Polyparaphenylene Benzobisoxazole Research Articles

Fire Performance of FRCM-Confined RC Columns: Experimental Investigation and Parametric Analysis

This study presents an experimental investigation of the fire response of six columns strengthened with polyparaphenylene benzobisoxazole (PBO) FRCM system, and tested in a large-scale furnace following ASTM E119 standards. The parameters investigated included the number of PBO-FRCM layers and the presence of a fireproofing insulation layer. Test results highlighted the effectiveness of PBO-FRCM in insulating the column, with the strengthened column showing a substantial 31.9% reduction in temperature readings at the concrete surface compared to its unstrengthened counterpart. Furthermore, the presence of Sikacrete 213F fireproofing system reduced temperature readings within the column's section by an average of 65%. Based on the experimental results, a parametric numerical study were developed and verified using ABAQUS software. The parameters studied included the number of PBO-FRCM layers (0, 1, and 2 layers), the presence of a 30 mm thick insulation layer, and the axial preloading taken as 40, 60, and 75% of the ultimate column's capacity. The model accurately predicted the temperature readings across the columns. Strengthening the columns with PBO-FRCM significantly increased their resistance during fire, doubling fire-resistance duration with one layer. Adding fireproof insulation led to significant increase in load resistance duration. The percentage drop in temperature after 1 hour of fire exposure was around 70% at the FRCM surface for the insulated column strengthened with one layer of FRCM. Higher preload percentages reduced both the fire-resistance duration and ductility of the columns. For the group of columns strengthened with one layer, increasing the preloading percentage to 60% and 75% resulted in decreases in the fire-resistance duration of 35% and 73%, respectively.

FIRE RESPONSE OF CIRCULAR RC COLUMNS STRENGTHENED WITH PBO FRCM

The use of externally bonded fiber-reinforced system, specifically fiber-reinforced polymer (FRP) system, has increased over the past decades due to their demonstrated efficacy in enhancing the structural integrity of various RC members. However, the vulnerability of FRP systems to elevated temperatures has raised a major concern and led researchers to explore different strengthening systems. This paper investigates the fire performance of circular RC columns strengthened with poly-paraphenylene-ben-zobisoxazole (PBO) fabric-reinforced cementitious matrix (FRCM) system. Four identical columns were cast, three of which were strengthened with varying number of layers of PBO-FRCM. The fire exposure followed ASTM E119 standards. The temperature response curves were analyzed, and post-fire conditions were assessed. Initially, columns with a greater number of PBO-FRCM layers exhibited significantly lower temperatures. As the fire exposure time increased, FRCM strengthened columns experienced more significant spalling than the control column, where the reinforcement was visible from all sides. This excessive concrete spalling resulted in matching temperature readings in both the strengthened and non-strengthened columns.

FIRE RESPONSE OF CIRCULAR RC COLUMNS STRENGTHENED WITH PBO FRCM

The use of externally bonded fiber-reinforced system, specifically fiber-reinforced polymer (FRP) system, has increased over the past decades due to their demonstrated efficacy in enhancing the structural integrity of various RC members. However, the vulnerability of FRP systems to elevated temperatures has raised a major concern and led researchers to explore different strengthening systems. This paper investigates the fire performance of circular RC columns strengthened with poly-paraphenylene-ben-zobisoxazole (PBO) fabric-reinforced cementitious matrix (FRCM) system. Four identical columns were cast, three of which were strengthened with varying number of layers of PBO-FRCM. The fire exposure followed ASTM E119 standards. The temperature response curves were analyzed, and post-fire conditions were assessed. Initially, columns with a greater number of PBO-FRCM layers exhibited significantly lower temperatures. As the fire exposure time increased, FRCM strengthened columns experienced more significant spalling than the control column, where the reinforcement was visible from all sides. This excessive concrete spalling resulted in matching temperature readings in both the strengthened and non-strengthened columns.

Experimental and numerical investigation of two–span RC beams strengthened with fiber–reinforced cementitious matrix (FRCM)

This paper investigated both experimentally and numerically the flexural performance of two–span beams after being strengthened with polyparaphenylene benzobisoxazole (PBO) fiber–reinforced cementitious matrix (FRCM) systems at different hogging–to–sagging (H/S) strengthening ratios. The test results revealed that the enhancement in the flexural response of the strengthened beams was highly dependent on the strengthening configuration and the number of layers used in both the hogging and sagging sections. The H/S ratio had a notable effect on the failure modes of the hogging sections only whereas the sagging sections showed similar failure modes regardless of the H/S used. Strengthening the sagging sections governed the ductility of the tested beams with a slight effect of the H/S ratio on their ductility. Despite strengthening, the hogging sections were capable to redistribute up to 37% of their moments to the sagging sections, which represented 93% of the redistribution capacity of the unstrengthened sections. This finding suggests the revision of the CSA and ACI formulations that prohibit any moment redistribution in the design of externally–bonded strengthened elements. The developed finite element model accurately predicted the experimental results in terms of the failure modes, the load–carrying capacity, the ductility, and the moment redistribution ratios between the critical sections.

Seismic assessment and strengthening of a historical masonry bridge considering soil-structure interaction

A holistic methodology for developing the digital twins and conducting seismic vulnerability assessments of masonry arch bridges is proposed and applied to a historical stone masonry bridge. In this light, digital cameras, drones, and 3D laser scanners were utilized for 3D geometric documentation of the bridge. 3D finite element (FE) models were constructed and calibrated based on the operational modal analysis results derived from the accelerometer sensors. The fragility curves for different limit states were derived by performing a multi-stripe analysis (MSA). The effect of soil-structure interaction (SSI) on the calibration results and seismic response of the bridge was evaluated. The results of the visual inspection, model calibration, and seismic analysis revealed that the central pier and the arches are the most susceptible parts of the bridge. Therefore, three strengthening techniques were proposed, and corresponding numerical models were developed. The first model was developed by enhancing the mechanical properties of the vulnerable parts of the bridge, and the two other models were built by covering the central pier’s outer surface with polyparaphenylene benzobisoxazole (PBO) and carbon fiber-reinforced concrete mortar (FRCM) layers. Results revealed that the strengthening techniques improved the seismic response of the bridge when subjected to transverse seismic excitations. Negligible differences in the displacement response and crack width of the strengthened models were observed from the nonlinear dynamic analysis.

Symmetric and Asymmetric Strengthening of Two-Span RC Beams Using FRCM Systems

This paper reports on the feasibility of using fabric-reinforced cementitious matrix (FRCM) systems to strengthen two-span reinforced concrete (RC) beams that are structurally deficient in their sagging regions. In addition to one unstrengthened control beam, nine beams strengthened either symmetrically or asymmetrically with polyparaphenylene benzobisoxazole (PBOFRCM), carbon (CFRCM), and carbon fiber–reinforced polymer (CFRP) sheets were tested under a five-point load configuration. Test results showed that increasing the strengthening ratio resulted in significant increases in the yielding and load-carrying capacity of the beams. Beams symmetrically strengthened with PBOFRCM showed high ductility indices ranging between 100% and 121% of that of the control beam, whereas those strengthened with CFRCM and CFRP showed ductility indices of 45% and 34% of that of the control beam, respectively. Moreover, beams symmetrically strengthened with PBOFRCM systems encountered moment redistribution ratios between 42% and 82% of that of the control beam compared with 10% and 9% only for those strengthened with CFRCM and CFRP systems, respectively. The asymmetric strengthening configuration in which FRCM systems were used along with CFRP sheets proved to be an efficient method to enhance the ductility and moment redistribution capacity of the strengthened beams. Analytically, the rigid-body-rotation approach was modified to predict the moments and curvatures at the plastic hinges of the strengthened sections. The predicted moments and curvatures showed a notable agreement with the experimental values.

Shake-table testing and numerical simulation to select the FRCM retrofit solution for flexure/shear deficient RC frames

This paper presents shake-table and numerical investigations to select a retrofit strategy for reinforced concrete (RC) frame structures using fiber-reinforced cementitious matrix (FRCM) composites. Two FRCM alternatives are investigated, namely polyparaphenylene benzobisoxazole (PBO) and carbon FRCM composites, denoted as ‘P-FRCM’ and ‘C-FRCM’, respectively. The study focuses on implementing the selected retrofit material with spike anchorage systems to delay the debonding failure and addresses different failure modes of RC framing systems, including shear or flexure failure. The first phase of this study involves pre shake-table test (STT) simulation to investigate the effectiveness of the selected retrofit technique in delaying local and global damage states and failure modes. STT campaigns are undertaken in the second phase to assess the seismic performance of framing systems retrofitted with different FRCM materials and verify their fiber-based modeling approach. The verified numerical modeling approach of the retrofit techniques is utilized in the third phase to upgrade a benchmark RC moment-resisting frame (MRF) building. A parametric study involving inelastic pushover analyses (IPAs) and multi-record incremental dynamic analyses (IDAs) is finally conducted to assess the vulnerability of the retrofitted building with different FRCM alternatives. It is concluded that the adopted two retrofit techniques significantly reduced the collapse damage state at the design and maximum considered earthquake intensities by up to 59% and 46%, respectively. Although the P-FRCM composite has 38% higher tensile strength and 76% higher ultimate tensile strain than C-FRCM, it slightly improves the overall seismic performance by up to 9% based on the adopted seismic performance index. Owing to the higher cost of P-FRCM compared with its counterpart, a performance-to-cost index confirmed that the C-FRCM composite is the preferred retrofit technique for MRF structures.

Experimental investigation of pre‐damaged circular RC columns strengthened with fabric‐reinforced cementitious matrix (FRCM)

AbstractThis paper aims at investigating the efficiency of strengthening pre‐damaged circular reinforced concrete (RC) columns with Polyparaphenylene Benzobisoxazole fabric‐reinforced cementitious matrix (PBO‐FRCM). The investigated parameters were the degree of pre‐damage (non‐damaged, damaged monotonically up to yielding, or fatigue damaged), the number of PBO‐FRCM layers (0, 2, or 4), and the tie spacing (180 or 90 mm). The experimental results of testing 12 short columns under axial compression showed that PBO‐FRCM systems enhanced the capacity of the non‐damaged columns and successfully restored and further enhanced the capacity of the pre‐damaged columns. Columns strengthened with two and four PBO‐FRCM layers showed a gain in the capacity of up to 40% and 75%, respectively. Furthermore, PBO‐FRCM wrapping enhanced the ductility of both the non‐damaged and the pre‐damaged columns, in which ductility improvement was more noticeable in columns with the larger tie spacing. Finally, the theoretical load‐carrying capacity calculated using ACI 549 provisions showed a good agreement with the experimental capacity of all tested columns.

Open issues on the investigation of PBO FRCM-Concrete debonding

This paper addresses some open issues of the bond behavior of fiber-reinforced cementitious matrix (FRCM) composites applied to a concrete substrate. The study is focused on the effect of the number of fiber layers on the peak load, the effect of the loading rate on the load response, the relationship between peak load and bonded length (considering also bonded lengths substantially longer than the effective bond length), and the information that can be gained by measuring the slip at the free end of the bonded composite. The FRCM composite investigated is comprised of polyparaphenylene benzobisoxazole (PBO) fibers and a polymer-modified cementitious mortar. The experimental results are compared with results from the literature. The results indicate that the peak load must be carefully interpreted considering the effect of friction (interlocking), which is observed to occur between fibers and matrix and the fibers themselves. In addition, the effect of the loading rate requires additional investigation. Finally, the peak load of specimens with two layers of PBO fiber mesh is approximately double the peak load of tests with one layer of fiber mesh if the bonded length is longer than the effective bond length determined from tests with one layer of fiber mesh.

FINITE ELEMENT ANALYSIS OF FRCM RETROFITTED PRE-DAMAGED SLENDER CIRCULAR RC COLUMNS

Reinforced Concrete structures face adverse deterioration during their life cycle. Fiber reinforced cementitious matrix (FRCM) is a strengthening system combining fiber reinforced polymer (FRP) bonded with traditional cement-based mortar. This strengthening system is easy to apply and eliminates the toxic hazard associated with epoxy bonded FRP. ABAQUS is used to develop nonlinear three-dimensional finite element (FE) models to investigate the potential of this novel retrofitting system to restore the original axial capacity and behavior of corrosion pre-damaged slender circular reinforced concrete columns. Poly-paraphenylene-ben-zobisoxazole (PBO) fibers are used in the strengthening system due to favorable mechanical properties. Nonlinearities in concrete, cementitious matrix and PBO fibers are accounted for in the FE model. Published literature is used to verify the FE models based on column axial capacity and observed failure mode. A parametric study is carried out through varying the number FRCM layers (1, 2, 3 and 4), corrosion pre-damage level (30%, 50% and 70%), slenderness ratio (short/800mm and slender/1200mm) and ratio of eccentricity (0.0, 0.3, 0.5, 0.75, 1.0, 1.25 and 1.5). Compressive strength of 30 MPa is used in all columns and along with 2% reinforcement ratio and recommended CDP parameters. Results are presented and contrasted and the potential of the novel retrofitting system to repair and enhance the behavior of slender circular columns is evaluated.

FINITE ELEMENT ANALYSIS OF FRCM RETROFITTED PRE-DAMAGED SLENDER CIRCULAR RC COLUMNS

Reinforced Concrete structures face adverse deterioration during their life cycle. Fiber reinforced cementitious matrix (FRCM) is a strengthening system combining fiber reinforced polymer (FRP) bonded with traditional cement-based mortar. This strengthening system is easy to apply and eliminates the toxic hazard associated with epoxy bonded FRP. ABAQUS is used to develop nonlinear three-dimensional finite element (FE) models to investigate the potential of this novel retrofitting system to restore the original axial capacity and behavior of corrosion pre-damaged slender circular reinforced concrete columns. Poly-paraphenylene-ben-zobisoxazole (PBO) fibers are used in the strengthening system due to favorable mechanical properties. Nonlinearities in concrete, cementitious matrix and PBO fibers are accounted for in the FE model. Published literature is used to verify the FE models based on column axial capacity and observed failure mode. A parametric study is carried out through varying the number FRCM layers (1, 2, 3 and 4), corrosion pre-damage level (30%, 50% and 70%), slenderness ratio (short/800mm and slender/1200mm) and ratio of eccentricity (0.0, 0.3, 0.5, 0.75, 1.0, 1.25 and 1.5). Compressive strength of 30 MPa is used in all columns and along with 2% reinforcement ratio and recommended CDP parameters. Results are presented and contrasted and the potential of the novel retrofitting system to repair and enhance the behavior of slender circular columns is evaluated.

Strengthening pre-damaged RC square columns with fabric-reinforced cementitious matrix (FRCM): Experimental investigation

This study investigates the effectiveness of using fabric-reinforced cementitious matrix (FRCM) systems in repairing pre-damaged reinforced concrete (RC) square columns. Two groups of columns were fabricated and tested under concentric loading up to failure. Columns of each group had different spacing between their transverse reinforcement to investigate the effectiveness of FRCM reinforcement in confining the columns. The columns were subjected to two pre-damaging criteria prior to strengthening. Four columns were loaded up to their yielding capacity and then unloaded while the other two columns were subjected to three cycles of fatigue loading that ranged between 2% and 75% of the unstrengthened column’s capacity. The pre-damaged columns were then strengthened with either two or four layers of polyparaphenylene-benzobisoxazole (PBO)–FRCM system. Test results showed that confining the pre-damaged columns with PBO–FRCM systems resulted in 7–42% enhancement in their load–carrying capacity and 47–272% improvement in their ductility. The predicted columns’ capacity calculated as per ACI 549 guidelines showed a good agreement with the experimental results. The experimental–to–predicted capacity ratio ranged between 0.82 and 1.03 for columns with tie spacing of 180 mm and between 0.92 and 1.09 for columns with tie spacing of 90 mm.

Long-Term Behavior of PBO FRCM and Comparison with Other Inorganic-Matrix Composites.

Fabric-reinforced cementitious matrix (FRCM) composites, comprising high-strength fiber textiles embedded within inorganic matrices, represent an effective, cost-efficient, and low-invasive solution for strengthening and retrofitting existing masonry and reinforced concrete structures. Among different textiles employed in FRCM composites, polyparaphenylene benzo-bisoxazole (PBO) textiles are adopted due to their high tensile strength and good adhesion with the matrix. Although several experimental, numerical, and analytical works were performed to investigate the mechanical properties of PBO FRCM composites, limited information is available on their long-term behavior, as well as in the case of exposure to aggressive environments. This paper presents and discusses the results of a wide experimental campaign aimed at investigating the effect of different environmental conditions on the long-term tensile behavior of a PBO FRCM composite. Tests are performed using a clamping-grip tensile test set-up. The effect of various aggressive environments on the composite matrix cracking stress, composite tensile strength, ultimate strain, and fully cracked stage slope is investigated by comparing the results of nominally equal conditioned and unconditioned (control) specimens. These results are also compared with those of other FRCM composites comprising glass and carbon textiles subjected to the same conditionings, collected from the literature. The results show only limited reductions in the tensile properties, even after long exposure to aggressive environments.

Experimental Qualification of PBO-FRCM Composites for Retrofitting Masonry Structures

This paper discusses the experimental qualification process of Fabric Reinforced Cementitious Matrix (FRCM) composites with Polyparaphenylene BenzobisOxazole (PBO) textiles. FRCMs consist of fiber textiles incorporated within inorganic cement or lime mortar matrices and have emerged as composite materials suitable for the retrofit of unreinforced masonry structures. The Italian Ministry of Infrastructures and Transportation and the European Organization for Technical Assessment have developed guidelines defining standard tests to certify the FRCM mechanical properties for qualification and acceptance purposes. This paper presents part of the experimental qualification results for PBO-FRCM composites with two PBO textiles (unidirectional and bidirectional) applied to two different masonry substrates (clay bricks and tuff blocks), considering tensile, bond and durability behavior. Direct tension tests were carried out on PBO textiles and FRCM specimens, with or without textile lap splices. Single-lap tests allowed determining the bond properties of both FRCMs on clay-brick and tuff-block masonry substrates. The stability of the tensile properties with respect to degradation induced by environmental actions was evaluated by performing direct tensile tests also on FRCM specimens conditioned in humid, saline, and alkaline environments, or subjected to high-temperature stress.

Finite Difference Model for the Bond Behaviour of Polyparaphenylene Benzobisoxazole (PBO) Fibre-Reinforced Composite System for Retrofitting Masonry

This study addresses a numerical investigation of the bond behaviour exhibited by an FRCM system when subject to tensile and single direct shear tests. A reinforcement system, based on a polyparaphenylene benzobisoxazole (PBO) bi-directional fibre mesh and a mixed cement-pozzolanic mortar is selected. The system is characterized by the presence of coated glass-fibre yarns and dry polypropylene yarns alternated to the PBO yarns in the warp and weft directions, respectively. The mechanical characterization of composite constituent materials is carried out together with tensile and direct shear tests. Concerning mechanical interpretation of the tests, within a mode II fracture mechanics, and assuming a trilinear cohesive material law (CML), the stress transfer law between the fibre and the matrix is back calibrated from single direct shear test results. The CML obtained is employed into a finite-difference model developed for the purpose. Tensile tests are modelled providing adequate boundary conditions. Results satisfactorily agree with the tested behaviour of the FRCM system.

Relationship between Results of Tensile Test of FRCM Composites and the Fiber-Matrix Bond Properties

The mechanical properties of fiber-reinforced cementitious matrix (FRCM) composites are derived from tensile tests of composite coupons and shear tests of composite strips bonded to the substrate. Different test set-ups are used for tensile coupons, which lead to different tensile responses depending on the mechanical properties of the matrix and bond properties of the fiber-matrix interface. Direct shear tests are employed to study the stress-transfer between the composite and the substrate onto which the composite is bonded. These tests can be employed to obtain the cohesive material law (CML) that describes the bond behavior at various interfaces, such as the matrix-substrate, matrix-matrix, and fiber-matrix interface. In this paper, the cohesive material law associated with the fiber-matrix interface of a polyparaphenylene benzo-bisoxazole (PBO) FRCM composite is employed in an analytical model to reproduce the tensile response of the FRCM composite, when the fibers are gripped directly. The results of the model are compared with corresponding experimental results of tensile tests of the same FRCM composite employed to calibrate the CML. The experimental work includes digital image correlation (DIC) analysis of the cracking process. A comparison between the analytical and the experimental results is performed in terms of load response focusing on the coupon deformation and opening of the cracks.

Calibration of a Rigid-Trilinear Cohesive Material Law to Describe the Matrix-Fiber Bond Behavior in FRCM Composites

Fiber-reinforced cementitious matrix (FRCM) composites have been increasingly adopted as externally bonded reinforcement (EBR) of existing concrete and masonry members. Being debonding at the matrix-fiber interface one of the most frequent failure mechanisms of externally bonded FRCM, the matrix-fiber bond behavior represents a fundamental aspect for the effectiveness of the external reinforcement. A cohesive material law (CML) that describes the interface where debonding occurs can be used to model the bond behavior observed. In this paper, a rigid-trilinear CML is used to solve the differential equation that governs the bond problem at the matrix-fiber interface of an FRCM composite. The CML adopted has peculiar characteristics that entail for a finite length of the bond stress transfer zone (BSTZ). Furthermore, it allows for a simple and accurate analytical solution of the bond problem. The analytical solution obtained is compared with the results of an experimental campaign comprising single-lap direct shear tests of a polyparaphenylene benzobisoxazole (PBO) FRCM composite specifically designed for masonry substrates. Different calibrations of the rigid-trilinear CML are proposed, also considering the matrix-fiber free end slip.

FRCM Strengthening of Corrosion-Damaged RC Beams Subjected to Monotonic and Cyclic Loading

Abstract An experimental investigation assessed the effectiveness of carbon and polyparaphenylene benzobisoxazole (PBO) fabric-reinforced cementitious matrix (C-FRCM and PBO-FRCM) systems in rehabi...

Strengthening the hogging and sagging regions in continuous beams with fiber-reinforced cementitious matrix (FRCM): Experimental and analytical investigations

This paper reports on the flexural performance of ten reinforced concrete (RC) continuous beams strengthened with fabric-reinforced cementitious matrix (FRCM) systems. The test parameters included the type of the strengthening system used, the location of the deficient section that required strengthening, and the number of the fabric layers used. Apart from two unstrengthened control beams, two beams were strengthened with two layers of Polyparaphenylene benzobisoxazole (PBO) FRCM. The other six beams were strengthened with four layers of PBO-FRCM, two carbon FRCM (C-FRCM), and one layer of carbon fiber-reinforced polymer sheet (CFRP), all having the same axial stiffness. The test results confirmed the excellent rotational capacity of the FRCM-strengthened beams and their ability to efficiently redistribute moments between their critical sections. The moment redistribution ratio ranged between 20 and 31% for beams strengthened with FRCM in their hogging regions (51 and 77% of that of the control beams) compared to 8 and 13% for those strengthened in their sagging regions (42 and 65% of that of the control beams). The FRP-strengthened hogging and sagging sections showed moment redistribution ratios that ranged between 15 and 2%, respectively (37 and 9% of that of the control beams). The FRCM-strengthened beams also showed a remarkable ductile response with an average ductility index of 90% of that of their control beams compared to 42% only for the FRP-strengthened ones. Analytically, the capacity of the FRCM-strengthened beams predicted using a strain model that was previously developed by the authors agreed well with the experimental capacity obtained during the tests with an experimental-to-predicted ratio of 0.99 ± 0.02.

Continuous Reinforced Concrete Beams Strengthened with Fabric-Reinforced Cementitious Matrix: Experimental Investigation and Numerical Simulation

This paper aims to examine the nonlinear flexural behavior of continuous RC beam specimens strengthened with fabric-reinforced cementitious matrix (FRCM) composites through experimental testing and numerical modeling. A total of nine two-span RC beam specimens were constructed and tested. Test parameters included the type of FRCM (carbon (C-FRCM) and polyparaphenylene benzobisoxazole (PBO-FRCM)), location of strengthening (sagging and hogging regions) and number of FRCM layers (two and four layers). Test results indicated that sagging strengthening resulted in a strength gain in the range of 17 to 29%, whereas hogging strengthening increased the load capacity by 9 to 17%. The use of C-FRCM resulted in a higher strength gain than that provided by PBO-FRCM composites. Specimens strengthened with PBO-FRCM exhibited, however, higher ductility and deformational capacity than those of their counterparts strengthened with C-FRCM. Doubling the number of FRCM layers resulted in no or insignificant increase in the load capacity but reduced the beam ductility. Specimens strengthened in the sagging regions exhibited moment redistribution ratios of 13 to 26% between the hogging and sagging regions. Insignificant moment redistribution was recorded for the specimens strengthened in the hogging region. Three-dimensional (3D) numerical simulation models, with and without an interfacial bond-slip law at the fabric–matrix interface, were developed. The inclusion of the bond-slip law in the modeling had an insignificant effect on predicted response. Although the models tended to underestimate the deflection, the predicted load capacities were within a 12% error band. Numerical findings were in agreement with those obtained from laboratory testing.