The literature review presented in this chapter highlights several research issues that need to be addressed in the determination of the composite k value of a rigid pavement system and the layer moduli of a multi-layer flexible pavement system.
a. The use of plate load test to determine composite k value is possible and has been conducted by PCA and AASHTO using full-scale tests. However, this approach has obvious limitations in practical applications, such as the high cost and the long time required. Because of these two reasons, this test is seldom conducted in actual construction projects. For in-service roads, this test also
requires the surface layer of the road to be removed before the test can be performed.
The determination of resilient moduli by means of laboratory or field tests becomes more popular as another method to characterize the layer moduli.
Although this procedure also can be used to determine the subgrade modulus as another alternative to the conventional plate load test, the relationship between k value and the resilient modulus is still difficult to be established due to the difference of the characteristics of the parameters measured.
NDT methods have become a logical choice in the determination of pavement layer moduli today. This method can be used for either new road construction or in-service pavements. The selection of the method to evaluate nondestructive test result is an important decision. There exist many nondestructive evaluation methods based on backcalculation analysis. However, because of the complexity of the characteristic of pavement systems to be modeled, the performance of the backcalculation methods could vary considerably. A careful analysis is necessary to identify the best method that can produce backcalculated layer moduli which matches closely with measured layer moduli.
b. The AASHTO and PCA methods have simplified the process of determination of composite k value for easy application in pavement design. However, the recommended charts or tables of values are not accurate enough for the purpose of condition evaluation of pavement sections. It needs an analytical method that can give better accuracy, offer important information such as the factor of safety, load transmission and its mechanism; and take into account the interaction of subgrade, subbase and pavement slab.
c. The regression method is also not an ideal backcalculation approach because the method lacks theoretical mechanistic basis. It depends on the correlation among various problem parameters. A regression model is only applicable for environment in which the model is developed. It does not provide any insight into the mechanism involved.
In summary, there is a need to develop an analytical procedure with sound theoretical basis for determining the layer moduli for the design of new pavements as well as the rehabilitation design of existing in-service pavements. This is in line with the latest research trend towards establishing a mechanistic design for new and rehabilitated pavements. Nondestructive evaluation techniques based on FWD tests and backcalculation analysis appear to be the most promising approach in this regard.
This is the approach to be adopted in the present research to establish a theoretically sound analytical procedure for the determination of the composite k value of a concrete pavement with a subbase layer, and the determination of layered moduli of a flexible pavement system.
Table 2.1: Effect of Untreated Subbase on k Values (PCA, 1984) Subbase k value, MN/m3 (pci) Subgrade
k value, MN/m3 (pci)
0.102 m (4 in.)
0.152 m (6 in.)
0.203 m (8 in.)
0.254 m (10 in.) 13.5 (50) 17.6 (65) 20.3 (75) 23.0 (85) 29.7 (110)
27 (100) 35.1 (130) 37.8 (140) 43.2 (160) 51.3 (190) 54 (200) 59.4 (220) 62.1 (230) 72.9 (270) 86.4 (320) 81 (300) 86.4 (320) 89.1 (330) 99.9 (370) 116.1 (430)
Table 2.2: Design k Values for Cement Treated Subbases (PCA, 1984) Subbase k value, MN/m3 (pci)
Subgrade k value, MN/m3 (pci)
0.102 m (4 in.)
0.152 m (6 in.)
0.203 m (8 in.)
0.254 m (10 in.) 13.5 (50) 45.9 (170) 62.1 (230) 83.7 (310) 105.3 (390)
27 (100) 75.6 (280) 108.0 (400) 140.4 (520) 172.8 (640) 54 (200) 126.9 (470) 172.8 (640) 224.1 (830) -
Table 2.3: Values for coefficient A, B, C and D in Equation (2-8) (Ioannides et al., 1989)
AREA A B C D
A7 60 289.708 -0.698 2.566
A5 48 158.40 -0.476 2.220
A4 36 1812.279 -2.559 4.387
A3 24 662.272 -2.122 4.001
Remark: A7, A5, A4 and A3 are AREA parameter with 7, 5, 4 and 3 sensor configurations, respectively.
Table 2.4: Values for coefficient x, y and z in Equation (2-10) (Ioannides et al., 1989) Radial Distance
(m / in.)
x y z
0 / 0 0.12450 0.14707 0.07565
0.203 / 8 0.12323 0.46911 0.07209
0.305 / 12 0.12188 0.79432 0.07074
0.457 / 18 0.11933 1.38363 0.06909
0.610 / 24 0.11634 2.06115 0.06775
0.914 / 36 0.10960 3.62187 0.06568
1.524 / 60 0.09521 7.41241 0.06255
Figure 2.1: Representation of Dense Liquid Foundation p
w k
Figure 2.2: Chart for Estimating Composite k value Based on 1972 AASHTO Interim Guide (AASHTO 1972)
Figure 2.3: Chart for Estimating Composite k value Based on 1993 AASHTO Guide (AASHTO, 1993)
Figure 2.4: Approximate Relationship between k values and Other Soil Properties (PCA, 1966)
Figure 2.5: Approximate Relationship between MR and Other Soil Properties (Van Til et al., 1972)
(a) Subgrade as the layer of interest in calculation
(b) Surface layer as the layer of interest in calculation
Figure 2.6: Representation of multi-layer pavement structure as equivalent two-layer system
Surface layer E1, h1, à1 Base layer E2, h2, à2
Load P
Ee, àe, ht
Subbase layer E3, h3, à3 Subgrade Es, às
Equivalent layer
Subgrade Es, às Load P
(Actual Pavement) (Equivalent Pavement)
Surface layer E1, h1, à1 Base layer E2, h2, à2
Load P
Ee, àe Subbase layer E3, h3, à3
Subgrade Es, às
Equivalent layer Load P
(Actual Pavement) (Equivalent Pavement)
Surface layer E1, h1, à1
CHAPTER 3
EVALUATION OF BACKCALCULATION ALGORITHMS FOR RIGID PAVEMENT SYSTEM