Quality Impairments in Flexible Road Pavements

*Samuel I. Egwunatum, Ovie I. Akpokodje and Andrew I. Awo-Osagie*

#### **Abstract**

The purpose of this chapter is to present the reader with the physical processes of how flexible road pavements progressively fail and impair the quality of finished roads arising from non-adherence to roads construction quality outlines and requirements. This was achieved by investigating eight (8) roads from a sample of nineteen (19) roads based on purposive sampling. Using instruments of steel tapes, paints for failed sections, rolling rule and pictures, measurement of length, width and depth of various failed sections were taken for five (5) daily measurements at three (3) monthly visit intervals for Four Hundred and Thirty Five (435) days to show the rate of deterioration. Data obtained were analyzed for reliability of pavements using Weibull distribution statistics on ReliasoftWeibull++to extrapolate pavement reliability from bathtub function. Findings showed that roads failed progressively within six (6) months after finished construction and deteriorated fast with increased failures on length, depth and width of pavements. The practical implications of this is that the process of construction did not conform with required/stipulated quality control metrics of flexible road construction especially in the areas of geomaterials compaction, temperature and density of materials laid. It was recommended that organization adhere to quality control guidelines and requirements to forestall quality impairment.

**Keywords:** flexible pavement, Weibull test, quality control, quality impairment, deterioration rate, reliability

### **1. Introduction**

Issues of total quality management implementation in different construction industries around the world are well validated in studies to be at various levels of implementation between developing and developed countries [1]. Structural failures of roads before the designed lifetime are regular features especially amongst developing countries in the form of evidential failure of a small structural component, accelerative failure with visible weakness such as cracks and abrupt, sharp failures [2] etc.

Non-compliance to specification outlines of projects demand –amongst others- the use of non-standard materials, ineffective/unqualified team members of quality control rangers, fast track construction, poor detailed designs, etc. and may be regarded as are remote and immediate factors leading to failures [3]. Quality Control as a

process in road construction ensures conformity of the finished road pavement with required standards [4]. Quality defects are obtainable from the difference in the coefficient of variation of required elasticity modulus (*Creq <sup>v</sup>* ) from the standard elasticity modulus (*Cstd <sup>v</sup>* ) which is based on deflection patterns of geomaterials composition and dynamic load intensity on pavements. The wider the difference between such elasticity moduli, the higher the propensity to failure of pavements [5]. Owing to such probability outlook, their reliability estimate, takes the form of

$$R\_{p\_t} = \mathbf{0.5} + F \left[ \frac{E\_{eq} - E\_m}{\sqrt{\sigma\_{eq}^2 + \sigma\_m^2}} \right] \tag{1}$$

where *Eeq* is the equivalent modulus of elasticity, *Em* is the maximum modulus of elasticity, *σeq* is the equivalent modulus of elasticity and *σ<sup>m</sup>* is the mean square deviation of the maximum modulus of elasticity.

The process of quality control in road pavements follows the examination and test of composite materials towards meeting the correct specifications and required quality. Quality control in road projects follow stratification checks by separating roads composite materials and bringing them to specialized and accredited laboratories in order to conduct a series of tests on them. However, it is worth noting at this point that specific tests may also be done on site using checklists as the construction progresses.

Absence of quality control checks has often resulted to impaired quality outputs and poor workmanship [6]. Quality impairment in road construction processes shows that finishing road surfaces, construction process, labour workforce and materials used are in need of quality review and standardization for improvement [7]. The same applies to the workforce involved. Evidences of quality failures in constructed roads is revealed in their reliability values from their mean survival time to failure time, which are consequential fall-outs of quality management principles not being implemented. Quality in the context of road construction is when functionality is at equilibrium with a construction process output based on road utilization from effective road performance, durability, conformance, reliability, uniformity and serviceability [8]. Further to this, impaired quality of constructed roads are revealing in varying forms of cracks, potholes, bulges and surface depressions that often results in poor transportation systems, and delayed economic growth [9]. Quality impairment of roads indicates an increased level of reliability failures. The aim of this paper is to parametrically estimate their durability.

#### **2. Road construction and quality practice**

Road constructions are either flexible or rigid highway pavements with most or all of the following construction materials *viz.*, soil, aggregates, admixtures, Portland cement concrete, Bituminous materials, structural steel and pavement markers [10]. All of these materials are compositely layered together in a definite mix and proportion to output a quality road carriageway [11]. Determinants of high quality roads are subjects of quality tests on the various road materials enumerated above. Test on highway materials such as, Moisture Content Value (MCV), Los Angeles Abrasion Value, Dynamic Cone Penetrometer, Flakiness Index, Penetration Test on Bitumen,

#### *Quality Impairments in Flexible Road Pavements DOI: http://dx.doi.org/10.5772/intechopen.105697*

California Bearing Ratio (CBR), Softening point test on Bitumen and Ground Penetrating Radar tests are various laboratory test prerequisites for quality road [12].

**Table 1** presents road construction tests for quality assured output.

Flexible road pavements construction primarily consist of 70% asphalt bitumen content that provides binder mix with aggregate to produce asphalt concrete. This is laid on a bituminous base of a binder course. Stabilization of this process is followed by the application of tack coat of 0.75 kg per sq. metre [8]. Quality control standard as required in the preparation and placing of premix material is that bitumen is heated in the temperature range of (150–177<sup>0</sup> ) C within which aggregate temperature must not differ by 14°C from the binder temperature [13]. The hot mixed material of the bitumen and the aggregate together with the binder is then paved at a satisfactory temperature of not more than 163°C. This is followed for a smoother surface with a roller compaction at a speed not exceeding 5 km per hour. Preliminary or breakdown rolling uses 8 to 12 tonnes rollers and further pressurized or intermediate rolling is done using 15 to 30 tonnes fixed wheel pneumatic rollers.

During construction, the routine quality control checks carried-out to ensure quality output are often stipulated in the watch-out for resulting pavement mix, temperature at point of laying and pavement gauge or thickness. Other checks not necessarily routine but periodical are checks for aggregate grading, bitumen content grade, temperature of aggregate temperature of paving mix at mixing and compaction [14]. At every 100 tonnes of mix discharged by the hot mix plant samples are collected for the above tests. Another test for quality compliance is carried-out by implementing the Marshall test for every 100m<sup>2</sup> paved and compacted [15]. This is also followed by the field density check to see if 95% of laboratory density obtained shows congruency in the field. Tolerance of 6 mm per 5 m length of paved surface is allowed for variations in depth of pavements [16]. Variations from longitudinal undulations along the straight edge at every 3.0 m check must not exceed 8.00 mm and the number of undulations higher than 6.0 mm should not exceed 10 for every 300 m of road. Near absence of quality checks in road construction projects are traceable to road failures in the form of cracks, potholes, bulge and creter depressions. A typical quality controlled road pavement construction is shown in **Figure 1**.

Failed roads maybe regarded as evidences of quality neglects. Road failures are progressive in nature with monotonic properties of lebesgue measure theory with respect to progressive road component failures. A collection of road used in a similar traffic pressured fashion normally will show propensity to fail within predictable time measures [17]. Determination of such failings owing to quality neglect is provided for in Weibull reliability analysis under the scheme of plotting the percentage of road sections that have yielded to failure over a randomized time period measurable in cycle-starts, hours of run-times, miles driven, etc. [18]. Usually, classification of quality impairment is obtainable from Weibull reliability analysis with non-linear bathtub graph having to be approximated with line of best-fit, with *β* describing the classification in:

*β* <1*:*0= > Infant mortality = > Optimum quality impairment in construction.

*β* ¼ 1*:*0= > Randomized failure = > Progressive quality impairment during construction.

*β* >1*:*0= > Wear-Out Failure = > High quality impairment during construction. Most decent and prudent statistical inferences in Weibull test are parametrized with Time-to-Failure component of the road. This is historically accounted for by B (F) with 'F' representing the percentage of road section that have failed, while some parametrize by lifetime L(F) and 'B' representing bearing time. In the Weibull



*Quality Impairments in Flexible Road Pavements DOI: http://dx.doi.org/10.5772/intechopen.105697*

#### **Table 1.**

*Quality test metrics in flexible road pavements.*

**Figure 1.** *Components of flexible pavements in Hassan and Sobhan [13].*

statistics, the distribution shows the relationship between failed percentage with respect to time governed by constant shape factors '*β*' and '*η*' that determines shape and scale of distribution respectively by the function:

$$F(t) = \mathbf{1} - e^{\left(\frac{-t}{\eta}\right)^{\theta}} \tag{2}$$

Summing the monotonic progressive failures over time to the point of measurement generates a probability density function (PDF) describing the frequency of failures over time estimates as:

$$f(t) = \left(\frac{\beta}{\eta}\right) \left(\frac{t}{\eta}\right)^{\beta - 1} e^{-\left(\frac{t}{\eta}\right)^{\beta}}\tag{3}$$

Quality control checks on compacted geomaterials such as sub-base by a more precise measuring light weight deflectometer (LWD) device in the study of Duddu and Chennarapu [19] as against density and stiffness base methods with the aim of obtaining pavement deformation modulus (*ELWD* have shown better predictive ability of deformations). For instance LWD tests on geomaterials such as soils, aggregates, and asphalt had output of 35/60 *MPa* and 120/170 *MPa.* As a quality control reference, LWD tests presents the user with information on longer life cycle pavement performance and predictive failure indicator time. Confirmation of such parametric evaluations follows the regressive test between LWD and other density/stiffness methods with better coefficient of determinations *(R<sup>2</sup> ).* For instance, as outlined in the work of aforementioned researchers investigation of Sandy soil regression-correlation on California bearing ratio (CBR) and *ELWD* by Dwivedi and Suman [4] gave *R<sup>2</sup>* values of 0.807 for unsoaked sand (US), 0.805 for soaked (S) sand and dry density 0.77 with the following relationship:

$$\begin{aligned} \text{CBR}\_{(US)} &= \mathbf{0.0009E}\_{LWD} \, ^2 \\ \mathbf{CBR}\_{(S)} &= \mathbf{0.0001E}\_{LWD} \, ^2 \\ \text{Y}\_d &= \mathbf{1} \times \mathbf{10}^{-5} E\_{LWD} \, ^2 \end{aligned} \tag{4}$$

Quality controlled output limits using their coefficient of determination *(R2 )* on lime based stabilized subgrade soil from correlative studies with *ELWD* by in the literature of Bisht, Dhar and Hussain [20] for unconfined compressive strength (UCS) at *R*<sup>2</sup> = 0.99 and CBR at *R<sup>2</sup>* = 0.93 showed the following relation:

$$U\text{CS} = 4.9E\_{LWD} \tag{5}$$

$$\text{GBR} = \mathbf{0.15}E\_{\text{LWD}} \tag{6}$$

Studies by Nazzal, Abu-Farsakh, Alshibli and Mohammad [21] on crushed limestone and sandy soil geomaterials gave *R*<sup>2</sup> value of 0.83 between CBR and *ELWD* with the following relation:

$$\text{CBR} = -\mathbf{14} + \mathbf{0.66}E\_{LWD} \tag{7}$$

$$E\_{v2} = (\mathbf{600} - \mathbf{300})/(\mathbf{300} - E\_{LWD-L\_3})\tag{8}$$

as a correlate between Static modulus of layer 2 (*Ev*2Þ and modulus of deformation measured by a Zorn LWD device with 300 mm diameter plate. Such stress/strain on flexible pavement layers often transfer elasticity modulus for determining pavement structural durability between layers. This is governed from the computation of road's elastic modulus (*Egen*) based on 'g' the bearing capacity reserve of road bed and pavement in:

$$E\_{gen} = \frac{E\_1 E\_2 \left[ \mathbf{1} + \left( \frac{2h}{D} \right)^2 \left( \frac{E\_1}{E\_2} \right)^{\frac{2}{3}} \right]^{\frac{1}{2}}}{E\_1 - E\_2 \left\{ \mathbf{1} - \left[ \mathbf{1} + \left( \frac{2h}{D} \right)^2 \left( \frac{E\_1}{E\_2} \right)^{\frac{2}{3}} \right]^{\frac{1}{2}} \right\}} \tag{9}$$

A similar correlation investigation on soil classification test between static modulus of pavement layer 1and deformation modulus using light weight deflectometer (LWD) by Alshibli, Abu-Farsakh and Seyman [22] showed a quality allowable *R*<sup>2</sup> �value of 0.84. That of Rao, Shiva and Shankar [23] on subgrade geomaterials between CBR and *ELWD* gave an *R*<sup>2</sup> value of 0.90 with the following regression result;

$$E\_{v1} = \mathbf{0.91} E\_{LMD-P\_3} - \mathbf{1.81} \tag{10}$$

$$\text{CBR} = -2.754 + 0.2867 E\_{LWD} \tag{11}$$

where *ELWD*�*P*<sup>3</sup> is the modulus of deformation measured by Prima 100 Cohesive and non-cohesive soils. Adam and Kopf [24] provided regression functions between static modulus of layer 1 (*EvI*) and modulus of deformation from a Zorn LWD device with a 300 mm plate diameter. Deformation thresholds are predictable for quality control reasons for cohesive soils by the relationship:

$$E\_{v1} = \mathbf{0.833} \times E\_{LWD-x3} \tag{12}$$

And for non-cohesive soils with the relation;

**Figure 2.**

*Schematic sketch of the location and type of transducer: a geophone measures velocity and is located on the compacted material, b accelerometer measures vibrations and is located in the plate. Photo credit: Duddu and Chennarapu [19].*

$$E\_{v1} = \mathbf{1.25} \times E\_{LWD-x3} - \mathbf{12.5} (E\_{LWD-x3}) \vee\_{range} at \, \mathbf{10} - \mathbf{90} MPa \tag{13}$$

Quality control checks by light weight deflection (LWD) devices are conducted by velocity tracks using geophones or vibration tracks using accelerometer which is located on the test plate (see **Figure 2** from Duddu and Chennarapu [19]).

On the basis of limit state engineering designs, there are progressive failures at retail scales to yield a point of total failure beyond which roads become unserviceable to users before their expected lifetime span. Bazhanov and Saksonova [25] and Hassan and Sobhan [13] have shown that yield point in a quality impaired constructed road is attainable after a dynamic load is applied on pavements surface originating from a plastic deformation. Forms and types of road failures are shown in the accompanying **Table 2**.

According to Gupta [26], points of statistical references in reliability of pavement estimations are marked in the pavements failure rate (hazard rate) defined by:

$$r\_F(k) = \frac{P(k)}{\sum\_{i=k} P^{(i)}\text{,}}\tag{14}$$

$$\frac{P(X=k)}{P(X \le k)}, k = 0, 1, 2, \dots$$

With *P k*ð Þ¼ *P X*ð Þ ¼ *k* being the mass function, cumulative distribution function *f k*ð Þ¼ *P X*ð Þ <sup>≤</sup>*<sup>k</sup>* and pavement survival function *F k* ð Þ¼ <sup>1</sup> � *f k*ð Þ respectively. The pavements' mean residual life, (*μF*ð Þ*k* is indicated by estimation bias as:

$$\mu\_F(k) = E(X - k | X \ge k) = \frac{\sum\_{x=k} \bar{F}(x)}{F(k-1)}, k = 0, 1, 2, \dots \tag{15}$$

This estimation is premised on the deterioration force of decrement on the pavement lifespan which bears representation in plastic deformation in other to understand pavement tolerance [27]. Consequently, the pavement failure rates or hazard rates which are competing in risk value by a mortal force of decrement with mean residual life of pavement are relationally obtained by:

$$r\_f(k) = \frac{\mathbf{1} + \mu\_f(k+1) - \mu\_f(k)}{\mathbf{1} + \mu\_f(k+1)} \tag{16}$$

*Quality Impairments in Flexible Road Pavements DOI: http://dx.doi.org/10.5772/intechopen.105697*

*Quality Impairments in Flexible Road Pavements DOI: http://dx.doi.org/10.5772/intechopen.105697*


**Table 2.** *Types of road failure.* *Quality Impairments in Flexible Road Pavements DOI: http://dx.doi.org/10.5772/intechopen.105697*

$$1 - \frac{\mu\_f(k)}{1 + \mu\_f(k+1)}, k = 0, 1, 2, \dots$$

The augmented pavements failure rate, mean residual life and its survival which are estimable consequences of an impaired engineering works is signified in a quality deficit index by relating the three statistical variables as:

$$\bar{F}(k) = \prod\_{0 \le i \le k} \left[ \mathbf{1} - r\_{\mathcal{f}}(i) \right]$$

$$\prod\_{0 \le i \le k} \left[ \frac{\mu\_{\mathcal{f}}(i)}{\mathbf{1} + \mu\_{\mathcal{f}}(i+\mathbf{1})} \right], \mu(\mathbf{0}) = E(\mathbf{x}) \tag{17}$$

Following the competing mortal forces of decrement on pavements with failure induced components yield from several real time traffic loadings, correspond to variations in the lifetime survival of pavement obtainable by:

$$
\sigma\_F^2(k) = \text{Var}(\mathbf{x} - k \forall \mathbf{x} \ge k)
$$

$$
k^2 + \frac{\sum\_{i=k}^{\infty} (2i + 1)\bar{F}(i)}{\bar{F}(k-1)} - \left(\frac{\sum\_{i=k}^{\infty} \bar{F}(i)}{\bar{F}(k-1)} + k\right)^2
$$

$$
2\frac{\sum\_{i=k}^{\infty} \bar{F}(i)}{\bar{F}(k-1)} - (2k - 1)\mu\_F(k) - \mu\_F^2(k)\tag{18}
$$

In order to idealize how quality is impaired by statistical reliability variables, the pavement's failure rate, mean residual life and variance residual life functions have causal aggregation and estimated by:

$$
\sigma\_F^2(k+1) - \sigma\_F^2(k) = r\_F(k).
$$

Consequently, decreasing pavement variance residual life is X if X

$$
\sigma\_F^2(k+1) \le \mu\_F(k)[\mathbf{1} + \mu\_F(k+1)].
$$

and it is an increasing variance residual life if

$$
\sigma\_F^2(k+1) \ge \mu\_F(k)[1 + \mu\_F(k+1)],
$$

These statistical narrations in their numerical values are indicators of progressive failures with monotonicity properties for quality impairments assessment. In recent times, researches into deterioration rates of road pavements particularly in Riveros and Arredondo [28] and Al-Zahrani and Stoyanov [29] with transition probabilities indicated changes from one state to another (owing to deterioration). This illustrates precision predictability by Weibull distribution estimation. The probability density function are parametrized by ∝- and *β*- for which ð Þ ∝ >0, *β* >0 and given as:

$$F\_{(t)} = \int\_{\frac{\alpha}{\beta}}^{\rho} \left(\frac{t}{\beta}\right)^{\infty - 1} \exp\left[-\left(\frac{t}{\beta}\right)^{\infty}\right] \begin{cases} \text{for} t < 0\\ \text{for} t \ge 0 \end{cases} \tag{19}$$

And its distribution function as:

$$F(\mathbf{x}) = \int\_{1}^{0} \exp\left[-\left(\frac{\mathbf{x}}{\beta}\right)^{\infty}\right] \begin{cases} \text{for } \mathbf{x} < \mathbf{0} \\ \text{for } \mathbf{x} \ge \sigma \end{cases} \tag{20}$$

Under the Weibull test for pavement deterioration, expected values and variance are estimated by:

$$\mu = \beta^{-1} \left( 1 + \frac{\mathbf{1}}{\infty} \right), \sigma^2 = \beta^2 \left[ \left( 1 + \frac{2}{\infty} \right) - \mathbf{1}^2 \left( \mathbf{1} + \frac{\mathbf{1}}{\infty} \right) \right] \tag{21}$$

In this case, rather than Laplacian integral, the Weibull distribution is predicted on the gamma function

with: ð Þ ð Þ *<sup>x</sup>* ð Þ¼ *x* ð<sup>∞</sup> *o t x*�1 *e* �*t dtforx*>0 (22)

This chapter deployed the use of Weibull test to obtaining the deterioration rates of selected Benin city roads in cluster from generating their deterioration model by linear regression having deterioration state as a dependent variable and pavement as an independent variable.

#### **3. Methodology**

In this research study, quality impairment in road construction was assessed by field investigation of eight (8) failing roads from a purposive sampling from 19 failed roads in the Benin city metropolis of Nigeria. Obtaining life right censored data through measurements of component failed depth, width and length with a start and end observation times were obtained. In achieving this, a seven (7) days growth rate study of failed portions in five (5) different field visitations at an interval of three (3) months for each visit was conducted to enable the capture of variation in growth rate between visits. The research team also engaged four daily undergraduate students to support obtaining measurements and controlling traffic. From the historical data gathered, mixed Weibull distribution software (Reliasoft Weibull++) was used to analyze data goodness-of-fit test. Their reliability function was also tested in terms of their failure rate function and mean life function by estimating the parameters that makes the reliability function most closely fit the life data set. A review of the statistical criterion reference analytically for model fitness, shape parameters, assumed *βs* and graphically for fit to line, S-shape and minimum life was done from the reliability bathtub curve plot while computing their statistical function at 90% confidence bounds. **Tables 3**–**5** depict life data measurement of failed roads.

#### **4. Results and discussion**

**Figures 3**–**12** and **Tables 3**–**5** are discussed in this section.

*Quality Impairments in Flexible Road Pavements DOI: http://dx.doi.org/10.5772/intechopen.105697*

**Figure 3.** *Showing how water aids road failure.*

**Figure 4.** *Showing how water aids road failure.*

**Figure 5.** *Showing how failed portion of roads affects or increase journey time.*

**Figure 6.** *Failed portion in Luckyway Road.*

**Figure 7.** *Failed portion in Mission Road.*

**Figure 8.** *Failed portion in New Benin Road.*
