 Open Access
 Total Downloads : 132
 Authors : John Ngaya Mukabi
 Paper ID : IJERTV5IS090124
 Volume & Issue : Volume 05, Issue 09 (September 2016)
 Published (First Online): 06092016
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Unique Analytical Models for Deriving Fundamental QuasiMechanistic Design Parameters for Highway and Airport Pavements
John Ngaya Mukabi
R&D/Design Dept.
Kensetsu Kaihatsu Consulting Engineers Ltd.
Nairobi, Kenya
Abstract Characterization of practically all engineering materials adopted in design and construction is based on their intrinsic elastic properties, which are mathematically defined by elastic/resilient/shear moduli, Poissons ratio and the stresses and strains that are prevalent within the linear elastic recoverable zone. Nevertheless, determination of these parameters of fundamental importance in not only design, but also simulation modelling and structural performance prediction of civil engineering structures, based on laboratory and insitu mechanical testing, has been and continues to be one of the foremost challenges to Engineers. Furthermore, an even greater challenge is the meticulous quantitative determination of the elastic stress and strain limits which provide the extrapolative platform for subsequent deformation characteristics based on concepts defined within the Kinematic Hardening Soil Yield Surface (KHSYS) context.
This Study takes advantage of the prodigious advances made in computer science, modelling and the research and methods of laboratory small strain testing to propose TACHMD universal analytical models that have been predominantly developed on the basis of these advances. The proposed analytical models provide considerable solutions to the aforementioned challenges and are versatile in application with appreciably high degree confidence levels. Case examples of applications of the proposed models for characterization of various types of geomaterials, generation of performancebased value engineering designs, as well as development of special/particular specifications and construction QCA procedures are also introduced. It is also derived that appropriate application of the proposed analytical models can be useful in the generation of highly precise elastic/resilient parameters that can be directly adopted for design, numerical modelling and modules of modelling geotechnical and civil engineering computer software.
KeywordsAnalytical models, elastic; quasimechanistic design; pavements; stress; strain.

INTRODUCTION

Limitations of CBR Based Resillient Modulus Models and Design Parameters
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 behavior of pavement materials under conditions that more closely simulated quasireal 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 generated from these findings and the CBR approach. 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 [1].

Limitations of the MEPD Methodlogy
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 [2].
Since the resilient/elastic modulus is most integral and elactic properties (including Poissons ratio, elastic and lateral limit strains) are of great significance in the MEPDG, 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 CBRMR models is demonstrated in [2] through examples comparing characteristics and values determined from varying models. Limitations associated with the MEPDG mainly emanate from the fact that most models applied in correlating the design parameters are still widely based on CBR concepts,

Limitations of Numerical Modelling
Mathematical and numerical modeling is a fairly established yet vibrant research area in geotechnical engineering. Its advancement has been accelerated in recent years by many emerging computational techniques as well as the increasing availability of computational power. A wide spectrum of approaches, developed on the basis of continuously advancing understanding of soil behavior, have been extended and applied to solve various problems in geotechnical engineering. These methods are increasingly playing important roles not only in achieving better understanding of fundamental behavior of geomaterials and geostructures but also in ensuring the safety and sustainability of largescale complex geoengineering projects [3].
On the other hand, in the past decennia, the Finite Element Method (FEM) has been increasingly used for the analysis of geotechnical engineering applications. However, as with every other method, the FEM also has its limitations. These limitations are not always recognized by users of finite element software, which can lead to unreliable designs. Despite the development of easytouse finite element programs, it is difficult to create a good model that enables a realistic analysis of the physical processes involved in a real project and which provides a realistic prediction of design quantities (i.e. displacements, stresses, pore pressures, structural forces, bearing capacity, safety factor, drainage capacity, pumping capacity, etc.). This is particularly true for geotechnical applications because the highly nonlinear and heterogeneous character of the soil material is difficult to capture in numerical models. When using the finite element method, soil is modelled by means of a constitutive model (stressstrain relationship) which is formulated in a continuum framework. The choice of the constitutive model and the corresponding set of model parameters are the most important issues to consider when creating a finite element model for a geotechnical project. It forms the main limitation in the numerical modelling process, since the model (no matter how complex) will always be a simplification of the real soil behavior with limitations in capturing a number of
realistic features of actual geomaterial behavior [3].

PerformancedBased Design Approach
PerformanceBased Design (PBD) fundamentally entails that, deformation in ground, pavement materials and geo structures along with the reciprocal sructural deformation and stress states, be comprehensively analyzed by adopting appropriate sophisticated analytical methods, particularly for structures with high exposure to seismic action.
The basic prerequisite of the PBD is that the acceptable level of the damage criteria be specified in engineering terms such as displacements, elastic limit stress state and ductility/ strain limit based on the function; as well dynamic loading and/ or seismic response of the structure.
Based on this background therefore, the method employs initial deformation resistance parameters, namely; Resilient/Elastic Modulus, Initial Shear Modulus and Poissons Ratio defined within the Region of Initial Deformation (RID), Axial Elastic Limit Strain and the Lateral/Radial Elastic Limit Strain parametrically represented:
for all design purposes. Prefailure deformation is modeled using the Kinematic Hardening SubYield Surface Limits [4]. This method, which incorporates the CMD (Comprehensive Method of Design), fosters comprehensive analyses, rigorous characterization and advanced performance evaluation through the correlation of the principle physical (soil model/index) and mechanical properties of insitu ground (subgrade, foundation) and geomaterials; to the main design parameters.
The analytical approach also maintains that all parameters employed for design and geomaterials characterization be directly linked to the insitu test measurements.
This development has been achieved for the quasiND (Non Destructive) mechanical Dynamic Cone Penetration (DCP) and the ND Seismic Surveys as well as the Vertical and Transient Electrical Sounding (VES/TES) geophysical insitu methods of testing [5].

Advantages and Limitations of Proposed QM Design Approach
The main advantages of the QuasiMechanistic (QM) Design approach include, but are not necessarily limited to: i) virtually all parts of the designs can be mechanistically generated with limited empirical reference providing allowance to the Design Engineer to conveniently vary structural, environmental and economic conditions in order to achieve the most optimum PBVE (Performance Based Value Engineering) balanced design; ii) the basic and intermediate designs can be expeditiously generated from insitu DCP test results that are analyzed based on analytical models that generate the design parameters directly from insitu (field) measurements from, for example, the rate of penetration, PR or Penetration Index (DCPI) in the case of DCP (Dynamic Cone Penetration) tests [6]; this ensures achievement of high precision and confidence levels of the determined design parameters, and enables the Design Engineer to expeditiously deliver the basic/intermediate designs that facilitate speedy decision making and strategic planning of project implementation on the part of Policy and/or Decision Makers;
iii) the analysis procedures, model equations and supporting nomographs allow the user to expeditiously obtain counter check solutions through hand computations; iv) all main model equations are developed with counterpart equations that enable the designer to immediately check and confirm the accuracy of their computations [7]; complex solutions can be obtained from simplified computer programs in the form of worksheets, which facilitates speedy computation [8], [9] and [10]; v) vital engineering parameters necessary in ensuring the achievement of a balanced, economic and PB VE designs can be computed in optimal form from the model equations; vi) modifications, advances and further sophistication can be realized without much complication.
Limitations of the proposed QM method are rather similar, although to a lesser extent due to the incorporation of the laboratory and insitu testing aspects, to the ones mentioned in Section C.


EXPERIMENTAL TESTING

Design of Laboratory Testing Regime

Main objective: The comprehensive laboratory testing regime was designed with the main objective of acquiring reliable data and information for advancing Research & Innovation for Sustainable Development (RISD) aimed at evolving geoscientific theories, geomathematical models and geotechnical engineering concepts that would culminate in the development of high precision confidence levels of sophisticated simulation and advanced structural performance prediction models applicable for enhanced Value Engineering Designs and Technologies (VEDs and VETs).

Application of appropriate soil mechanics principles: In designing the laboratory testing regime, considerations were made in ensuring appropriate application of the fundamental principles of soil meachanics. In particular, the contribution and influence of the nature, size, and texture of the soil particles, mechanical stability due to interparticle interaction, particle agglomeration due to cementation and longterm secondary consolidation (creep) on the strength, elastic/resilient and failure characteristics of pavement and subgrade geomaterials.
Essentially, the considerations were made for: i) reconstituted/remolded materials for pavement layers (the actual form in which they are usually used); and, ii) natural materials existing in an undisturbed state that have undergone an appreciable amount of secondary consolidation (as would be considered for foundation ground and subgrade).

Main conditions of testing considered: The basic conditions of testing considered include, but are not limited to: i) materials storage; ii) geomaterials batching and sample preparation; iiii) conditions of specimen moulding; iv) mode of compaction; v) curing conditions; vi) soaking conditions;

vii) mode of consolidation; viii) loading conditions; and, ix) appropriate method of stage and postshearing deformation
stabilized; and, xi) OPMCGRI (Geosynthetics Reinforcement/Improvement) geomaterials.
Various modes of batching were employed consisting of a number of the aforementioned geomaterials. Details on the basic properties and characteristics of the geomaterials tested for purposes of developing the proposed analytical models are provided in [11] and [12].
C. Method of Determining Optimum Batching Ratio (OBR)
75% of OMC (0.75OMC):
UBL @ PI=6%: CBR=84%
75% of OMC (0.75OMC):
UBL @ PI=6%: CBR=84%
100
CBR80 = 2.2309PI + 80.145
100
CBR80 = 2.2309PI + 80.145
CBR100 = 2.7862PI + 100.
CBR100 = 2.7862PI + 100.
80
80
Upper Boundary Limit (UBL)
for Unsoked @ PI=6%: CBR=67%
Upper Boundary Limit (UBL)
for Unsoked @ PI=6%: CBR=67%
60
60
Soaked/Unsoked Average UBL
@ PI=6%: CBR=50%
Soaked/Unsoked Average UBL
@ PI=6%: CBR=50%
California Bearing Ratio, CBR (%)
California Bearing Ratio, CBR (%)
Since the blending involves mixing proportions of clays, gravels and aggregates, determination of the OBR is basically carried out on the basis of: i) the evaluation of the Plasticity Index (PI) limiting values in relation to the specified design values (refer to graphical example in Fig. 1); and, ii) based on the results from i) and mechanical laboratory tests, generation of quasimechanistic characteristic curves upon which the OBR is determined as depicted in Fig. 2.
Upper Boundry Limits of CBR @ PI Specifications: Determination of OBR
Upper Boundry Limits of CBR @ PI Specifications: Determination of OBR
120
CBR40 = 1.1154PI + 40.073
120
CBR40 = 1.1154PI + 40.073
CBR60 = 1.6755PI + 60.195
CBR60 = 1.6755PI + 60.195
20
CBR Measured
From DCPT
in Field [CBR = 28.5%]
CBR Measured
in Lab. [CBR = 7%]
20
CBR Measured
From DCPT
in Field [CBR = 28.5%]
CBR Measured
in Lab. [CBR = 7%]
0
5
10 15 20 25 30 35 40
Plasticity Index, PI (%)
0
5
10 15 20 25 30 35 40
<>Plasticity Index, PI (%)
CBRmax=60: Median of Soaked/Unsoaked CBRmax=80: Unsoaked
CBRmax=100: 75% OMC CBRmax = 40: 4days Soak
CBRmax=60: Median of Soaked/Unsoaked CBRmax=80: Unsoaked
CBRmax=100: 75% OMC CBRmax = 40: 4days Soak
40
40
Soaked UBL @ PI=6%:
CBR=33%
Soaked UBL @ PI=6%:
CBR=33%
0
0
Fig. 1. Example of graphical evaluation of PI limits for determination of OBR.
Stiffness Threshold Values for OBR [Baraawe Silty Clay : Natural
measurements.
2500
Gravel + Binder [0.5% Cement + 0.5% Lime]
Four main conditions of molding of test specimens were adopted; namely: i) OBRM batching ratios; ii) OPMC binder ratios; iii) mode of geosynthetics reinforcement; and, iv) multilayer configuration.
B. Basic Properties of Geomaterials Tested
2000
Stiffness, E0/MR,ss (MPa)
Stiffness, E0/MR,ss (MPa)
1500
1000
Eo = 2234.6e0.021SCr
OBR: Optimum Batching
Ratio
MR,ss: Small Strain Resilient Modulus
Stiffness Threshold Values
@ Design Batching Ratios [Natural Gravel : Silty Clay] of: 1. 60:40 (622/180 MPa)
2. 80:20 (428/149 MPa)
3. 90:10 (362/136 MPa)
In this research study, eleven types of geomaterials were tested including: i) expansive black cotton soils from the Lake Basin Region of Kenya and the Jonglei State in
500
0
1.
Eo = 394.66e0.012SCr 2. 3.
Southern Sudan; ii) finegrained silty clays from the Baraawe Region of Somalia; iii) granular lateritic gravels from Isiolo
0 10 20 30 40 50 60 70 80 90 100
Silty Clay Ratio, SCR (%)
County in Kenya, Juba City in Southern Sudan and Eo/Mr,ss Max = 2338MPa (Unsoaked)
Bujumbura City in Burundi; iv) calcarous gravel from Baraawe Region of Somalia; v) limestone and quartzic gravels from Bossaso City in Puntland State of Somalia; vi) volcanic ash, weathered lateritic gravel, crushed graded rock (stone) aggregates from the Oromo Region of Ethiopia; vii) pozzolanic geomaterial from Songwe in Tanzania; viii) unbound mechanically stabilized at OBR (Optimum Batching Ratio); ix) unbound mechanically stabilized with geosynthetics; x) OPMC (Optimum Mechanical & Chemical)
Eo/Mr,ss Max = 424MPa (Soaked)
Fig. 2. Determination of OBR based on stiffness and silty clay ratio.

Mode of Deformation Measurement
The mode of deformation measurement (vertical/axial and lateral/radial strains) is depicted in Fig. 2. This mode of measurement was espoused for all UCS (Unconfined Compression Strength) and triaxial tests.
Y
High Resolution
Strain Transducers or
Loading Cycles – Time Protocol for MultiStage Dynamic Loading
Loading Cycles – Time Protocol for MultiStage Dynamic Loading
400000
350000
300000
400000
350000
300000
Reload 4
Reload 4
Cumulative Loading Cycles, Nvd (No.)
Cumulative Loading Cycles, Nvd (No.)
Continuous loading
Measurement Points
Measurement Points
lateral strain
Sensors
(R<0.01mm)
Top
measurement
Reload 3
Reload 3
locations @ failure
250000 RT =
Reload 2
RT4 = 60mins.
250000 RT =
Reload 2
RT4 = 60mins.
Phosphor Bronze Strips for Deformation
t Center
X
Multistage Lateral
15mins.
15mins.
200000
150000
100000
50000
0
200000
150000
100000
50000
0
Strain measurement
Reload 1
Reload 1
locations @ every
measurements
stage before and
RT3 = 40mins.
RT3 = 40mins.
after ebound
RT: Rebound Time
RT: Rebound Time
1/5t
RT2 = 30mins.
RT2 = 30mins.
0 50 100 150 200 250 300
Cumulative Loading Time, Lt (mins.)
0 50 100 150 200 250 300
Cumulative Loading Time, Lt (mins.)
Z
Fig. 3. Mode of deformation measurements for UCS and triaxial tests.

Laboratory Testing Protocols
Three modes of loading were adopted under the UCS and triaxial testing protocols to simulate static loads for parked motor vehicles/aircrafts, quasidynamic loads for motor vehicles/aircrafts that are taxing and dynamic loads for motor vehicles/aircrafts that are speeding/landing and taking off.
90000
80000
70000
60000
50000
40000
30000
20000
10000
0
90000
80000
70000
60000
50000
40000
30000
20000
10000
0
Dynamic Static Loading Protocol for Two Initial LC
Perform Standard UCS
Dynamic Static Loading Protocol for Two Initial LC
Perform Standard UCS
Testing After Each Set
of Dynamic Loading
Testing After Each Set
of Dynamic Loading
DL UCS
DL UCS
LC2.1: DLfor 5mins
then UCS to PostFailure
LC2.1: DLfor 5mins
then UCS to PostFailure
MS UCS
MS UCS
LC2.1: DLfor
30mins then UCS to PostFailure
LC2.1: DLfor
30mins then UCS to PostFailure
Cumulative Loading Cycles, Nvd (No.)
Cumulative Loading Cycles, Nvd (No.)

Criteria for proposed multistage loading: In designing the multistage loading test regime, it is important to consider whether or not the highway or airport runway will be subjected to high intensity dynamic loading. In the case of low volume traffic it is then imperative that a more realistic approach to simulate loading that takes into account a rebound effect due to postdynamicstatic loading stress release, is adopted. However, a number of limited tests under sustained dynamic loading to simulate critical state conditions and future expansion considerations should also be undertaken. A graphical example of a multistage dynamic static dynamic testing protocol is given in Fig. 4.
Cumulative Loading Time, Lt (mins.)
LC2.1: DL for 5mins. LC2.2: DL for 30mins.
Cumulative Loading Time, Lt (mins.)
LC2.1: DL for 5mins. LC2.2: DL for 30mins.
LC: Loading Condition
DL: Dynamic Loading
LC: Loading Condition
DL: Dynamic Loading
0 10
0 10
MS UCS
20
MS UCS
20
30
30
40
40
Fig. 4. Example of multistage dynamic static dynamic protocol

Cumulative loading rebound time protocol: This protocol basically involves multistage dynamic loading of the specimens whereby a designated period of rebounding is allowed prior to proceeding to the next stage of reloading as depicted in Fig. 5. During the rebound stage, precise measurements are made of the axial and lateral deformation.
Fig. 5. Cumulative loading rebound time multistage testing protocol.


Insitu (Field) Testing Regime
For purposes of design and research, numerous insitu tests were carried out on existing native subgrades as well as existing and freshly constructed subbase, base course and asphalt concrete pavement layers [7] and [14].


CASE EXAMPLE OF MATERIALS CHARACTERIZATION

Background in Brief
Rigorous testing and comprehensive characterization of various types of geomaterials has been undertaken during the course of this research [11], [12 and [15], the findings of which have been adopted in developing the analytical models introduced in Section IV, PBVE design guidelines, standard specifications and QCA (Quality Control & Assurance) procedures, which have been widely adopted within the East and Central Africa Region [16] and [17].

Progressive Deformation Impacted by Dynamic Loading
Axial Strain, a (%)
Axial Strain, a (%)
An example of a black cotton soil specimen subjected to perpetual vibrational dynamic loadin is depicted in Fig. 6. The data was acquired from Feasibility Studies that were conducted under JICA (Japan International Cooperative Agency) Grant Aid for the Western Kenya Rural Roads Improvement Project.
Impact of Vibrational Dynamic Loading on Deformation of Black Cotton Soil
6
Neat
BCS
5 Failed @
Nvd=384000
Cycles
4
3
2
1
Impact of Vibrational Dynamic Loading on Deformation of Black Cotton Soil
6
Neat
BCS
5 Failed @
Nvd=384000
Cycles
4
3
2
1
0
1000
10000
100000
1000000
0
1000
10000
100000
1000000
Vibrational Dynamic Loading Cumulative Cycles, Nvd (No.)
Neat BCS 2% Lime Stabilized Con Aid + 2% Lime Stabilized 5% Lime Stabilized Baraawe Silty Clay: Predicted
Vibrational Dynamic Loading Cumulative Cycles, Nvd (No.)
Neat BCS 2% Lime Stabilized Con Aid + 2% Lime Stabilized 5% Lime Stabilized Baraawe Silty Clay: Predicted
Fig. 6. Impact of vibrational dynamic loading on the deformation properties of problematic black cotton soil from the Lake Basin Region in Kenya
The black cotton soils were sampled along the Homa Bay
– Mbita, Rongo – Ogembo and Bumala Port Victoria Roads. The variation in the magnitude and rate of deformation of the BCSs as a result of varying modes of stabilization and binder quantities can well be appreciated from this figure.

Elastic/Initial Resilient Properties
Elastic/Resilient properties for batched geomaterials to be adopted for the base layer construction of the Baraawe runway pavement, taxiway and aprons in Somalia are depicted in Figs. 7, 8 and 9, for the stiffness, Poissons ratio, and stiffness summary, respectively. The figures are a
Lime] is minimal: within a range of 1 ~ 1.4% by volume for geomaterials batched @ 60:40 and 80:20 and increase to 1.3
~ 1.7% for the 90:10 and 1.6 ~ 2% for the 100:0% for all the Elastic/Resilient properties [15]. The reciprocal influence of curing and binder content on the initial deformation resistance of batched Baraawe geomaterials can indeed be appreciated.
Influence of Binder Content on the Stiffness of Baraawe Batched Geomaterials
Resulting Stiffness, Eo (MPa)
Resulting Stiffness, Eo (MPa)
500
representation of nomographs that are to be adopted for Quality and Binder [Cement + Lime] Content Control with respect to the various parameters of the batched Baraawe geomaterials comprising of Baraawe Silty Clay and Calcarous Gravel.
450
400
350
300
250
SC: Silty Clay
G: Gravel
600
Resulting Stiffness, E0/MR (MPa)
Resulting Stiffness, E0/MR (MPa)
550
Effect of Binder Content on Stiffness of
Baraawe Gravel ( 60:40 OBRM + Binder)
CLc: Cement + Lime Content
Cp=1 Day
200
150
0 0.25 0.5 0.75 1 1.25 1.5 1.75 2
500
450
400
350
300
Cp: Curing Period
Cp=3 Days
Cp=7 Days Cp=14 Days Cp=21 Days
Design Cc
Binder [Cement + Lime] Content, CLc (%)
60:40 [SC:G] 80:20 [SC:G] 90:10 [SC:G] 100% Silty Clay]
Fig. 9. Summary of the stiffness characteristic curves for the [silty clay:gravel] batched geomaterials @ 7 days cure (particle agglomeration).

Performance Simulation
Performance simulation is carried out mainly in
250
200
Range
0 0.5 1 1.5 2
Binder [Cement + Lime] Content, CLc (%)
Cp=28 Days
consideration of extreme changes in environmental conditions and factors with respect to the limiting design and characteristic parameters of the batched geomaterials to be adopted for the construction of the base layer. Based on the prevailing climatic conditions in the project area, it is
Fig. 7. Nomograph for determining optimum binder content for design, special specifications and QCA for stiffness of the 60:40 [silty clay:gravel] batched geomaterials.
imperative that moisture ~ suction variation be analyzed for both suction and dilatant characteristics.
Characteristic simulation is based on TACHMSV models
0.53
Resulting Poisson's Ratio,
Resulting Poisson's Ratio,
0.52
Effect of Binder Content on Poisson's Ratio of
Baraawe Gravel (60:40 OBRM + Binder)
defined in detail in [18]and [19] for matric suction and moisture increase accordingly.
CLc: Cement + Lime Content
Cp=1 Day
0.51
0.5
0.49
0.48
0.47
0.46
Design CLc
Range
Cp: Curing Period
Cp=3 Days
Cp=7 Days Cp=14 Days Cp=21 Days Cp=28 Days

Matric suction effect (decrease in moisture content):
The simulation results for the matric suction (decrease in moisture content) effect for the Baraawe Region in Somalia are presented in Table I, whilst the characteristic curves are graphically plotted in Fig. 10. On the other hand, the simulation results for the dilatancy (increase in moisture content) effect are presented in Table II, whilst the characteristic curves are graphically plotted in Fig. 11. The following salient derivations can be made from the simulation
0 0.5 1 1.5 2
Binder [Cement + Lime] Content, CLc (%)
Fig. 8. Nomograph for determining optimum binder content for design, special specifications and QCA for Poissons ratio of the 60:40 [silty clay:gravel] batched geomaterials
Materials for the priority option design are batched @ ratios of 60:40 [Silty Clay : Gravel], whilst the Fall Back options are batched @ ratios of 80:20; 90:10 and 100:0; all of which are bound at different cement + lime ratios. It is essential to note that the Design Binder Content [Cement +
results for the suction effect: i) increase in suction stress causes an exponential increase in the stiffness of all batched geomaterials; in particular, the characteristic increase is more significant for the geomaterial batched @ the ratio of 60:40 containing more of the Baraawe calcarous gravel, a behavior which may be attributed to the sensitivity of gravel geomaterials to effects of confining stresses; ii) at least a 1% suction effect is necessary in order to achieve the required design stiffness for the all the batched base materials; iii) the simulation results indicate that the Ideal Limiting Suction
Effect (ILSE) should be maintained within 1 and 3%; i.e; . Given the hot and dry climatic conditions that are prevalent in Baraawe for most part of the year, further monitoring during construction in the dry season was recommended. The impact of plasticity index on the magnitude of the matric suction effect can also be well appreciated for all the geomaterials batched at varying ratios.
TABLE I. SUMMARY OF STIFFNESS PARAMETERS SUBJECTED TO MATRIC SUCTION EFFECTS
These results imply that the geomaterials batched at 90:10 and 100:0 would require additional mitigation measures such as implementation of a secondary shoulder to ensure that the moisture ~ suction variation within the pavement structure is contained to a minimal.
Dilatancy Effect (Increase in Moisture Content) for Batched BC
Moisture Content, Mc (%)
Resulting Stiffness for 60:40 Batching (MPa)
Resulting Stiffness for 80:20 Batching (MPa)
Resulting Stiffness for 90:10 Batching (MPa)
Resulting Stiffness for 100:0 Batching (MPa)
MRi (MPa)
180
149
136
126
PI (%)
12
14
16
0
175
144
131
122
1
164
135
123
113
1.3
160
132
120
111
2
153
126
115
106
2.5
148
122
111
102
3
143
118
107
99
3.9
134
111
101
93
5
124
102
93
86
5.4
121
100
91
84
6
116
96
87
81
6.6
111
92
84
77
7
108
89
81
75
8
101
83
76
70
9
95
78
71
66
10
88
73
66
61
12.3
75
62
57
52
14
67
55
50
47
Note: Highlighted Cells indicate the Required Design Values
Dilatancy Effect (Increase in Moisture Content) for Batched BC
Moisture Content, Mc (%)
Resulting Stiffness for 60:40 Batching (MPa)
Resulting Stiffness for 80:20 Batching (MPa)
Resulting Stiffness for 90:10 Batching (MPa)
Resulting Stiffness for 100:0 Batching (MPa)
MRi (MPa)
180
149
136
126
PI (%)
12
14
15
16
0
175
144
131
122
1
164
135
123
113
1.3
160
132
120
111
2
153
126
115
106
2.5
148
122
111
102
3
143
118
107
99
3.9
134
111
101
93
5
124
102
93
86
5.4
121
100
91
84
6
116
96
87
81
6.6
111
92
84
77
7
108
89
81
75
8
101
83
76
70
9
95
78
71
66
10
88
73
66
61
12.3
75
62
57
52
14
67
55
50
47
Note: Highlighted Cells indicate the Required Design Values
TABLE II. SUMMARY OF STIFFNESS PARAMETERS SUBJECTED TO DILATANCY EFFECTS
Effect of Suction (Decrease in Moisture Content) for Batched BC
Moisture Content, Mc (%)
Resulting Stiffness for 60:40 Batching (MPa)
Resulting Stiffness for 80:20 Batching (MPa)
Resulting Stiffness for 90:10 Batching (MPa)
Resulting Stiffness for 100:0 Batching (MPa)
MRi (Mpa)
180
149
136
126
PI (%)
12
14
15
16
0
151
127
121
111
1
200
169
161
148
2
266
224
214
196
3
353
297
284
261
4
469
395
377
347
5
623
525
501
461
Simulation of Suction Effect on Stiffness of
Baraawe Airstrip Batched Materials
Simulation of Suction Effect on Stiffness of
Baraawe Airstrip Batched Materials
650
550
450
60:40 [PI=12]
80:20 [PI=14] 90:10 [PI=15]
100:0 WMB [PI=16]
Simulation of Dilatancy Effect on Stiffness of Baraawe Airstrip
Batched Materials
650
550
450
60:40 [PI=12]
80:20 [PI=14] 90:10 [PI=15]
100:0 WMB [PI=16]
Simulation of Dilatancy Effect on Stiffness of Baraawe Airstrip
Batched Materials
350
250
150
350
250
150
PI: Plasticity Index
WMB: With Minimal Binder
PI: Plasticity Index
WMB: With Minimal Binder
50
50
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
Decrease in Moisture Content (Suction), wc (%)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
Decrease in Moisture Content (Suction), wc (%)
PI: Plasticity Index
MC: Moisture Content WMB: With Minimal Binder
PI: Plasticity Index
MC: Moisture Content WMB: With Minimal Binder
60:40 [PI=12]
80:20 [PI=14]
90:10 [PI=15]
100:0 WMB [PI=16]
60:40 [PI=12]
80:20 [PI=14]
90:10 [PI=15]
100:0 WMB [PI=16]
Limiting MC Increase
for 60:40 [=6.6%]
Limiting MC Increase
for 60:40 [=6.6%]
Resilient Modulus, MR (MPa)
Resilient Modulus, MR (MPa)
Resilient Modulus, MR (MPa)
Resilient Modulus, MR (MPa)
Fig. 10. Graphical representation of the simulaion results depicting the matric suction effect on the stiffness of batched geomaterials

Dilatancy Effect (Increase in Moisture Content): The simulation results for the dilatancy (increase in moisture content) effect indicate that, for the adopted PI values: i) the limiting value for increase in moisture for the 60:40 batched geomaterial is higher; ; ii) the limiting value for increase in moisture for the 80:20 batched geomaterial is moderate; ; iii) the limiting value for increase in moisture for the 90:10 batched geomaterial is low; ; and, iv) the limiting value for increase in moisture for the 100:0 batched geomaterial is very low;
.
Limiting MC Increase
for 80:20 [=3.9%]
Limiting MC Increase for 100:0 [=1.3%]
0 1 2 3 4 5 6 7 8 9 10 11 12 13
Limiting MC Increase
for 80:20 [=3.9%]
Limiting MC Increase for 100:0 [=1.3%]
0 1 2 3 4 5 6 7 8 9 10 11 12 13
Increase in Moisture Content (Dilatancy), +wc (%)
Increase in Moisture Content (Dilatancy), +wc (%)
200
180
160
140
120
100
80
60
40
20
0
200
180
160
140
120
100
80
60
40
20
0
Limiting MC
Increase for
90:10 [=2.5%]
Limiting MC
Increase for
90:10 [=2.5%]
Fig. 11. Graphical representation of the simulation results depicting the moisture content increase effect on the stiffness of batched geomaterials
Detailed analyses and discussions in relation to the impact of moisture ~ suction variation on the small strain elastic/resilient properties of tropical geomaterials subjected to dynamic loading are made in [18] and [19].


Specification Considerations Based on Test Results
Based on the laboratory and insitu (field) test results and analyses carried out for research and design purposes, several aspects considered vital in incorporating in the special/particular specifications were derived.
The main aspects of concern include, but are not necessarily limited to: i) determination of appropriate binder content and agglomeration (curing) period for strength and stiffness specifications; ii) structural and filter layer specifications; iii) determination of limit values (Table III).
TABLE III. SUMMARY OF LIMITING ELASTIC PROPERTIES
S/N
Type of Batched Geomaterial
QCA Parameter
Values for Varying Soaking Conditions
4 Days Soak Partially Unsoaked Soaked
1.
60:40
Batching
Elastic/Resilient
160
180 ~ 580
600
[Silty Clay :
Modulus (MPa)
Gravel] + Binder
2.
[0.5% Cement + Poissons Ratio
0.55
0.53 ~ 0.48
0.46
0.5% Lime]
3.
80:20
Batching
Elastic/Resilient Modulus (MPa)
120
140 ~3 80
400
[Silty Clay :
Gravel] + Binder
4.
[0.5% Cement + Poissons Ratio
0.57
0.55 ~ 0.47
0.49
0.5% Lime]
5.
90:10
Batching
Elastic/Resilient Modulus (MPa)
100
120 ~ 330
350
[Silty Clay :
Gravel] + Binder
6.
[0.5% Cement + Poissons Ratio
0.59
0.57 ~ 0.49
0.51
0.5% Lime]
7.
100:0
Batching
Elastic/Resilient Modulus (MPa)
90
100 ~ 280
300
[Silty Clay :
Gravel] + Binder
8.
[0.5% Cement + Poissons Ratio
0.6
0.58 ~ 0.5
0.52
0.5% Lime]

Analysis of Insitu Test Results
Detailed analysis and the findings from insitu (field) tests performed within the framework of this elaborate study are reported in [14].


TACH ANALYTICAL MODELS DEVELOPED & PROPOSED
The proposed TACHMD analytical models are developed on the basis of geoscientific and geomathematical theories considering pragmatic engineering concepts and applications. The data adopted in its development covers a wide range of materials from very soft clays, stiff to hard clayey geomaterials, sands, silts, hydraulic and asphaltic bound materials, concrete and rocks [20].
The very basic procedure of developing the models involved: i) collection of universal data from small strain laboratory testing; ii) collection of universal data from field (insitu) geophysical testing; iii) development of correlating equations; iv) application of equations to correlate and generate relevant characteristic curves; v) application of the TACHMD universal iterative/regression concept to develop universal model equations; vi) application of CSSR (Consolidation Shear Stress Ratio) concepts for probing changes, and magnitudes thereof, in states of stress and strain during consolidation in relation to the original state of stress and stress paths perturbed [4]; vii) comprehensive study of the relevant and most pragmatically applicable constitutive and numerical models; and, vii) application of optiization mathematical concepts to simplify models. In the development of the proposed models, various influencing
factors were considered including, but not limited to, type and nature of geomaterials, voids ratio, porosity, density, clay content, confining stress, moisture ~ suction variation, mechanical stabilization, chemical stabilization, binder type, and temperature (thermal effects) particularly for asphaltic bound materials and concrete.
The importance of characterization of small strain properties in geotechnical engineering can very well be appreciated from Figs. 12 and 13. Whereas Fig. 12 clearly demonstrates the fact that, under normal circumstances, most civil engineering structures undergo deformation within the small strain region, both Figs. 12 and 13 clearly show that geomaterials exhibit very small linear elastic and recoverable elastic strain limits. As a consequence, it is imperative that concentration on proper interpretation and deep understanding of a wide range of geomaterials characteristics within this zone be invested.
This fact led to the extensive longterm research that culminated in the development of the analytical models proposed in the subsequent sections.
Fig. 12. Example of range of strains for various civil engineering structures under normal working loads and the stiffness decay characteric curve as influenced by the strain level.
Fig. 13. Example of range of elastic stress and strain limits.

Models for Deriving Elastic Modulus

Determination at varying states of stress:

Fundamental necessity for development of models: Changes consistently occur in the states of stress of foundation ground mainly as a result of external forces such as imposed loads and moisture ~ suction variations emanating from environmental conditions and factors. On the other hand, almost all construction materials utilized for civil engineering purposes are extruded, reconstituted (remolded) and subsequently factory and/or insitu processed through compaction and/or reconsolidation thereby causing insurmountable changes in the inherent structure and properties of the materials. This cerainly impacts strongly on the magnitudes of the design parameters and the post construction material characteristics. Various methods of sampling and laboratory testing have been developed in an effort to replicate the original conditions. Although noticeable advances have been made in this regard, it has proven impossible to achieve ideal replication. The development of models that can retrace the original stressstraintime histories is therefore an imperative.
An appreciably versatile quasimechanistic geo mathematical model for examining such changes (TACH GECPROM), is introduced [4]. GECPROM is designed to probe and estimate changes in vital geoproperties for clayey geomaterials and ground. The significant advantage of this model is that; various geotechnical changes and geo structural behavior can be modeled from a single sophisticated experimental test, whilst simultaneously catering for the effects of drainage conditions, loading rate, and consolidation stressstraintime history.
The fundamental model equation for the elastic modulus mainly developed from CSSR concepts and elastic theory, which defines the progressive changes in stiffness with corresponding changes in the states of stress for any given consolidationstressstraintime history (CSSTH), is expressed as (1) and (2).
(1)
(2)
where is the initial elastic modulus at a variable stress point , is the arbitrary or designated consolidation stress ratio traced to , is the initial
elastic modulus determined at insitu overburden pressure,
=0.86 and =0.35 are geomaterial constants, the values of which are applicable for most natural stiff to hard clayey geomaterials, while =1.16 and =0.4 for stress states in the 1st quadrant and =1 for stress states in the 4th quadrant accordingly determined in the p~ q stress plane.

Applicability: The model is characteristic over a wide range of applications including: i) retracing CSSH to provide data on the range of property and parametric changes that have occurred between the original and reconstituted states of clayey ground and geomaterials; ii) computation of the elastic modulus (stiffness) at any given current state of stress; iii) derivation of likely states of deformation; iv) derivation of likely kinematic hardening characteristics, among other applications. Refer to Figs. 15 and 16 for the applied demonstration in geomaterials characterization.


Determination at varying overconsolidation ratios
Practially all geomaterials adopted for civil engineering purposes are reconstituted subsequent to which they are remolded through compaction and/or reconsolidation. Essentially therefore, destructuration of the original structure of natural geomaterials always occurs. In this Study, critical destructuration caused by heavy overdensification is simulated by adopting the SHANSEP concept whereby the specimen is reconsolidated well beyond its field overburden stress, . It is appreciated that densification within the natural boundary limits of a geomaterial enhances its properties. However, the findings from this study confirm that excessive densification beyond the insitu yield stress leads to large scale straining (softening) and destruction of cementation, bonding and thixotropic components as well as causing change in the preferred particle orientation and inherent/induced anisotropic properties of natural clayey geomaterials. This characteristic can be modelled using (3) and (4).
(3)
where, is the resulting initial modulus and is the pseudoyield initial modulus determined at the stress level (pseudoyield stress) which is higher than the yield stress and from which the specimen is rebound, defined as;
(4)

Undrained conditions: Refer to (5)and (6).

As a classic function: In this case the elastic modulus is determined from the elastic limit stresses and
strains defined within the initial
yield surface, ; whereby the two parameters are determined from the analytical model equations proposed in [19].
(5)

As a function of ELS and mean effective stress:
(6)


Partially Drained: Refer to (7)and (8).

As a classic function:
(7)

As a function of ELS and mean effective stress:


Drained conditions: Refer to (9)and (10).

As a classic function:

As a function of ELS and mean effective stress:



Models for Deriving Shear Modulus
Refer to 1) a) for similar narrative.
(8)
(9)
(10)

Models for Deriving Poissons Ratio
The elastic modulus and Poissons ratio are the two most fundamental and principle parameters required in material science and the design of civil engineering structures. Nevertheless, measurement/physical modelling of the Poissons ratio, the advances in small strain measurements notwithstanding, in consideration of varying drainage conditions, has always posed challenges. This has led to the assumption and/or generalized estimation of Poissons ratio values in design, performance simulation, modelling, structural performance prediction and evaluation. On the other hand, geomathetical models used in determining crucially important analysis, design and modelling parameters from some of the most popular insitu methods of testing such as geophysical (near surface wave measurements), Plate Loading (PL) and Falling Weight Deflectometers (FWDs) involve the direct use of the Poissons ratio.
Given the importance of this parameter and its influence on some of the most vital design parameters including the shear modulus, this study concentrated on developing a straight forward model that is versatile in its application for civil engineering purposes and correlates extremely wel with other crucial measurement and design parameters. The

Determination at varying states of stress: Employing the TACHPR Model that correlates elastic modulus to Poissons ratio defined in (16), the shear modulus is then computed from (11).
(11)

Determination at varying overconsolidation ratios:
model, which was developed on the basis of geoscientific and geomathematical theories considering pragmatic engineering concepts and applications, is validated through comparative analysis with some of the typical values determined from advanced methods of measurement of elastic/dynamic properties. Comparison with typical values that are recommended for use with different civil engineering materials is made and the due corrective measures recommended accordingly. The proposed TACHPR model that correlates elastic modulus to Poissons ratio as defined in
G0 {(G0 )ss
/GR
OCR 0.39 }(G )
(12)

~ (22) for varying drainage conditions, can be useful in practically all cases of civil engineering applications [21].
0 ss
0 ss
where (G0 )ss is the initial modulus at the designated stress

Undrained conditions: Refer to (16) ~ (19).
point and
GR 290MPa
is the reference initial shear
modulus as determined in this study.
3) Undrained conditions: Refer to (13)

Partially drained conditions: Refer to (16).
(16)

Partially drained conditions: Refer to (14).
(13)
a) In correlation with undrained elastic modulus:
(17)
b) In correlation with drained and undrained moduli
ratio:

Drained conditions: Refer to (15).
(14)

In correlation with undrained moduli ratio:
(18)
(15) (19)



Drained conditions: Refer to (20) ~ (22).

In correlation with undrained elastic modulus:
(20)
(24)
where, is the resulting size of the initial yield strain,
ratio:

In correlation with drained and undrained moduli
(21)

In correlation with undrained moduli ratio:
is the initial yield strain determined at the pseudoyield stress level and is a constant
that is dependent on the stiffness and nature of the geomaterial.
b) Partial restructuration: The model equation for partially restructured ELS achieved through LTC (Long Term Consolidation) of overconsolidated foundation ground and/or geomaterials is defined in (25).




Model for Determining Elastic Limit Strain (ELS) Threshold
(22)
(25)

Undrained conditions: Refer to (26).
The ELS basically defines the range within which the constitutive behavior of any engineering material is linear elastic and fully recoverable upon loading unloading reloading. It indeed is one of the most vital parameters in science and engineering theory and practice. Given geomaterials predominantly nonlinear behavior from a region of extremely small strains, determination of their precise ELS threshold continues to pose major challenges to researchers and engineers alike. The proposed analytical model in (23) provides means to alleviate this problem. In this case, the factored insitu elastic modulus measured from the field and/or estimated from UCS tests is adopted in determining the ELS threshold for purposes of developing particular specifications for elastic stress strain limits and deriving permanent deformation characteristics based on the KHSSS models [4].

Determination of ELS at Varying States of Stress
On the other hand, the basic model equation defining the impact of stress states on the elastic limit strain that defines the initial yield surface is expressed as:
(26)


Partially drained conditions: Refer to (27) and (28).

In Correlation with elastic modulus:
(27)

In correlation with undrained ELS:
(28)


Drained conditions: Refer to (29) ~ (32).
a) In Correlation with elastic modulus:
(23)
where, constants =0.98, =0.32, =0.4, for
stress states in the 1st quadrant and, =1, in the 4th quadrant of the p ~ q stress plane, while =1.16.
Note that the multiplier on the RHS can be derived from the following [(24) ~ (32)] model equations for OCR, undrained, partially drained and drained conditions.

Determination at varying overconsolidation ratios

Destructuration: Deterioration leading to the
and,
also,

In correlation with undrained ELS:

(29)
(30)
(31)
(32)
reduction of the initial yield strain {(a)ELS(YI)} is modelled based on (24).

Model for Determining Elastic Limit Deviator Stress (ELSt) Threshold
In conjunction with the ELS defined in Section D, the ELSt has largely been estimated without any geoscientific basis of determination proposed hitherto. The proposed model
for defining the elastic limit threshold for the deviator stress is in juxtaposition with the one for the elastic limit strain. Model equations for deriving this vital parameter are provided in (33), (35) and (36) for undrained, partially drained and drained, respectively. The particular specification limits can be determined as per the discussions posed in Section D for determination of the elastic limit strain threshold.

Undrained conditions: Refer to (33).

H. Model for Correlating Elastic and Resilient Moduli
The model for correlating elastic and resilient moduli accounting for the effects of confining stress is developed based on the concepts of KHSSS (Kinematic Hardening Small Strain Stiffness) and resilient moduli determined in accordance with the Long Term Pavement Performance (LTPP) Protocol P46, a standard protocol set forth for MR testing in 1996, by the US Federal Highway Administration (FHWA). The model equations are defined in (38) and (39).
where,
(33)
(38)
(34)

Linked Modules
(39)
Note that; = = for undrained, partially drained and drained, respectively.
2) Partially drained conditions: Refer to (35).
(35)
1) Influence of confining stress on elastic/small strain resilient modulus:
(40)

Influence of confining stress on Poissons rato:

Drained conditions: Refer to (36).
(36)

Models for Determining Secondary StressStrain Yield Surfaces
The models for determining secondary stressstrain yield surfaces are discussed in [4].

Progressive Deformation Model
The importance of developing reliable models for characterizing the progressive deformation of foundation ground and pavement structures subjected to dynamic loading cannot be overemphasized. The proposed models can be applied in determining, more precisely, the characteristics and upper boundary limits within which permanent deformation

Influence of confining stress on shear modulus:

Influence of confining stress on elastic limit strain:
(41)
(42)
(43)
should be specified (refer to Fig. 14).
(37a)
(37b)
The lateral deformation can be determined based on the model equations defined in (37a) and (37b) by multiplying the RHS with the Poissons ratio, based on the relation: whereby is determined from (16) ~ (22).

Longterm consolidation effects on elastic modulus:
The effect of secondary consolidation on the elastic modulus is known to be minimal within the linear elastic and recoverable zone for intact specimens. This effect can be quantified by applying (44) for the intact and (45) for the reconstituted or disturbed specimen, respectively.
(44)
(45)

Longterm consolidatin effects on ELS:
(46)
The degree of recoverability can thence be confirmed from the following relations.
(53)
(47)
is the initial yield strain determined under normally consolidated conditions at a standard time period designated after the end of primary consolidation and is the secondary consolidation time measured in hrs. Note that .

Loading rate effects:
(48)

Quasirecoverability (quasirestructuration) models
Due to the diagenetic, intricate nature and complexity of natural well cemented and highly structured clayey geomaterials, perfect recoverability is most definitely not envisaged. Nevertheless, it is considered that, with ageing, restructuration can be achieved to a certain degree. As a consequence, the restructuration models are defined predominantly as functions of secondary consolidation time. The coupling effect of strain amplitude and loading rate controlled Cyclic Prestraining (CP) has not been exhaustively examined for its inclusion at this stage.
The postdestructuration TACH Structural Recoverability Models (TACHSRM) are mathematically defined in the following equations.
(49)
(54)
where, is the postrecovery elastic modulus, is the postrecovery elastic yield strain and =5.42, =1.4X103.

Simulating influence of mositure suction varation:
The influence of moisture ~ suction variation on the elastic/resilient properties can be referenced from [12].

APPLICATION OF PROPOSED MODELS FOR
GEOMATERIALS CHARACTERIZATION
As demonstrated in the subsequent subSections, the proposed TACHQM analytical models are universally applicable for characterizing a wide range of geomaterials encountered in the field, reconstituted for insitu improvement of subgrade and remolded for use as pavement materials.

Stiffness Degradation with Cumulative Progressive Loading
Fig. 14, generated from (37b), is a depiction of the impact of vibrational dynamic loading on the stiffness characteristics of varying pavement/structural subgrade layer geomaterials. The importance of precisely determining the required initial design stiffness and ultimate (permanent deformation) limit stiffness can well be appreciated.
Degradation of Pavement Layer/Subgrade Geomaterial Stiffness
The Secondary Consolidation Time (SCT) required to achieve the structural recoverability initial modulus is therefore computed from:
(50)
where, is the initial modulus after quasi structural recoverability, is the postdestructuration initial modulus determined after ShortTerm Consolidation (STC) and =19.3 is LTC related material constant. On the other
350
Secant Modulus of Deformation, Es (MPa)
Secant Modulus of Deformation, Es (MPa)
300
250
200
150
100
50
0
Zone of Erratic Data Due to Bedding Errors and System Complia nce
Resulting from Cumulative Dynamic Loading Progression
Eo: Elastic Modulus in MPa
hand, the elastic yield strain is computed from,
1000 10000 100000
(51)
(51)
Vibrational Dynamic Loading, NA,VL (Cumulative No. of Cycles)
Eoi=366 Eoi=316 Eoi=273 Eoi=219 Eoi=175 Eoi=141 Eoi=113 Eoi=73
Hence, the SCT required for SR is then determined as:
(52)
where is the elastic yield strain after quasistructural recoverability, while is that determined within STC and =7X104. Note that in all cases,
= = = .
Fig. 14. Example of application of (1): Degradation of pavement/subgrade layer stiffness due to effects of progressive cumulative dynamic loading.

Influence of stress state and drainage conditions
Kc=0.3U
Kc=0.5D
Kc=0.3U
Kc=0.5D
10000
10000
Kc=0.5U
Kc=0.7D
Kc=0.5U
Kc=0.7D
8000
8000
Kc=0.7U
Kc=0.7U
Elastic/Initial Resilient Modulus, Eo/MRi (MPa)
Elastic/Initial Resilient Modulus, Eo/MRi (MPa)

Small strain elastic/resilient modulus: The influence of the mean effective stress on the small strain elastic/resilient modulus is demonstrated in Fig. 15 as generated from (1).
Influence of Mean Effective Stress on Elastic/Initial Resilient Modulus for Varying CSR
under Drained, Partially Drained & Undrained Conditions
Influence of Mean Effective Stress on Elastic/Initial Resilient Modulus for Varying CSR
under Drained, Partially Drained & Undrained Conditions
14000
14000
Kc=0.3D
12000
Kc=0.3D
12000
0
0
0.0
0.3
0.5
0.8 1.0
1.3
1.5 1.8
2.0
2.3
2.5
0.0
0.3
0.5
0.8 1.0
1.3
1.5 1.8
2.0
2.3
2.5
Mean Effective Stress, po' (MPa)
Mean Effective Stress, po' (MPa)
6000
6000
Kc=1.0D
Kc=1.0U
Kc=1.0D
Kc=1.0U
4000
4000
Kc=0.3PD
Kc=0.5PD
Kc=0.3PD
Kc=0.5PD
2000
2000
Kc=0.7PD
Kc=1.0PD
Kc=0.7PD
Kc=1.0PD
Fig. 15. Example of application of (2): Influence of mean effective stress on stiffness for varying consolidation stress ratios (CSR) and drainage conditions.
Based on the results plotted in Fig. 15, it can be noted that, notwithstanding the drainage conditions and consolidation stress history, the mean effective stress impacts the characteristics and magnitude of the elastic modulus.
Kc=0.3D
Kc=0.3D
0.45
0.45
Kc=0.3U
Kc=0.3U
Partially Drained Unique Characteristic Curve DUCC):
Partially Drained Unique Characteristic Curve DUCC):
Kc=0.5D
Kc=0.5D
0.40
0.40
Kc=0.5U
Kc=0.7D
Kc=0.5U
Kc=0.7D
0.35
0.35
Initial NC Elastic Limit Strain, [a]ELS (%)
Initial NC Elastic Limit Strain, [a]ELS (%)

Small strain Poissons ratio: The characteristic curves graphically represented in Fig. 17 are generated from model equations defined in (16) ~ (22). It can mainly be inferred that: i) Poissons Ratio (PR) is highly dependent on drainage conditions; ii) the magnitude of the PR is influenced by both the CSR and drainage conditions; and, iii) when subjected to similar drainage conditions, the PR characteristics are unique to the effects of the CSR.
Influence of Elastic/Initial Resilient Modulus on Poisson's Ratio for Varying CSR under
Drained, Partially Drained and Undrained Conditions
Influence of Elastic/Initial Resilient Modulus on Poisson's Ratio for Varying CSR under
Drained, Partially Drained and Undrained Conditions
0.50
0.50
Undrained Unique Characteristic Curve UUCC):
Undrained Unique Characteristic Curve UUCC):
0.20
Kc=1.0PD
0.20
Kc=1.0PD
0.15
0.15
0
2000 4000 6000 8000 10000 12000 14000
0
2000 4000 6000 8000 10000 12000 14000
Elastic/Initial Resilient Modulus, Eo/MRi (MPa)
Elastic/Initial Resilient Modulus, Eo/MRi (MPa)
Kc=0.7U
Kc=1.0D
Kc=0.7U
Kc=1.0D
0.30
0.30
Kc=1.0U
Kc=1.0U
Drained Unique Characteristic Curve DUCC):
Drained Unique Characteristic Curve DUCC):
Kc=0.3PD
Kc=0.3PD
0.25
0.25
Kc=0.5PD
Kc=0.7PD
Kc=0.5PD
Kc=0.7PD
Fig. 16. Example of application of (16) ~ (22): Poissons ratio characteristics subjected to varing drainage conditions and consolidation stress histories.

ElasticLimit Strain (ELS): Characteristics similar to those exhibited by the elastic modulus can be observed for the elastic limit strain depicted in Fig. 17. The curves are generated from the model equations defined in (23) ~ (32).
Initu Effective Overburden Pressure, a0 (MPa)
Insitu Effective Overburden Pressure, a0 (MPa)
Effect of Insitu Overburden Pressure on Elastic Limit Strain for Varying CSR under
Drained, Partially Drained and Undrained Conditions
0.0200
0.0175
Kc=0.3D
0.0150 Kc=0.3U
Effect of Insitu Overburden Pressure on Elastic Limit Strain for Varying CSR under
Drained, Partially Drained and Undrained Conditions
0.0200
0.0175
Kc=0.3D
0.0150 Kc=0.3U
0.0125
0.0100
0.0125
0.0100
NC: Normally Consolidated [OCR=1];
CSR: Consolidation Stress Ratio
Values for ShortTerm Secondary Cons;
Reference Axial Strain Rate = 0.01%/min.
NC: Normally Consolidated [OCR=1];
CSR: Consolidation Stress Ratio
Values for ShortTerm Secondary Cons;
Reference Axial Strain Rate = 0.01%/min.
0.0075
0.0050
0.0025
0.0000
0.0075
0.0050
0.0025
0.0000
Kc=0.5D
Kc=0.5U Kc=0.7D Kc=0.7U Kc=1.0D Kc=1.0U Kc=0.3PD Kc=0.5PD Kc=0.7PD Kc=1.0PD
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
Kc=0.5D
Kc=0.5U Kc=0.7D Kc=0.7U Kc=1.0D Kc=1.0U Kc=0.3PD Kc=0.5PD Kc=0.7PD Kc=1.0PD
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
Initial NC Elastic Limit Strain, [a]ELS (%)
Initial NC Elastic Limit Strain, [a]ELS (%)
Fig. 17. Example of application of (23) ~ (32): Elastic limit strain characteristics for goematerials subjected to varying drainage conditions and consolidation stress histories defined by CSR.

ElasticLimit Stress (ELSt): The results plotted in Fig.
Elastic Limit Deviator Stress – Elastic Modulus Relations for Varying CSR
under Drained, Partially Drained and Undrained Conditions
Elastic Limit Deviator Stress – Elastic Modulus Relations for Varying CSR
under Drained, Partially Drained and Undrained Conditions
180
180
Drained Unique Characteristic Curve (DUCC):
Drained Unique Characteristic Curve (DUCC):
160
140
120
100
160
140
120
100
Kc=0.3D
Kc=0.3U Kc=0.5D Kc=0.5U Kc=0.7D Kc=0.7U Kc=1.0D Kc=1.0U
Kc=0.3D
Kc=0.3U Kc=0.5D Kc=0.5U Kc=0.7D Kc=0.7U Kc=1.0D Kc=1.0U
80
80
Partially Drained Unique Characteristic Curve (DUCC):
Partially Drained Unique Characteristic Curve (DUCC):
Kc=0.3PD
Kc=0.5PD
Kc=0.3PD
Kc=0.5PD
Elastic Limit Deviator Stress , [d]ELSt (kPa)
Elastic Limit Deviator Stress , [d]ELSt (kPa)
18 show the graphical correlations between the elatic modulus and the elastic limit stress simulating geomaterials subjected to varying conditions of drainage and reconsolidation stress histories. Observations, similar to those made in 2) for the Poissons ratio, can be made from this figure.
0
2000 4000 6000 8000 10000 12000 14000
0
2000 4000 6000 8000 10000 12000 14000
Elastic/Initial Resilient Modulus, Eo/MRi (MPa)
Elastic/Initial Resilient Modulus, Eo/MRi (MPa)
60
60
Kc=0.7PD
Kc=1.0PD
Kc=0.7PD
Kc=1.0PD
40
40
Undrained Unique Characteristic Curve (UUCC):
Undrained Unique Characteristic Curve (UUCC):
20
0
20
0
180
180
Influence of Overburden Pressure on Elastic Limit Deviator Stress for Varying CSR
under Drained, Partially Drained & Undrained Conditions
Influence of Overburden Pressure on Elastic Limit Deviator Stress for Varying CSR
under Drained, Partially Drained & Undrained Conditions
Kc=0.3D
Kc=0.3D
160
160
Kc=0.3U
Kc=0.3U
140
140
Kc=0.5D
Kc=0.5D
120
120
Kc=0.5U
Kc=0.7D
Kc=0.5U
Kc=0.7D
100
100
Kc=0.7U
Kc=0.7U
Elastic Limit Deviator Stress [ d]ELSt (kPa)
Elastic Limit Deviator Stress [ d]ELSt (kPa)
Fig. 18. Example of application of (33): Correlations between elastic modulus and elastic limit stress for varying drainage conditions and CSR.
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
Insitu Effective Overburden Pressure, ao (MPa)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
Insitu Effective Overburden Pressure, ao (MPa)
80
80
Kc=1.0D
Kc=1.0U
Kc=1.0D
Kc=1.0U
60
60
Kc=0.3PD
Kc=0.3PD
40
40
Kc=0.5PD
Kc=0.5PD
20
20
Kc=0.7PD
Kc=1.0PD
Kc=0.7PD
Kc=1.0PD
0
0
Fig. 19. Example of application of (33), (35) and (36): Influence of insitu overburden pressure on elastic limit stress for varying consolidation stress ratios and drainage conditions.
On the other hand, observations, similar to those made in Fig. 15 for the elastic modulus can be derived for the elastic limit stress characteristics depicted in Fig. 19.


Influence of LTC, Strain Rate and Plasticity Index on the Stiffness Decay Characteristic Curves
The influence of LongTerm Consolidation (LTC), strain rate and Plasticity Index (PI) are reported in [18] and [19]

Elastic/Resilient Characteristics of Various Geomaterials
As mentioned and tabulated in the introduction, various tropical unbound and bound, unbatched and batched geomaterials were tested and characterized in this study. The materials include, but are not necessarily limited to: i) fine grained silty clays; ii) granular lateritic gravels; iii) clacarous gravels; iv) quartzic gravels; v) limestone gravels; vi) crushed rock (stone) aggregates; geomaterials of pozzolanic nature;
vii) unbound mechanically stabilized conventionally and at

Determination of stress distribution with depth: The factored maximum vertical stress is computed from the tire pressure of the Design Aircraft by applying (55).
(55)

Vertical stress distribution: Determined based on the maximum vertical stress value and models reported in [9].
Interface Stress Values for Varying Layers for SPT 2
Required Interface Design Vertical Stress Capacity, v (MPa)
0 0.2 0.4 0.6 0.8 1 1.2 1.4
0
Pavement Depth (Thickness), Pd (mm)
Pavement Depth (Thickness), Pd (mm)
v = 0.459MPa
100
OBR; viii) unbound mechanically stabilized with geosynthetics; ix) OPMC stabilized; and, OPMCGRI stabilized. Details can be perused from [12].



APPLICATION OF PROPOSED MODELS FOR PB VE DESIGNS, SPECIFICATIONS AND CONSTRUCTION
200
300
400
500
600
v = 0.284MPa
v = 0.214MPa
v = 0.153MPa
Base/ Subbase Interface Stress Value
Subbase/ 0.5% Lime
Gravel Wearing Course/
Base Course Interface Stress Value
DCS
QCA
Examples of recent applications of the proposed TACH QM analytical models in the development of quasi mechanistic performance based value engineering designs, specifications and construction QCA are provided in Figs. 20
700
800
900
1000
Improved Subgrade
Improved/Native Processed Subgrade
DCS: Design Contact Stress in MPa;
DCS = 1.250 MPa (1250 kPa)
~ 26.
A. Design Applications
The analytical graphs depicted in Figs. 20 ~ 26 were used for generating appropriate design parameters required for the recently designed Baraawe Airport runway pavement, taxiway and aprons in Somalia, which prompted challenges due to the lack of suitable construction materials coupled with the existence of more than 4m of thick silty clayey subgrade layer.
Fig. 21. Vertical stress interface values for varying pavement and subgrade
layers determined based on the QM design concepts.

Lateral stress distribution: Determined based o correlation of the vertical stress multiplied with the Poissons ratio.
Lateral Stress Distribution with Runway Pavement Depth
Required Design Lateral Stress Capacity, Lat. (MPa)
0.0 0.1 0.2 0.3 0.4
1) Determination of appropriate Citical Replacement Depth (CRD): As depicted in Fig. 20 a new approach proposed in this Study was adopted.
Determination of Replacement Depth Based on Stiffness Distribution
Required Design Stiffness Capacity, E0/MR (MPa)
0 50 100 150 200 250 300 350 400
0
Pavement Depth (Thickness), Pd (mm)
Pavement Depth (Thickness), Pd (mm)
200
400
600
800
1000
1200
Range for Near Future Design Consideration & Structural Performance Evaluation
0
100
Pavement Depth (Thickness), Pd (mm)
Pavement Depth (Thickness), Pd (mm)
200
300
400
500
600
Vertical Stress Capacity Inadequate [E0/MRRequired >> E0/MRMeasured] Replacement Required
E0/MR = 75MPa
Factored
Design Curve
Replacement Depth (Dr);
Required Dr = 298 mm
Characteristic Curve from
Insitu (Field) Measured Data [NonFactored]
1400
1600
1800
2000
DCS: Design Contact Stress in MPa;
DCS = 1.250 MPa (1250 kPa)
DCS=1.25 DCS=1.5 DCS=2 DCS=2.6
700
800
900
1000
Stiffness Capacity Adequate: [E0/MRRequired << E0/MRMeasured] Does not Require Improvement and/or
Replacement Under Existing Undisturbed Consolidated State
Fig. 20. Determination of Critical Replacement Depth (CRD) based on QM design concepts from: a) insitu (field) stiffness measurements and, b) vertical stress distribution and insitu dcp measurements
Pavement Depth (Thickness), Pd (mm)
Pavement Depth (Thickness), Pd (mm)
0
100
Interface Lateral Stress Values for Varying Layers for SPT2
Required Interface Design Lateral Stress Capacity, Lat. (MPa)
0.00 0.05 0.10 0.15 0.20 0.25
Lat. = 0.084MPa
Poisson's Ratio Distribution with Runway Pavement Depth
Required Design Poisson's Ratio Limits,
0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70
0
200
300
Lat. = 0.054MPa
Base/
Gravel Wearing Course/Base Course Interface Stress Value
DMLS
200
Pavement Depth (Thickness), Pd (mm)
Pavement Depth (Thickness), Pd (mm)
400
Range for Near
Future Design
400
500
600
700
800
900
1000
Lat. = 0.041MPa
Lat. = 0.03MPa
Subbase Interface Stress Value
Subbase/ 0.5% Lime Improved Subgrade
Improved/Native Processed Subgrade
DCS: Design Maximum Lateral Stress in MPa;
DCLS = 1.250 MPa (1250 kPa)
600
800
1000
1200
1400
1600
1800
Consideration & Structural Performance Evaluation
DCS: Design Contact Stress in MPa;
DCS = 1.250 MPa (1250 kPa)
Fig. 22. Lateral stress interface values for varying pavement and subgrade layers determined based on the QM design concepts.

Determination of stiffness distribution with depth:
Determined based on multilayer elastic theory models
2000
DCS=1.25 DCS=1.5 DCS=2 DCS=2.6
Interface Poisson's Ratio Values for Varying Layers for SPT2
Design Poisson's Ratio Values @ Interface,
proposed and applied in [9].
0.500 0.525 0.550 0.575 0.600 0.625 0.650
0
Interface Stiffness Values for Varying Layers for SPT2
Required Interface Design Stiffness Capacity, E0/MR (MPa)
0 50 100 150 200 250 300
0 MR = 74MPa
100
Pavement Depth (Thickness), Pd (mm)
Pavement Depth (Thickness), Pd (mm)
200
300
400
DPRCV
= 0.5799
Gravel Wearing Course/
Base Course Interface
Poisson's Ratio Value (PRV)
Base/ Subbase Interface PRV
Pavement Depth (Thickness), Pd (mm)
Pavement Depth (Thickness), Pd (mm)
100
200
300
400
500
600
MR = 50MPa
MR = 39MPa
MR = 29MPa
Base/ Subbase Interface
Stiffness Value
Subbase/
0.5% Lime
Gravel Wearing Course/ Base Course Interface Stiffness Value
DMSt.
500
600
700
800
900
1000
DPRCV: Design Poisson's Ratio Contact Value; DPRCV = 0.5061
= 0.6046
= 0.6196
Improved/Native Processed Subgrade PRV
Subbase/ 0.5% Lime Improved Subgrade PRV
= 0.638
700
800
900
1000
Improved Subgrade Interface Stiffness Value
Improved/Native Processed
Subgrade Interface Stiffness Value
DMSt.: Design Maximum Stiffness in MPa;
DMSt. = 244 MPa
Fig. 24. Poissonss ratio interface values for varying pavement and subgrade layers determined based on the QM design concepts.
5) Determination of strain distribution with depth: The vertical ad lateral strain distributions are shown in Figs. 25
Fig. 23. Stiffness interface values for varying pavement and subgrade layers
determined based on the QM design concepts.

Determination of Poissons ratio distribution with depth: This is depicted in Fig. 24 for a wide range of vertical stresses, strains and stiffness (refer to Figs. 22, 23 and 25). Note that the interface values shown in Figures 21 ~ 26 indicate the design values required at the respective depths based on the QM analyses considering undrained conditions of the runway pavement foundation ground [10] and [15].
and 26, respectively. The lateral strains were derived from a function of the correlation with the vertical strains and Poissons ratio. It can be derived that maximum deflections and deformation propensity are concentrated in the upper layers of the pavement gradually reducing with the increase in depth.

Vertical Strain: It can, however, be inferred that the vertical strains prevail within the region of small strains.

Vertical Strain Distribution with Runway Pavement Depth
Required Design Vertical Elastic/Resilient Strain Limit, v (%)
0.000 0.001 0.002 0.003 0.004 0.005 0.006 0.007
Pavement Depth (Thickness), Pd (mm)
Pavement Depth (Thickness), Pd (mm)
0
200


CASE EXAMPLE OF RECENT APPLICATION FOR
AIRPORT PAVEMENT DESIGN
The comprehensive case example of a recent application of the TACHMD models and QuasiMechanistic (QM) approach adopted for the design of the Baraawe Airport runway pavement in Somalia can be referenced from
[10] and [15]. The pavement structural configuration of the400
600
800
1000
1200
1400
1600
1800
2000
Range for Near Future Design Consideration
& Structural Performance
DCS: Design Contact Stress in MPa;
DCS = 1.250 MPa (1250 kPa)
DCS=1.25 DCS=1.5 DCS=2 DCS=2.6
preferred priority design is depicted in Figure 27. Note that the configuration includes a subgrade structural layer thickness that is determined based on the QM approach. Based on this approach sufficiently adequate PBVE designs that culminated in construction costtime savings of more than 40% were developed.
TYPICAL PAVEMENT STRUCTURAL CONFIGURATION – 60:40 OBRM BC [KM0+000 to KM1+400]
PAVEMENT MATERIALS & COMPACTION
TYPICAL PAVEMENT STRUCTURAL CONFIGURATION – 60:40 OBRM BC [KM0+000 to KM1+400]
PAVEMENT MATERIALS & COMPACTION
Interface Strain Values for Varying Layers for SPT2
Interface Design Vertical Elastic/Resilient Strain Limits, v (%)
ASPHALT CONCRETE
ASPHALT CONCRETE
MAINTENANCE GWC
STRUCTURAL OPMCGWC
STRUCTURAL OPMC BASE COURSE
FILTER LAYER (ESB)
MAINTENANCE GWC
STRUCTURAL OPMCGWC
STRUCTURAL OPMC BASE COURSE
FILTER LAYER (ESB)
p/>
0.000 0.001 0.002 0.003 0.004 0.005 0.006 0.007
0
Pavement Depth (Thickness), Pd (mm)
Pavement Depth (Thickness), Pd (mm)
100
200
300
400
500
600
700
800
DCVSL: Design Contact Vertcal Strain Limit in %; DCVSL = 0.0043 %
Gravel Wearing Course/ Base Course Interface Strain Value
Base/ Subbase Interface Strain Value
Subbase/ 0.5% Lime Improved Subgrade
v = 0.005044%
75mm Filter Layer (ESB): [60:40 SILTY CLAY: GRAVEL] + BINDER [0.5% CEMENT
+ 0.5% LIME]
75mm Filter Layer (ESB): [60:40 SILTY CLAY: GRAVEL] + BINDER [0.5% CEMENT
+ 0.5% LIME]
v = 0.004625%
STRUCTURAL SUBGRADE
STRUCTURAL SUBGRADE
650mm Structural Thickness of Existing (Native) Silty Clay Subgrade Layer
650mm Structural Thickness of Existing (Native) Silty Clay Subgrade Layer
v = 0.004424%
900
1000
Improved/Native Processed
Subgrade
v = 0.00424%
COMPOSITE STIFFNESS = 893 MPa
COMPOSITE STIFFNESS = 893 MPa
Fig. 27. Example of the priority pavement structural configuration of the
Fig. 25. Vertical strain interface values for varying pavement and subgrade layers determined based on the QM design concepts.
b) Lateral Strain: It can be observed that the values of the lateral strains plotted in Fig. 26 occur within the range of small strains.
Interface Lateral Strain Values for Varying Layers for SPT2
Interface Design Elastic/Resilient Lateral Strain Limits, Lat. (%) 0.0020 0.0022 0.0024 0.0026 0.0028 0.0030
0
Barawe Airport in Somalia developed on the basis of the TACHQM approach employing the proposed analytical models

CONCLUSIONS
Universal and versatile analytical models equipped with a variety of application modules have been proposed in this paper. Application of the proposed models has been practically manifested through graphical examples for the characterization of geomaterials, generation of imperative design parameters and a pragmatic case example of a runway pavement structural design. The design characteristic curves
Pavement Depth (Thickness), Pd (mm)
Pavement Depth (Thickness), Pd (mm)
100
200
300
400
500
600
700
800
DCLSL
DCLSL: Design Contact Lateral Strain Limit in %; DCLSL = 0.002156 %
Gravel Wearing Course/ Base Course Interface Lateral Strain Limit
Base/Subbase Interface Lateral Strain Limit
Subbase/0.5% Lime Improved Subgrade Interface Lateral Strain Limit
Lat. = 0.002925
Lat. = 0.002796
Lat. = 0.002741
and parametric values clearly indicate the validity, lucidity and rationality of the proposed analytical models and the TACHQM method of PBVE design for highway and airport pavements.
ACKNOWLEDGMENT
The Author wishes to acknowledge, with gratitude, the Materials Testing & Research Department, Ministry of Transport & Infrastructure, Kenya, as well as the Research Teams of Kensetsu Kaihatsu Engineering Consultants Limited and the Kenya Geotechnical Society (KGS). Sincere
900
1000
Improved/Native Processed Subgrade Lateral Strain Limit
Lat. = 0.002705
appreciation is also expressed to the Japan International Cooperation Agency (JICA), Japan Bank of International Cooperation (JBIC), Construction Project Consultants Inc.,
Fig. 26. Lateral strain interface values for varying pavement and subgrade layers determined based on the QM design concepts.
Kajima Corporation and Kajima Foundation for funding a substantial part of the study conducted in Africa.
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J.N. Mukabi, Necessity for review of resilient properties and conventional resilient modulus models of characterizing pavement materials for MEPD, EPublication in academia.edu., 2015.

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J.N. Mukabi, Characterization of consolidation stressstraintime histories on the prefailure behavior of natural clayey geomaterials, Proceedings of the VIth International Symosium on Deformation Characteristics on Geomaterials, Buenos Aires, 2015.

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J.N. Mukabi, Review of DCP based CBR UCS and resilient modulus models for application in highway and airport pavement design, Preprint EPublication in academia.edu.,June 2016.

J.N. Mukabi, The Proposed TACHMDs: Revolutionary VEPB technologies and methods of design for pavements and ancillary geo structures, Proceedings of the World Road Congress, Seoul, November 2015.

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J.N. Mukabi and S.F. Wekesa, Case examples of successful application of a new PBVE design approach for runway pavements in East Africa, Proceedings of the World Road Congress Workshop on Airfields, Seoul, November 2015.

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J.N. Mukabi, Characterization of OBRMOPMCGRI stabilized geomaterials for enhanced pavement performance, unpublished.

D. Mounier, A new mechanistic design procedure for flexible airfield pavements, Conference of Airports in Urban Networks, Paris, 2014.

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