Long-Term Cured-In-Place Pipe (CIPP) Performance and its Design Implications

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1 Long-Term Cured-In-Place Pipe (CIPP) Performance and its Design Implications Robert K. Lee 1*, Steve Ferry 2 1 Malcolm Pirnie, Inc. 2 Hauser Laboratories. *To whom correspondence should be addressed. rlee@pirnie.com. ABSTRACT Cured-in-place pipe (CIPP) lining is an attractive alternative for rehabilitating pipes without the need for digging. However, the nature of CIPP is, in essence, a pipe manufactured below ground. And unlike prefabricated materials that have been through a series of long-term testing, below ground manufacturing introduces a host of variables (variable installation conditions, different installation methodologies, etc.) in the short and long-term reliability of CIPP as a pipe material. Contractors, engineers, and utility owners have generally accepted that CIPP has a 50-year design life and most CIPP designs assume that the longterm properties of the liners will retain 50% of their initial value. This paper addresses the various ways to test and anticipate the long-term performance of CIPP liners and verify the true design life. The paper also presents options available to Owners and Engineers if test results are not as expected. KEYWORDS: Cured-in-place pipe, CIPP, long-term testing, ASTM D2990, CIPP design, CIPP design life, pipe rehabilitation. INTRODUCTION Since the first North American cured-in-place pipe liner was installed in 1971, CIPP has increasingly become an attractive method to rehabilitate buried infrastructure without the invasiveness of digging up the old line and replacing it with new materials. However, new materials are fabricated in a controlled environment with strict manufacturer quality control practices and rigid testing requirements. Cured-inplace pipe liners, on the other hand, are often subject to potentially volatile environmental conditions and often unmonitored quality control practices. Materials used in the installation of CIPP, such as uncured resin, are often processed in a wet-out facility, shipped in (hopefully) a controlled environment, and installed in varying conditions. In essence, cured-in-place pipe liners are field-fabricated pipes. Despite these variable installation and fabrication practices, the CIPP industry has generally accepted a 50- year design life based on manufacturer-published long-term strength properties of their cured-in-place liners. METHODOLOGY When rehabilitating pipelines using CIPP, liners are designed based on a number of criteria. These criteria include: Existing pipe shape and condition Depth Geotechnical conditions Proposed CIPP materials (i.e., flexible tube and resin) Groundwater and other loads All CIPP have four essential components: a flexible tube, a thermosetting resin that impregnates the tube, a method to install and expand the impregnated tube, and a method to cure (i.e., harden) the resin. The tube

2 Lee & Ferry and resin are normally manufactured by separate manufacturers. A third-party normally purchases these materials, impregnates the tube with the resin, and then installs the CIPP. Round (or generally round) CIPPs (both gravity pipes and pressure pipes) are often designed using the ASTM Standard F1216, Appendix X1 design equations. Non-round pipes are designed using non- American standards, such as the Water Research Council (WRc) manual. In either method, the design equations utilize the long-term physical properties of the liners to determine the appropriate thickness necessary to withstand sustained loading over the design life of the pipe. Depending on the existing pipe to be lined and the criteria listed above, the required thickness is calculated from a series of design equations, and the largest thickness is then selected for the installation. Table 1 Long-Term CIPP Properties Used in ASTM Design Equations. ASTM F1216 Appendix X1 Applicability / Design Condition Long-Term CIPP Physical Property Used in Design Equation Equation X1.1 Support hydraulic loads (groundwater) Long-Term Modulus of Elasticity Equation X1.2 Minimum thickness if pipe is out-of-round Long-Term Flexural Strength Equation X1.3 Support soil, hydraulic, and live loads Long-Term Modulus of Elasticity Equation X1.4 Minimum thickness for round pipe None Equation X1.6 Repair of hole in pressure pipe Long-Term Flexural Strength Equation X1.7 Withstand internal pressure (pressure pipes) Long-Term Tensile Strength The modulus of elasticity of a material is a measure of the material s stiffness. It is also commonly used to indicate the elasticity of the material (McGraw Hill, 2003). The modulus of elasticity can aid in predicted the behavior of a material under a given load. For gravity pipes, this is key parameter is understanding the response of the round pipe in withstanding loads. Flexural strength is the ability of a material to withstand bending (McGraw Hill, 2003). It is also known as bending stress. The flexural strength is the critical parameter in withstanding buckling of the CIPP, either in the straight sections of non-round pipe or repair of holes in pressure pipe. Tensile strength is the resistance of a material to rupture when subject to tension (McGraw Hill, 2003). When a pipe is subject to internal pressure, stress is exerted in all directions from the inside of the pipe outward. As Table 1 illustrates, these long-term properties of cured-in-place pipe liners are critical to proper design. But since each liner is installed under unique and varied conditions, the true long-term properties of each particular liner are unknown. Typical Engineering Design Approach The typical approach taken by engineers and designers in the past involved using short-term laboratory testing data on the modulus of elasticity (also known as flexural modulus), flexural strength, and tensile strength, and apply the widely-accepted industry standard of a 50% reduction to each parameter. This approach is flawed in several ways: 1. Samples used in laboratory testing are often created above-ground in a controlled setting. 2. Laboratory testing on samples are typically performed at the request of the resin manufacturers, but the samples often do not specify the flexible tube used which can either increase or decrease the short and long-term properties. 3. The field-fabricated nature of CIPP may result in actual physical properties differing from the above-grade controlled-environment samples. 4. The testing used to determine long-term physical properties is often performed in laboratory conditions that are vastly different than that of buried pipelines (e.g., controlled curing, stable temperatures, etc.). Laboratory prepared samples often demonstrate much higher test results (Schiro et al., 2007). 5. The long-term physical properties of the liners, in addition to the problems mentioned above, are often determined using questionable or unverified extrapolation methodology. 2

3 Long-Term Cured-In-Place Pipe (CIPP) Performance Unfortunately, it is not always possible to use actual testing results from field-installed samples of CIPP during the design phase; manufacturer-published literature may be the only option. Information Provided by Manufacturers In past few years, it has been difficult finding published long-term values from CIPP-component manufacturers for use during design. Discussions with three different resin manufacturers resulted in the following conclusions: 1. Resin manufacturers rarely had long-term data readily available. 2. When long-term data was available, laboratory test conditions were either unknown (and therefore unspecified) by the manufacturer or were in a dry environment with an arbitrary loading. 3. Testing was sometimes performed by an outside-certified laboratory and sometimes performed by the manufacturer s internal laboratory. 4. Testing was not always performed in accordance with ASTM D2990 standards, such as the frequency of taking data readings during long-term testing. 5. Samples used in testing were normally prepared using non-reinforced polyester tube. However, specific data on the tube was not available. 6. Extrapolation of results was usually performed using all data points, resulting in high extrapolated values. Using these long-term values during the design and submittal phase of any CIPP project would be questionable engineering practice at best. Engineering judgment must be used before accepting and using manufacturer information in designing CIPP. It is of critical importance that the design incorporates an understanding of the ASTM testing requirements, reporting of results, and extrapolation of results out to the stated design life in a reasonable and scientific manner. For example, Figure 1 shows an example of manufacturer-submitted test results on a CIPP resin. In this submittal, the 50-year flexural modulus was equal to 990 megapascals (MPa) (143,000 pounds per square inch (psi)). However, the trendline is taken through all the data and the trendline does not fit the last several data points, the most critical points in extrapolating out to 438,000 hours or 50-years. Extrapolation of the data points from 700 to 10,000 hours reveals a 50-year flexural modulus of 430 MPa (62,000 psi), less than 50% of the manufacturer-published long-term flexural modulus (Figure 2). 3

4 Lee & Ferry Figure 1 Manufacturer-Submitted Long-Term Test Data Manufacturer Extrapolation. Figure 2 Manufacturer-Submitted Long-Term Test Data, Independent Extrapolation. 4

5 Long-Term Cured-In-Place Pipe (CIPP) Performance Long-term testing is typically performed for 10,000 hours. The knee of the curve is often observed around 1,000 hours on standard CIPP materials. Therefore, the data between 1,000 and 10,000 hours is the most linear and thus most reliable for extrapolating out to the design life. It is recommended that the extrapolation method for both manufacturer-submitted data and for evaluation of actual field-sample test results (discussed later) be clearly outlined in the Contract Documents. Definitions of Various CIPP Physical Properties In discussing material property testing, it is sometimes best to start with definitions of the various parameters involved. We will be discussing stress, strain, flexural modulus, and creep, specifically flexural creep. Starting with the basics, using definitions from Roark s Formulas for Stress and Strain (2002): Stress is defined as the internal force exerted by either of two adjacent parts of a body upon the other across an imagined plane of separation. Strain is defined as any forced change in the dimensions of a body. The equations for calculation of flexural stress and strain can be obtained directly from ASTM D790, Standard Test Methods for Flexural Properties of Unreinforced and Reinforced Plastics and Electrical Insulating Materials with mathematical formulae as follows: Flexural Stress (Strength) = 3PL/2bd 2 and Flexural Strain = 6Dd/ L 2. Thus, with any modulus generally defined to be the rate of change of unit stress with respect to unit strain, the mathematical formula for flexural modulus of elasticity is E B = L 3 m/4 bd 3. For all of these equations, the calculated stress is defined to be at the outer fibers at midspan, P is the load, L is the support span, b and d are the width and depth of the beam specimen respectively, D is the midspan deflection, and m is the slope of the tangent to the initial straight-line portion of the load-deflection curve. The rate of straining as described within ASTM D790 Procedure A is 0.01 cm/cm/min, or 1% per minute. These tests are typically run to 5% strain, or approximately 5 minutes per test specimen. Within the product specification ASTM D5813, Standard Specification for Cured-In-Place Thermosetting Resin Sewer Piping Systems, the test protocol for the determination of flexural strength and tangent flexural modulus and the product requirements are well defined. Specifically, ASTM D790 Test Method I- Procedure A is called out, with minimum flexural strength of 31 MPa (4500 psi) and minimum flexural modulus of 1724 MPa (250,000 psi) required. Creep is defined by Roark (2002) as continuous increase in deformation under constant or decreasing stress. Additionally, creep is defined within ASTM D883, Standard Terminology Relating to Plastics as the time-dependent part of strain resulting from stress. Note that within ASTM D5813 there is no mention of creep, either from a product requirement or test method perspective. Creep is mentioned within ASTM F1216, Standard Practice for Rehabilitation of Existing Pipelines and Conduits by the Inversion and Curing of a Resin-Impregnated Tube. It is mentioned in vague terms in Note A of Table 1 CIPP Initial Structural Properties as long-term structural properties, and also in the Appendix X1. Design Considerations as E L = long-term (time corrected) modulus of elasticity for CIPP, psi. Creep retainage would therefore be defined as the percentage of the initial flexural modulus as determined by ASTM D790 at the specified design life (e.g., 50-years). Testing Parameters At this stage in the product specification and installation practice there is somewhat of a breakdown in the instructions to testing laboratories as to how to test and calculate creep resistance of CIPP materials. There currently are no details to this process contained within any ASTM document. Hauser does adhere to the requirements of D2990 wherever applicable, but in general the testing performed would be considered a limited D2990 protocol in that only one set of 5 specimens are tested through 10,000 hours duration at 23 C. This is in agreement with the verbiage of ASTM D2990 Section 10, Selection of Test Conditions: Selection of temperatures for creep and creep-rupture testing depends on the intended use of the test results and shall be made as follows. (Section 10.1) To obtain design data, the test temperatures and environment shall be the same as those of the intended end-use application. (Section ) 5

6 Lee & Ferry However, one of the main items required for creep testing, the imposed flexural stress at the start of the creep exposure, is not defined in any of the relevant documents. There is some guidance in the international literature indicating that an imposed stress equal to 0.25% of the short-term flexural modulus is to be used. Note that this would correspond to the stress required to impose 0.25% initial strain in the test specimens. This 0.25% test criterion is contained within a now-unavailable British Water Research Council fiberglass pipe rehabilitation product specification (with embedded test methods). Creep is typically performed in accordance with ASTM D2990, Standard Test Methods for Tensile, Compressive, and Flexural Creep and Creep-Rupture of Plastics. The basic equipment is quite simple, consisting of a rack to hold the specimens in 3 point flexure, dial indicators to measure deflection at midspan, and deadweights to load the specimens at midspan. The testing is performed at constant stress (load), and must be maintained at the prescribed environmental conditions (temperature and humidity) throughout the 10,000 hour duration of the test. Deflections are measured periodically, with moduli calculated using the initial stress and the midspan deflection at each time period. Figure 3 Typical Creep Testing Setup. Per D2990, log strain in percent versus log time in hours is required to be reported, although Hauser typically also reports all raw data, modulus versus time for each individual specimen, and a log/log plot of the average of all specimens tested at identical conditions. While numerous data presentation methodologies are given in D2990 Appendix X4, since the creep testing performed is at a single stress and temperature, a simplified approach is sufficient. A single linear extrapolation to 50-year service life, similar to what is portrayed within Appendix X7.1, using standard trendline analysis such as that contained within Microsoft Excel is used. However, based upon experience gained in extrapolation of hydrostatic design basis data sets for pressure pipe, and since knees are sometimes encountered in the test data, only the most linear portion of the log-log plot is used for the extrapolation. Figure 4 displays three typical CIPP field-generated samples being laboratory tested under various loadings for long-term creep retention. When the extrapolation is performed over the complete test duration starting at time zero, the resultant trendline has a poor fit. Figure 5 shows the same test results but instead the trendline is generated using the most linear portion of the data from 100 hours to the end of the data set; the trendline has a much stronger fit. 6

7 Long-Term Cured-In-Place Pipe (CIPP) Performance Log Modulus (psi) y = x R 2 = psi 1250 psi 1657 psi Linear (1657 psi) Linear (1250 psi) Linear (400 psi) 5.65 y = x R 2 = y = x R 2 = Log Time (hours) Figure 4 D2990 Creep Sample Sets Under Various Loadings Log Modulus (psi) y = x R 2 = y = x R 2 = psi 1250 psi 1657 psi Linear (400 psi) Linear (1250 psi) Linear (1657 psi) 5.62 y = x R 2 = Log Time (hours) Figure 5 Same Three D2990 Creep Sample Sets, Most Linear Portion of Data Set. Hauser has performed creep tests with imposed stresses as low as 2.76 MPa (400 psi), and as high as approximately 13.8 MPa (2000 psi) in the past. It was previously reported to Hauser that this 2.76 MPa value was based upon a maximum hydrostatic head (external pressure) design approach. 7

8 Lee & Ferry For this paper, Hauser conducted creep testing on one material, an unsaturated polyester resin with felt laminate (approximately 6mm in thickness). The sample was tested at imposed initial flexural stress levels of 2.76 MPa (400 psi), 8.62 MPa (1250 psi), and 0.25% of the short-term modulus of the material. Upon completion of approximately 2000 hours of testing, the retained creep modulus at the 50-year intercept was evaluated to determine if imposed stress had a significant factor on the retained modulus. For the material tested, which displayed short-term flexural properties of 47.4 MPa (6873 psi) maximum flexural strength and 4569 MPa (662,700 psi) flexural modulus, the initial imposed flexural stresses correspond to approximately 6% to 24% of the short term flexural strength (See Table 2). Table 2 Flexural Modulus Under Various Loadings. Test Stress = 2.76 MPa (400 psi) Test Stress = 8.62 MPa (1,250 psi) Test Stress = 11.4 MPa (1,657 psi) Test Stress as Percent of 5.8% 18.2% 24.1% Initial Flexural Modulus per D790 (%) Most Linear 50-Year Flexural Modulus (psi) 2203 MPa (319,489 psi) 2291 MPa (322,342 psi) 2329 MPa (337,845 psi) Creep Retainage (%) 48.2% 48.6% 51.0% Simple inspection of these results would indicate that for a wide range of imposed stresses, the 50-year retained moduli as calculated using trendline analysis in these D2990 data sets are not significantly different. There are then two ways for designing engineers to use this data. The first is to take a creep reduction approach whereby the 50-year extrapolated modulus is divided by the short-term D790 modulus, resulting in a percentage reduction. The second is to evaluate the 50-year modulus in comparison to some minimum requirement, such as 862 MPa (125,000 psi). The second approach is more typical of a material-science based design approach and does not unduly penalize a material which may have significantly higher starting modulus but larger creep response. While not mandated, it is always best for the testing laboratory to hold some type of accreditation for the testing being performed. The most common certification for testing laboratories today is performed in accordance with ISO17025 by organizations such as the American Association for Laboratory Accreditation (A2LA). This accreditation assures that the testing laboratory has appropriate Quality Assurance mechanisms in place, equipment calibration, base knowledge, experience and overall understanding of the scientific principles involved. Field Samples And Testing Considerations In an ideal situation, each CIPP liner installed will have identical short-term and long-term properties. But realistically, each CIPP will differ. Field samples for each liner are critical for both the Owner and Contractor to determine the quality of the installation and negotiate payment, if necessary. Restrained samples are ideal when possible. Restrained samples (as opposed to plate samples) are most indicative of the actual liner installed for several reasons: 1. Restrained samples are a part of the installed CIPP, rather than a separate piece of uncured CIPP from the wet-out facility. 2. Restrained samples can reduce the effects of entry/exit flare-out and resultant stretching when portions of the liner are unrestrained. 3. Restrained samples are often subject to the same installation parameters, such as installation pressures, as the installed liner. 8

9 Long-Term Cured-In-Place Pipe (CIPP) Performance Figure 6 Picture of restrained sample taken during installation of CIPP. Samples should be sized appropriately for all required testing. For example, depending on pipe size and thickness, the test samples required by ASTM D638 (tensile testing) are typically longer than the samples required by ASTM D790. It is good practice to take duplicate field samples; one sample for laboratory testing and a second backup sample stored in the same environmental conditions as the installed CIPP (e.g., hung in the same manhole as the actual CIPP). Tests typically required for CIPP include: ASTM D658, Tensile Properties ASTM D790, Flexural Properties ASTM D2990, Determination of Tensile, Compressive, and/or Flexural Creep ASTM F1216 or D5813, Chemical Resistance ASTM D5813, Thickness When submitting samples for testing, the Engineer should clearly specify certain testing parameters that are not currently defined by the ASTM standards for specific applications of CIPP (e.g., the stress used in creep tests, as discussed previously). There are financial limitations to some laboratory tests; in particular, the ASTM D2990 test is a fairly expensive test (several thousand dollars) and takes approximately 14 months to complete. The D5813 Chemical Resistance test is also an expensive test. These financial limitations and time constraints should be considered when submitting field samples for testing. However, thickness tests and short-term tensile and/or flexural property tests (depending on the type of CIPP project) should be performed on each inversion sample. For example, in a typical gravity sewer rehabilitation project, the flexural properties will drive the thickness; tensile testing is not necessary to determine the long-term performance of gravityservice CIPP. RESULTS The acceptability of any given CIPP and its ability to perform appropriately for the duration of its design life depends greatly on the physical properties of the actual installed liner. Once short-term test results are received, an initial evaluation should be made per the following table: Table 3 Evaluation of Short-Term ASTM Test Results. Test Comparison ASTM D638, Meets or exceeds minimum value listed in ASTM F1216 and Tensile Properties meets or exceeds value used in design? ASTM D790, Meets or exceeds minimum value listed in ASTM F1216 and Flexural meets or exceeds value used in design? Properties ASTM D5813, Meets or exceeds design thickness? Thickness 9

10 Lee & Ferry In recent years, engineers have stopped with this comparison, assuming that the long-term properties are equivalent to 50% of the short-term properties. Knowing now that this assumption can have strong repercussions on the CIPP sustaining performance for the specified design life, long-term test results need to be considered prior to giving final approval on any installed liner. In the case of a gravity pipeline rehabilitated with CIPP with a design life of 50-years, the long-term flexural properties will dictate the ability of the liner to meet the design requirements. Assuming the design thickness was driven by Equation X1.3 of ASTM F1216, the long-term flexural modulus is the key physical property. When ASTM D2990 test results come back with 10,000 hours (or 1.14 years) worth of data, the first engineering evaluation is to appropriately extrapolate the data out to 438,000 hours (or 50 years). Ideally, this extrapolation methodology is specified in the Contract to avoid disputes after the CIPP has been installed and test results received. The extrapolated 50-year flexural modulus from the actual field sample(s) can then be compared against the value used in the design. However, given the cost of the long-term test, it is not practical to have a test performed on every sample. Financially, it may be better to take a representative field sample and perform the long-term tests on that single sample, while all other field samples should continue to have the shortterm tests performed. In this case, a creep retainage factor can be calculated from the one representative field sample: E L C L = E where: C L = Creep Retainge Factor E = Short-Term Flexural Modulus (MPa), from ASTM D790 test results E L = Long-Term Flexural Modulus (MPa), extrapolated appropriately from ASTM D2990 test results Once the Creep Retainage Factor is calculated from the representative field sample, it can then be applied to every other field sample s short-term flexural modulus (E) to obtain each CIPP s long-term flexural modulus (E L ). Then each CIPP s E L can then be compared against the E L values used in the design to determine acceptability. DISCUSSION If the field samples long-term flexural modulus values are less than the design value, there are several options at an Owner s disposal. An Owner must consider the difficulty and invasiveness of removing a substandard liner and replacing it with either a new liner or new pipe, the hydraulic and operational implications of installing another liner over the top of the first liner, and the long-term risks of accepting a substandard liner. One of the most reasonable options at the Owner s discretion is the ability to reduce payment for substandard work or products. Two testing results will determine the design life of an actual field-installed CIPP liner the thickness and the long-term properties. The Owner can reduce payment in several ways: 1. Compare Field Sample Long-Term Properties with Manufacturer-Submitted Long-Term Properties. This is accomplished by dividing the actual long-term flexural modulus for each liner by the long-term flexural modulus submitted by the Contractor during the design phase and reducing payment proportionally. This method, while the simplest, does not take into account the actual thickness of the installed CIPP or the effect the actual long-term properties have on the design life. 2. Calculate True Design Life Based on Field Sample Long-Term Properties, Disregarding Thickness. Calculate the true design life of each installation by taking the field sample(s) calculated long-term flexural modulus (or flexural strength or tensile strength, depending on the 10

11 Long-Term Cured-In-Place Pipe (CIPP) Performance governing ASTM F1216 equation), inserting it into the regression equation generated from the manufacturer-submitted ASTM D2990 tests, and calculating the design life (i.e., solving for time). Payment can then be reduced in proportion to the reduced design life. This method only accounts for the actual long-term physical properties and does not take into account the thickness of the installed CIPP. 3. Calculate True Design Life Based on Field Sample Long-Term Properties, Considering Thickness. Determine the required thickness of the CIPP by using the field sample long-term flexural modulus in the appropriate ASTM F1216 equations. Then compare the calculated design thickness to the actual thickness of the field sample to determine if the installed thickness, if greater than the newly calculated design thickness, may compensate for the lower long-term properties of the liner. This method recognizes the relationship between thickness and long-term properties, but also potentially rewards a Contractor for installed a liner that may be thicker than allowed tolerances. Regardless of the method the Owner might select for reduction of payment, the Contract Documents should clearly outline the methodology to minimize disputes. In addition, the Owner should also recognize the length of time needed to generate long-term laboratory test results (approximately 14 months after the field sample is submitted) and develop appropriate contractual steps (e.g., bonding, warranty) to account for such a long duration. CONCLUSIONS Long-term testing of CIPP has been underemphasized in the trenchless industry, by manufacturers, contractors, owners, and engineers alike. The determination of long-term properties, both in the design phase and post-construction phase, are of critical importance. The industry standard of 50% creep retainage has been widely-accepted without the test data necessary to translate the laboratory results to actual field installations. And it is vital that all involved parties understand the testing methodology, the design implications, and methods of recourse available should the cured-in-place pipe be less than specified. REFERENCES ASTM D658, Standard Test Method for Tensile Properties of Plastics, American Society for Testing and Materials, West Conshohocken, PA. ASTM D790, Standard Test Methods for Flexural Properties of Unreinforced and Reinforced Plastics and Electrical Insulating Materials, American Society for Testing and Materials, West Conshohocken, PA. ASTM D883, Standard Terminology Relating to Plastics, American Society for Testing and Materials, West Conshohocken, PA. ASTM D2990, Standard Test Methods for Tensile, Compressive, and Flexural Creep and Creep-Rupture of Plastics, American Society for Testing and Materials, West Conshohocken, PA. ASTM D5813, Standard Specification for Cured-In-Place Thermosetting Resin Sewer Piping Systems, American Society for Testing and Materials, West Conshohocken, PA. ASTM F1216, Standard Practice for Rehabilitation of Existing Pipelines and Conduits by the Inversion and Curing of a Resin-Impregnated Tube, American Society for Testing and Materials, West Conshohocken, PA. McGraw-Hill, Dictionary of Scientific and Technical Terms, McGraw-Hill Companies, Inc.,

12 Lee & Ferry Schiro, Jason, Rahaim, Kaleel, Herzon, David, and Bennett, Anthony, A Comparison of CIPP Mechanical Properties Lab versus Field Generated Cured-in-Place Samples, North American No-Dig Conference, San Diego, CA, Young, W. and Budynas, R. (2002). Roark s Formulas for Stress and Strain, McGraw Hill, Blacklick, OH, 7 th Ed. 12