.96	100	100	79

Figure 8. (a) Schematic of the test structure (Saevarsdottir & Erlingsson, 2014). (b) Measured vs. modelled PD in different layers.

Table 8. Model parameters for the different layers of the pavement section.

	Model parameters
	Moist		Wet
Layer	a	b	a	b
Base	2.2	60	2.5	60
Subbase (upper part)	2.5	250	2.5	250
Subbase (lower part)	4.0	250	4.0	250
Subgrade (upper part)	2.0	250	9.5	250

Figure 9. Rut development in the two test structures: ERAPave PP predictions versus HVS test data.

Table 9. Properties of the test structures.

	Structure 1				Structure 2
			Parameter	Stiffness			Parameter	Stiffness
		Thickness	a	modulus		Thickness	a	modulus
Layer	Material	(mm)	(b = 250) (–)	(MPa)	Material	(mm)	(b = 250) (–)	(MPa)
Concrete block	Permeable blocks	80	15	500	Non- permeable blocks	100	18	600
Bedding layer	2–5 mm crushed rock	30			0–4 mm crushed rock	88
Base layer	4–32 mm crushed rock	80	10	300	0–32 mm crushed rock	205	15	350
Subbase layer	4–90 mm crushed rock	685	12	200	0–90 mm crushed rock	666	15	350
Subgrade	Sand	2125	20	80	Sand	1941	20	80

Figure 10. PSDs of some additional materials tested.

Table 10. Properties and test conditions of the additional materials.

Material	Type	D10 (mm)	Cu (–)	Cc (–)	Fc (%)	Gs (–)	ρd (ton/m3)	w (%)	S (%)
M9	Crushed rock	0.14	59.3	1.8	7.1	2.72	2.18	5.7	62.6
M10	Crushed natural gravel	0.25	32.0	0.3	4.5	2.49	2.10	3.5	32.2
M11	Incinerated bottom ash	0.14	75.0	13.8	5.0	2.30	1.74	11.9	57.5
M12	Incinerated bottom ash	3.00	3.7	0.9	1.5	2.30	1.52	4.1	14.1
M13	Crushed natural gravel	3.00	5.3	1.0	1.2	2.61	1.89	3.5	21.7
M14	Crushed natural gravel	4.00	5.0	2.5	0.9	2.61	1.85	3.5	20.2
M15	Incinerated bottom ash	0.06	64.5	2.0	12.0	2.35	1.65	8.0	33.6
M16	Incinerated bottom ash	0.06	10.5	1.6	16.0	2.35	1.42	25.6	76.1

Table 11. Model parameters determined for some additional materials.

Model parameter	M9	M10	M11	M12	M13	M14	M15	M16
a	4.8	3.1	9.9	6.2	6.7	9.1	1.1	4.2
b	122	155	106	176	177	156	307	214
R^2	0.95	0.95	0.91	0.98	0.97	0.95	0.99	0.99

Table 12. Suggested range of model parameters for UGMs with d_max = 31.5 mm, DOC: 95–97% (modified Proctor method).

Parameter	Well-graded	Coarse and open graded	Fine graded
a	1–15	1–10	1–30
b	100–250	150–250	200–350

Saevarsdottir, T., & Erlingsson, S. (2014). Modelling of responses and rutting profile of a flexible pavement structure in a heavy vehicle simulator test. Road Materials and Pavement Design. https://doi.org/10.1080/14680629.2014.939698

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