Qualitative comparision - Analyses of semi-rigid pavement design methods and a proposal for Vietnam’s

công nghệ lần thứ XXII Trường Đại học Giao thông vận tải 
-747- 
reduces the strengths of base and subgrade materials and makes material of asphalt 
surface layer(s) surrounding the crakings separated from each other. Reflective 
crackings with remarkable width will become pavement joints, which cause stress 
concentration phenomenon in semi-rigid pavements [3]. Reflective cracking 
failure can be eliminated by increasing the thickness of flexible surface layer, or 
installing aggregate base layer or geo-fabric material on rigid subbase layer but 
under flexible surface one [1]. 
2. SEMI-RIGID PAVEMENT DESIGN METHODS 
Until now, a number of methods have been used by different institutions to design 
semi-rigid pavements. Before 1960, almost all the institutions determined the thickness 
of flexible surface layer when basing on professional experience and assessment. Since 
1960, employing non-demolishing tests to measure pavements’ deflection has been 
being acceptable and more and more semi-rigid pavement design methods (SRPDM) 
based on pavement deflection measurements have been developed. Thus, nearly every 
single institution has got its own SRPDM. 
1. AASHTO 1993 SRPDM [3][12] 
[12] can be used to design semi-rigid pavements in two situations: (I) flexible 
surface layer on cement-treated base layer and (II) AC surface layer on PCC base layer 
being possibly jointed PCC or continuously steel-reinforced PCC layer. 
The key performance of this SRPDM when flexible surface layer placed on 
cement-treated base layer is to choose layer coefficient a2 which should be fit for 
determination of structural factor SN: 
 (1) 
where a1, a2 and a3 are layer coefficients, m2 and m3 are drainage coefficients, 
and D1, D2 and D3 are the thicknesses of pavement layers from the top to the bottom of 
pavement structure including flexible surface, rigid base and the subgrade, 
respectively. Specifically, layer coefficient a2 is determined through chord modulus Ec 
(MPa) in accordance with the research results of Richardson in 1996: 
 (2) 
 (3) 
where qu is unconfined compressive strength (MPa). 
In the second alternative when AC surface layer is on PCC base layer, [12] guide 
designers to apply the formulas (4) to (6): 
 (4) 
 (5) 
 (6) 
where: 
DOL = required thickness of AC overlay; 
A = factor to convert PCC thickness deficiency to AC overlay thickness; 
Df = PCC slab thickness to carry future traffic (in); 
Deff = effective thickness of existing PCC slab (in); 
Hội nghị Khoa học công nghệ lần thứ XXII Trường Đại học Giao thông vận tải 
-748- 
Fjc, Fdur, Ffat = adjustment factors for joints and cracks, durability, and fatigue. When 
semi-rigid pavement structures are newly constructed, these factors are all valued at 1 
because both rigid base and flexible surface layers have not been deteriorated; and 
D = original PCC slab thickness. 
2. US Army and Air Force SRPDM [3] 
In 2004, US Department of Defence had developed a Pavement Design Manual for 
Roads, Streets, and Open Storage Areas when basing on asphalt’s deformation 
standard: 
 (7) 
 (8) 
 (9) 
where: 
AC = allowable strain at the bottom of asphalt layer; and 
E = elastic modulus of AC (psi). 
3. Illinois Department of Transportation SRPDM [3] 
In 2002, the Illinois Department of Transportation had issued a design manual 
when hot-mixed asphalt (HMA) overlay is on PCC base course. Pursuant to this 
method, HMA overlay thickness calculated by using formula (10) should be compared 
to minimum required thickness values corresponding to four various ranges of 
structural factor SNc regulated by the Department: 
 (10) 
where: 
D0 = thickness of HMA layer for new composite pavement (in); 
SNc = structural number of composite pavement (obtained from a nomograph in their 
guidelines); and 
DB = thickness of new PCC base course (in). 
4. UK SRPDM [3] 
The Highways Agency in the UK published two output parameters to design semi-
rigid pavements. The first one which is rigid base thickness is obtained by using a 
nomograph when resulted from minimum compressive strength at 7th-old-day of base 
material and the foundation stiffness (modulus of resilience). The second one which is 
flexible overlay thickness is determined corresponding to accumulated traffic volume: 
 (11) 
where Ha is asphalt layer thickness (mm) when 50MSA < N < 80MSA and N is 
accumulated traffic volume (MSA is noted as one million design axles). 
5. Danish Road Institute SRPDM [3] 
The Institute’s research is focused on fatigue failure of the rigid base, in which a 
parameter showing the failure is tensile strain at the bottom of rigid base. The design 
standard resulted from formula (12) should be used to prevent semi-rigid pavement 
structures from fatigue failure at 75 percent reliability: 
 (12) 
Hội nghị Khoa học công nghệ lần thứ XXII Trường Đại học Giao thông vận tải 
-749- 
where  is maximum strain at the bottom of cement-treated base course,  micro-strain 
(10-6 strain) and N number of load repetitions to failure. 
6. Austroads SRPDM [2] 
In pursuant to [2], the minimum lifespan of semi-rigid pavements is 50 years 
under conditions when the overlay must be renewed periodically during their operation 
process to secure pavement friction level and driving qualities. Thus, flexible surface 
layer, rigid base layer and the subgrade are computed by using formular (13) to (15) so 
that horizontal tensile strains within flexible overlay and rigid base could be always 
less than 33 and 36, respectively. 
 (13) 
 (14) 
 (15) 
where: 
N = equivalent standard axles (ESA); 
RF = reliability Factor; 
VB = volume of bitumen (%); 
E = asphalt layer stiffness (MPa); 
 = micro horizontal tensile strain in asphalt fatigue determination (13) and cemented 
materials fatigue calculation (14) or micro vertical compressive strain in permanent 
subgrade deformation computation; and 
 = 1.1 = 12.0 and = 1.6. 
7. Spanish SRPDM [4] 
Pursuing this method, semi-rigid pavement structures must be design to make sure 
that fatigue cracking phenomenon will not happen within rigid base layer by 
controlling maximum tensile strain at this layer not greater than 36 according to the 
research carried out by Parmeggiani [2] and constraining maximum tensile stress at the 
same layer defined in fatigue model proposed by Eduardo Torroja Institute (16) not 
greater than 40% of the long-term flexural strength RF,LT. 
 (16) 
where: 
t = maximum tensile stress supported by the material; 
RF,LT = long-term flexural strength; 
N = number of load repetitions; 
 = calibration factor whose value is typically assumed to be 0.8; and 
a = fitting parameter whose value is typically assumed to be 0.065. 
8. US mechanistic-empirical SRPDM [5] 
Among input data of rigid base layer design in accordance with US mechanistic-
empirical SRPDM, the maximum dry unit weight is obtained through standard Proctor 
test, the optimum moisture content is determined according to ASTM D698, the 
resilient modulus in compression is attained by implementing AASHTO T307 test, and 
Hội nghị Khoa học công nghệ lần thứ XXII Trường Đại học Giao thông vận tải 
-750- 
the resilient modulus in tension is resulted from the average recoverable deformation 
and average load of the last 5 loading cycles (17) when every loading pulse of electro-
hydraulic test system has a duration of 0.1 second and a rest period of 0.9 second. 
 (17) 
where: 
Mrt = resilient modulus in tension of rigid base layer; 
t = thickness of the specimen; 
P = repeated load when electro-hydraulic test system is used to load the specimen; 
HT = total recoverable horizontal deformation; 
D = diameter of specimen; 
 = Poisson’s ratio whose value ranges from 0.1 to 0.3; and 
Dg = distance between LVDTs measuring horizontal deformations. 
Among input data of flexible surface layer, [5] requests that resilient modulus of 
AC is calculated pursuant to the proposal of Navratnarajah: 
 (18) 
where: 
Mra = resilient modulus AC layer; 
T = temperature (i.e., 210C); 
S = stress ratio; 
Va = air void percentage; and 
Vb = effective binder content. 
Output data of US mechanistic-empirical SRPDM are maximum tensile strain at 
the bottom of rigid base (19) and fatigue life of AC (20). The maximum allowable 
tensile strain is determined by conducting four-point beam fatigue test with the number 
of allowable loading repetitions can be forecasted through Prozzi & Aguitar-Moya 
Model. The fatigue life of asphalt surface layer which expresses overall pavement 
performance efficiency is evaluated by using a fatigue cracking model. 
 (19) 
 (20) 
 (21) 
 (22) 
 (23) 
where: 
Nf = number of cycles to fatigue failure; 
t = tensile strain at bottom of rigid base layer; 
m = maximum allowable strain at bottom of beam from flexural strength tests; 
ta = maximum tensile strain below the AC layer; 
Hội nghị Khoa học công nghệ lần thứ XXII Trường Đại học Giao thông vận tải 
-751- 
hac = thickness of AC layer; 
Mra = resilient modulus of asphalt concrete layer; 
Vb = effective binder; and 
Va = air void percentage. 
9. Vietnam’s SRPDM [6] 
Thickness calculation of PCC base layer below AC overlay mentioned in [6] is the 
first guidance in semi-rigid pavement design of Vietnam. Pursuant to [6], equivalent 
thickness of PCC base layer htđ (cm) is determined by applying slab on elastic 
foundation theory and thickness of AC overlay hbtn (cm) is proposed through economic 
principles: 
 (24) 
where: Ebx and Ebtn are elastic modulus of PCC and AC, respectively (daN/cm2). 
3. ANALYSES AND COMPARISION 
Synthetically, SRPDMs are classified into three groups: Effective thickness 
method group, deflection one and mechanistic-empirical one [1]. Among methods 
presented in this article, 2.1(I) is empirical method using linear multi-variable 
regression function applied into the situations when flexible surface layer is on 
cement-treated base one and Ec and a2 are repetitively computed via linear univariable 
regression function. 2.1(II) is an effective thickness method when output data of 
pavement structures including AC overlay on PCC base layer are repetitively 
computed via linear multi-variable regression function. 2.2 had been developed in 
order to secure fatigue resistance of flexible surface layer by establishing non-linear 
multi-variable functions and its calculations must be repetitive. 2.3 is an empirical 
effective thickness method because of its random and repetitive calculation, which is 
proceeded from 2.1(II). 2.4 is an empirical approach when rigid base layer is 
determined in order to secure fatigue resistance of flexible overlay. Danish Road 
Institute (2.5) did the research on semi-rigid pavement behavior and developed a 
mechanistic semi-rigid pavement design method by conducting a full-scale test on six 
real highway segments (every two segments had a different pavement structure) and 
choosing a generalized incremental-recursive model based on tensile strain at the 
bottom of the cement-treated base layer in order to verify the pavement deterioration 
model (Thogersen et al., 2004). Moreover, comparison between the research results 
and operational conditions of constructed semi-rigid pavements that had been in 
service for more than 20 years show that the proposed deterioration model was 
accurate. According 2.6 method, semi-rigid pavements are proposed through 
mechanistic analyses to make sure that fatigue crackings will not occur in flexible 
overlay (13), rigid base layer will always work in pre-cracking stage during design 
span (14), and permanent deformation will not happen within the subgrade (15). In 2.6 
contents, wheel-tracking which is one of primary deterioration modes of semi-rigid 
pavements was mentioned but not modelled through mechanistic analyses. However, 
wheel-tracking resistant properties of flexible layer(s) are possibly attained by using 
this method due to preventive fatigue cracking design standard. In accordance with 2.7 
guidance, semi-rigid pavement behavior being demonstrated via strain and stress 
Hội nghị Khoa học công nghệ lần thứ XXII Trường Đại học Giao thông vận tải 
-752- 
values is analyzed by applying layered theory in which all materials were assumed to 
be homogeneous, isotropic and linearly elastic and characterized bye their elastic 
modulus and Poisson’s ratio. 
The basis of empirical semi-rigid pavement design methods is tests measuring 
factual working strengths of pavements and monitoring data base during the 
pavements’ operational process. Mechanistic-empirical semi-rigid pavement design 
approach also includes behavioral calculation of the pavements under vehicular 
impacts causing pavements’ failure and accumulated fatigue deterioration, specifically 
calculation of strains and stresses causing structural working capacity decline with 
respect to time. On mechanistic-empirical approach (2.8), elastic multi-layer theory 
was employed to attain structural behavior of semi-rigid pavements expressing via 
stresses, strains and deflection. According to 2.8, semi-rigid pavements are considered 
as elastic multi-layer system with assumptions that all their layers are linear elastics 
below circular surface loading distribution area and vehicular loading is analyzed in 
axis-symmetric space causing stresses, strains and vertical deflections at specified 
locations within pavement structures. Within this design approach, working properties 
of semi-rigid pavements are assumed to be taken as default values corresponding to a 
chosen design level of flexible pavements. 
Being compared with empirical method, specifically method of [12], mechanistic-
empirical allows using actual load distributions so semi-rigid pavement behavior is 
assessed under wheel load of 40 kN on the surface layer. A tire pressure of 120 psi 
(826.8 kPa) is assumed to be the contact pressure applied to a circular area on the 
surface area. Nevertheless, mechanistic-empirical method needs more input data than 
empirical one such as annual average daily traffic distribution, design axle loading 
distribution coefficient, traffic lane width, operation speed of traffic flow, tire pressure, 
gravitational center of vehicular wheel, and standard deviation of traffic flow. Poisson’ 
ratio, Atterberg limits, maximum unit dry weight, optimal moisture content, failure 
modulus and unit weight must be also determined as input data of rigid base 
calculation. The properties of AC including binder type and content, aggregate curve 
of material mixture, unit weight of material mixture, Poisson’s ratio and dynamic 
modulus are also determined to compute flexible overlay. 
The current SRPDM of Vietnam (2.9) is effective thickness method in which rigid 
base layer thickness is calculated with respect to non-linear relation with elastic 
modulus and flexible surface layer thickness is determined through professional 
experience of designers. Pursuant to 2.9, however, generalized elastic modulus on the 
surface of rigid base layer is determined by referring to the nomograph established for 
dual-layer system of flexible pavements regulated in [7] and this nomograph is kept 
being used in [8]. This regulation is not conformable because factual working 
characteristics of semi-rigid pavements are different from flexible pavements’ ones. In 
2001, semi-rigid pavement design was mentioned in Vietnam’s [11] but design 
proposals within these specifications belong to American Association of State 
Highway and Transportation Officials while empirical data of semi-rigid pavements in 
Vietnam are still restricted. In addition, there have been no calculation and design 
Hội nghị Khoa học công nghệ lần thứ XXII Trường Đại học Giao thông vận tải 
-753- 
contents to prevent reflective crackings in [11] but some relating cautions or notes 
have been mentioned [10]. 
In 2008, [3] carried out semi-rigid pavement calculations and designs by using 
methods in 2.1 to 2.5 with the same input data set to obtain an output data set as shown 
in Figure 2. Via statistical evidence in Figure 2, it is visual to reveal that methods 2.3 
and 2.4 have got similar results, methods 2.2 and 2.5 give lowest thickness of AC 
layer, and only method 2.5 propose an aggregate base layer. 
Figure 2: Calculation and design results of semi-rigid pavements pursuant to [3] 
4. CONCLUSIONS 
Semi-rigid pavements include flexible overlay on rigid base layer(s) have been 
being used worldwide but their mechanistic analyses are the most difficult because 
they involves in two different material types. Theoretically, it is possible to apply 
finite element method when using slab emements if AC is upper layer and PCC lower 
one. However, it has been very difficult to model the lower layer because of this rigid 
base layer’s presence of crackings. [1] supposes that it is likely to apply slab theory 
into stress determination within bending slabs under an assumption that AC surface 
layer adhered to rigid base layer which is the mainly loading resistance component. On 
the other hand, semi-rigid pavements will be able to be analyzed by applying elastic 
layerd theory if stress adjustment factors are determined when loading position is at 
the slab edge and corner. [1] also asserts that it will be possible to apply layered theory 
when loading position at the the slab edge but both layered and slab theories when slab 
center. However, semi-rigid pavements will be suitable for new freeway, expressway, 
runway and taxiway construction and widely appropriate for existing PCC highways in 
Vietnam owing to the combination of different merits of their flexible overlay and 
rigid base layer. But semi-rigid pavement should be researched when pursuing 
mechanistic-empirical approach to apply effectively into Vietnam because of various 
climate, material, economic and technological conditions of different countries and 
Hội nghị Khoa học công nghệ lần thứ XXII Trường Đại học Giao thông vận tải 
-754- 
working charasteristics of the structures. 
References 
[1]. Yang H. Huang (2004): Pavement Analysis and Design, 2nd Edition, Pearson 
Education Inc. 
[2]. Giovanni Parmeggiani (2007): Three dimensional structural design of asphalt 
pavments, AAPA Pavements Industry Conference. 
[3]. Virginia Transportation Research Council (2008): Composite pavement systems 
- Synthesis of design and construction practices. 
[4]. David Hernando & Miguel A. del Val (2016): Guidelines for the design of 
semi-rigid long-life pavements, International Journal of Pavement Research and 
Technology 9. 
[5]. Pranshoo Solanki & Musharraf Zaman (2017): Design of semi-rigid type of 
flexible pavement, International Journal of Pavement Research and Technology 
10. 
[6]. Vietnam’s Ministry of Transport (1995): 22TCN 223-95 Rigid highway 
pavement design standards. 
[7]. Vietnam’s Ministry of Transport (1993): 22TCN 211-93 Specifications for 
flexible pavement design. 
[8]. Vietnam’s Ministry of Transport (2006): 22TCN 211-06 Standards and 
Specifications for flexible pavement design. 
[9]. Prof. Dr. Phạm Huy Khang & MSc. Trần Thị Thuý (2017): Some noticeable 
issues of rigid and semi-rigid base utilization in highway and airport pavement 
structures in Vietnam, Journal of Transportation 07/2017. 
[10]. MSc. Nguyễn Văn Thành & MSc. Lưu Ngọc Lâm (2013): Semi-rigid pavement 
structures and their applicable orientation in Vietnam, Journal of Transportation 
09/2013. 
[11]. Vietnam’s Ministry of Transport (2001): 22TCN 274-01 Specifications for 
flexible pavement design. 
[12]. American Association Of State Highway and Transportation Officials (1993): 
AASHTO Guide for Design of Pavement Structures.