Evaluation of Limitations of Some Popular CBR - UCS Based Resilient Modulus Models for Applications in the Structural Design of Pavements PDF

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Evaluation of Limitations of Some Popular CBR - UCS Based Resilient Modulus Models for Applications in the Structural Design of Pavements John N. Mukabi  resilient modulus as determined from repeated cyclic Abstract— Notwithstanding their limitations and incongruity, unconfined compression loading....

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Evaluation of Limitations of Some Popular CBR - UCS Based Resilient Modulus Models for Applications in the Structural Design of Pavements John N. Mukabi 

Abstract— Notwithstanding their limitations and incongruity, the CBR based resilient modulus models based on failure concepts are still popular in application and do dictate the recommended default values provided in practically all of the conventional Design Guidelines including the most recently developed MechanisticEmpirical Pavement Design (MEPD) Guidelines. However, given the recent developments in computer science leading to advances in the measurement of small strain stiffness using computer-aided automated systems, recently developed sophisticated models depict a certain degree or significant deviation in the resilient/elastic modulus characteristics and specified default values. Since the resilient/elastic modulus is most integral and resilient properties (including Poisson’s ratio, elastic and lateral limit strains) are of great significance in the MEPD, it is increasingly vital that the same be reviewed based on relatively sophisticated and advanced models. The necessity and importance of reviewing some of the default resilient modulus values and resilient properties that are specified in most guidelines as well as the conventional CBR-MR models is demonstrated through examples comparing characteristics and values determined from varying models. On the other hand, the versatility and rational of the TACH-MD models including the CBR-MR and UCS-MR is validated and demonstrated through various relevant examples.

Keywords—CBR, resilient modulus, model, UCS, limitations, mechanistic-empirical, structural design. I. INTRODUCTION Pavement thickness design prior to the 1986 AASHTO Design Guide was, for all practical purposes, based on experience, soil classification, and the plastic response of pavement materials to static load, e.g., Marshall stability for asphalt concrete and CBR for unbound materials. The potential for fatigue cracking of asphalt concrete and the accumulation of permanent deformations in the unbound materials in flexible pavements under essentially elastic deformation conditions were not considered. Researchers in the 1950s began using repeated load triaxial tests in the laboratory to evaluate the stiffness and other behaviour of pavement materials under conditions that more closely simulated real traffic loadings in the field [1]. Substantial pioneering contributions in this area were made by a number of Researchers in their work on the deformation characteristics and resilient modulus of compacted subgrades [1]. They found significant differences between values of initial tangent modulus measured from single-cycle unconfined compression tests as compared to values of

resilient modulus as determined from repeated cyclic unconfined compression loading. The conclusion from this work was that the behavior of soils under traffic loading should be obtained from repeated load tests whenever possible. This conclusion was substantiated by field data obtained by the California Department of Highways that showed the marked difference in pavement deflections occurring under, standing and slowly moving wheel loads. The culmination of this work was the adoption of resilient modulus testing by AASHTO in 1982 with modifications and advances made in 1991 [2]. The AASHTO T274 standard was the first modern test protocol for resilient modulus. The concept of resilient modulus was subsequently incorporated into the AASHTO Guide for Design of Pavement Structures [2]. As a result of such advances and the recent developments in computer science leading to advances in the measurement of small strain stiffness using computer-aided automated systems, recently developed sophisticated models have clearly depicted a certain degree or significant deviation in the resilient/elastic modulus characteristics and specified default values, the interpretation of which is dependent on the boundary limits, method and mode of testing as well as other geoscientific factors. Furthermore, it is indeed an appreciable fact that, since the demand on road and air transport and the reciprocal pavement structural performance requirements have become increasingly intensified, it is imperative to develop advanced and sophisticated methods of design that can simulate, more precisely, the prevalent dynamic changes. In [3] for example, a new mechanistic-empirically derived thickness-modulus ratio theory is introduced and applied in developing mechanistic model equations for uniquely determining the optimal layer and full-depth pavement structural thicknesses required, considering changes in subgrade/foundation stiffness, geomaterial/ individual layer stiffness/properties, loading factors and environmental conditions. II. REVIEW OF POPULAR CBR – UCS - MR MODELS A. Models Widely Applied by Agencies A1. Introduction of models and characteristic results It is indeed common knowledge that the California Bearing Ratio (CBR) is not a fundamental material property and thus is

John N. Mukabi is with the R&D/Design Department of Kensetsu Kaihatsu Consultants (phone: +254-716-228318; e-mail: eng.mukabi@ gmail.com). Academia.edu E-Publication Pre-Print

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unsuitable for direct use in mechanistic and mechanistic-empirical design procedures. However, it is a relatively easy and inexpensive test to perform with a long history in pavement design. Consequently, it continues to be used in practice, including the Mechanistic-Empirical Pavement Design Guide (MEPDG). Developing reliable models that can correlate this parameter to elastic/resilient modulus is therefore of paramount importance. The various models that correlate CBR to the resilient modulus − �� introduced in this paper have been developed by various Researchers and adopted by most Highway Agencies worldwide ([4], [5], [6] & [7]). A comparison of the ~ �� correlation models is presented Figures most popular 1a ~ 1g for various pavement layer geomaterials and CBR Boundary Limits (BL). The most popular ~ �� correlation models are introduced in Equations 1 ~ 7, whilst a comparison of the corresponding characteristic curves are presented Figures 1a ~ 1g, depicted for varying pavement layers and bearing strength ~ resilient modulus BLs.

�� =

� �

��

(1)

U.S. Army Corps of Engineers (After Green and Hall, 1975) �� = , .

.

.

��

� �

�� =

.

.

��

� �

.

��

� �

�� =

.

.

��

(4)

�� =

(6)

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− .

{ . .

.

<

.

−

< .

.

��

+ −

×

.

��

�� }

� − . � + � < . �� � . � . �� + .

(8) % (9) (10a) (10b) (11)

(12a) (12b) (13)

Comparison of Most Popular CBR-MR Agency Models

40000

AASHTO/AAI

35000

US Army Corps

30000

CSIR

25000

TRRL/MEPD/IAN GDOT

20000

KRDM TACH-MD

15000 10000

5000 0 0

500

1000

1500

2000

Figure 1a Comparison of popular Agency adopted models correlating CBR and resilient modulus, �� @ wide range of CBR levels to 2000%

35000

Comparison of Most Popular CBR-MR Agency Models AASHTO/AAI

US Army Corps

30000

CSIR

25000

TRRL/MEPD/IAN GDOT

20000 15000

KRDM TACH-MD

10000 5000 0 1000

1200

1400

1600

1800

2000

CBR (%)

Kenya Road Design Manual (KRDM) �� = . . ��

.

�=− .

40000

�� =

� �

�

�� � = . � �� �� =

��

+ %

(3)

Georgia Department of Transportation �� = .

=

.

− .

CBR (%)

Transportation and Road Research Laboratory (TRRL)/MEPD/IAN (Powell et al., 1984) �� = , . .

�� � = . �� � =

(2)

South African Council in Scientific and Industrial Research (CSIR) �� = , .

�� =

Resilient Modulus, MR (MPa)

�� = .

�� = . .

Resilient Modulus, MR (MPa)

AASHTO/AAI (After Shell, Heukelom and Klomp, 1972)

TACH-MD CBR-UCS-� -MR Models

+

(7)

Figure 1b Comparison of popular Agency adopted models correlating CBR and resilient modulus, �� for extremely stiff and concrete base course materials Page 2

Comparison of Most Popular CBR-MR Agency Models 500 ≤ CBR ≤ 1000%

AASHTO/AAI

AASHTO/AAI

20000

US Army Corps CSIR

15000

TRRL/MEPD/IAN GDOT

10000

KRDM TACH-MD

5000

0 500

600

700

800

900

CSIR

400

GDOT

300

TACH-MD

200 100

KRDM TACH-MD

4000 2000 0 200

300

400

500

CBR (%)

Resilient Modulus, MR (MPa)

CSIR TRRL/MEPD/IAN

1000

GDOT

800

KRDM TACH-MD

600

CSIR

400

TRRL/MEPD/IAN

GDOT

300

KRDM TACH-MD

200 100 0 0

5

10

15

20

Notes: AASHTO: American Association of State Highway and Transportation Officials; AAI: American Asphalt Institute; CSIR: Council of Scientific and Industrial Research, South Africa; TRRL: Transport & Road Research Laboratory, UK; MEPDG: MechanisticEmpirical Pavement Design Guide (AASHTO/NCHRP, USA); IAN: Interim Advisory Note, UK; GDOT: Georgia Department Of Transportation; KRDM: Kenya Roads Design Manual; TACH-MD: Recently Proposed Mechanistic-Empirical Methods of Design [3].

50 ≤ CBR ≤ 100%

US Army Corps

1200

US Army Corps

500

Figure 1g Comparison of popular Agency adopted models correlating CBR and resilient modulus, �� @ low stiffness Subbase and low ~ high stiffness Subgrade levels

Comparison of Most Popular CBR-MR Agency Models AASHTO/AAI

50

CBR (%)

Figure 1d Comparison of popular Agency adopted models correlating CBR and resilient modulus, �� for stiff and lean concrete base/subbase course materials 1400

40

AASHTO/AAI

Resilient Modulus, MR (MPa)

Resilient Modulus, MR (MPa)

GDOT

100

30

Comparison of Most Popular CBR-MR Agency Models

600

100 ≤ CBR ≤ 500%

TRRL/MEPD/IAN

6000

20

Figure 1f Comparison of popular Agency adopted models correlating CBR and resilient modulus, �� @ low ~ medium stiffness Subbase and high stiffness Subgrade levels

CSIR

8000

10

CBR (%)

US Army Corps

10000

KRDM

0

Comparison of Most Popular CBR-MR Agency Models

12000

TRRL/MEPD/IAN

0

1000

Figure 1c Comparison of popular Agency adopted models correlating CBR and resilient modulus, �� for very stiff and concrete base course materials AASHTO/AAI

US Army Corps

500

CBR (%)

14000

Comparison of Most Popular CBR-MR Agency Models

600

Resilient Modulus, MR (MPa)

Resilient Modulus, MR (MPa)

25000

400

The significant differences in the various models can be clearly noted.

200 0 50

60

70

80

90

CBR (%) Figure 1e Comparison of popular Agency adopted models correlating CBR and resilient modulus, �� @ Subbase and relatively stiff Subgrade CBR levels Academia.edu E-Publication Pre-Print

100

A2. Evaluation of characteristics within the low ~ moderate range stiffness (untreated/partially treated subbase/subgrade) The characteristics of the various models are evaluated in consideration to the low ~ moderate range stiffness exhibited Page 3

UCS, qu (MPa)

Regressional Analysis of UCS vs. CBR Relations mostly by untreated/unbound and partially treated subbase and Proposed by Some Researchers & Agencies 1.4 subgrade geomaterials. Subgrade It can be noted that: i) most models are incongruent; the 1.2 UCS = 0.031CBR Kleyn (1975)/InDOT/CSIR proposed TACH-MD model shows closer agreement with the 1.0 McElvaney & Djatrika TRRL/MEPDG and CSIR at lower CBR values; ii) a UCS = 0.0242CBR (1991) Patel M.A & Patel H.S 0.8 comparison of the results particularly in Figures 1f and 1g (2012) TACH-MD: Mukabi (2004) UCS = 0.0245CBR clearly indicates that, except for the AASHTO/AAI, the US 0.6 IDOT UCS = 0.0164CBR Army of Corps Engineers (USACE) and the TACH-MD 0.4 models, the characteristic curves of the other models tend to a 0.2 residual state and therefore cannot determine high stiffness UCS = 0.0205CBR values typically specified for base and subbase layers; as a 0.0 consequence they are essentially limited in application to low 0 10 20 30 40 50 stiffness subbase and typical subgrade resilient moduli values; CBR (%) iii) it can be derived from Figure 1g that, at typically specified Figure 2 UCS – CBR correlation models depicting significant subgrade CBR-MR values, a fairly good agreement exists incongruity and diverse deviation within low ~ moderate range of between all the models except for USACE model which bearing and compressive strengths overestimates the stiffness by an average factor of 3 (three) over the whole range [{ % �� The results in Table 1 show that, except for the TACH-MD and �� }]; iv) resilient modulus values determined from the IDOT models, the UCS values determined on the basis of the TACH-MD model in Figure 1g can be deduced to be rest of the models are largely inconsistent with the specified representative of the average values of the rest of the models CBR and counterpart UCS values. (except the USACE); v) although the KRDM model agrees quite well with the rest of the popularly adopted models A3. Evaluation of limitations within the high range stiffness including the TACH-MD (but excluding the USACE) within (stabilized base/subbase and PCC base course) the range depicted in Figure 1g, it drastically deviates exponentially @ > % �� > �� basically Under this section, the limitations of the models popularly implying that the model was developed and is specifically adopted by the various Agencies are evaluated in limited to the determination of subgrade stiffness of up to Class consideration to the high range stiffness exhibited mostly by S5 as per KRDM specification: well stabilized base/subbase and Portland Cement Concrete [{ % �� (PCC) base course geomaterials/layers. �� ℎ ℎ − It can be can clearly be noted from Figure 3a and 3b that: ⁄ � } � = i) except for the IDOT and TACH-MD models, extreme . % �� = �� ]; inconsistency is exhibited in the UCS – CBR correlation From the foregoing observations, it can be inferred that most depicted by the other models; ii) based on the observation in i) CBR based �� models were developed for and are limited to it can be considered that these models are limited to the range the determination of subgrade resilient modulus. of low strength/stiffness values; the results show that very high Further verification of this inference is made in Table 1 and value of CBR would be required in correspondence to UCS Figure 2. Table 1 is a summary of UCS and CBR values that that is characteristic of long-term cured cement stabilized base are normally specified by transportation Agencies worldwide materials, lean concrete and high strength concrete. for subgrade, subbase and base course pavement layers. Figure 2 makes a comparison of some of the UCS-CBR models. Regressional Analysis of 60 0.8583

0.8583

0.7654

Pavement Layer

Subgrade

Subbase

UCS Computed from Specified CBR Values (Mpa) Typical UCS McElvaney Typical CBR Kleyn Patel M.A TACH-MD Values and IDOT Values (1975)/ & Patel H.S Mukabi Specified Djatrika (2002) Specified (%) InDOT/CSIR (2012) (2004) (MPa) (1991)

Min.

8

Aver.

19

>

60

Min.

60

Aver.

80

>

100

>

160

0.3 ~ 1.5

1.5 ~ 3

0.098

0.101

0.146

0.194

0.248

0.205

0.195

0.307

0.460

0.589

0.551

0.471

0.823

1.452

1.860

0.551

0.471

0.823

1.452

1.860

0.705

0.587

1.053

1.936

2.480

0.854

0.696

1.276

2.420

3.100

1.278

0.997

1.910

3.872

4.960

50 UCS = 0.0242CBR UCS = 0.0245CBR0.8583

40

UCS = 0.0164CBR0.8583

30 Kleyn (1975)/InDOT/CSIR

20

McElvaney & Djatrika (1991) Patel M.A & Patel H.S (2012) TACH-MD: Mukabi (2004)

10 UCS = 0.0205CBR0.7654

3~6

Notes: InDOT: Indiana Department of Transportation, USA; CSIR: Council of Scientific & Industrial Research, South Africa; IDOT: Illinois Department of Transportation, USA. Academia.edu E-Publication Pre-Print

IDOT

0 0

Base Course

UCS vs. CBR Relations Proposed by Some Researchers & Agencies

UCS = 0.031CBR

UCS, qu (MPa)

Table 1 Comparison of specified and model computed UCS values for varying pavement layers

2000

4000 CBR (%)

6000

8000

Figure 3a UCS – CBR correlation models depicting significant incongruity and diverse deviation within a very wide range of bearing and compressive strengths

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AustROADS model drastically deviates from the others after > �� indicating that the model may have been developed to specifically cement treated/cement stabilized base course materials; iv) the measured values mostly locate between the ACI and TACH-MD models at intermediate and higher stiffness ranges with the TACH-MD models exhibiting much better agreement; v) the TACH-MD model shows consistent agreement over the whole w...