Performance Specifications for Rapid Highway Renewal (2014)

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55 A p p e n d i x C Recent developments and improvements to in situ testing devices and integrated machine sensors (e.g., intelligent com- paction rollers with accelerometer-based measurements of ground stiffness) have provided opportunities to develop more performance-oriented specifications in the areas of embankment and pavement subgrade/subbase construction. Two specifications related to pavement foundation systems were prepared under the SHRP 2 R07 project. The first, and perhaps easiest to implement, entails replacing traditional forms of proof rolling with roller-integrated compaction monitoring (RICM) proof mapping to verify that pavement subgrade support conditions are satisfactory. Compared with traditional proof rolling, proof mapping can provide • Geospatially referenced documentation of an RICM mea- surement value (MV); • Real-time information to the contractor during the con- struction process; and • Results that can be correlated to subgrade support values, such as bearing capacity and stiffness. The second specification represents a more comprehensive attempt to specify the construction of embankment and pave- ment foundation materials in terms of performance measures and quality statements. Key features of this specification include the following: • Use of RICM technology to provide 100% sampling cover- age to identify areas needing further work; • Acceptance and verification testing using performance measures and parameters—such as elastic modulus test- ing, shear strength, and permeability—that relate to design assumptions; • Protocols for establishing target values for acceptance; • Quality statements and assessment methods that require achievement of at least some overall minimal value during construction, and achievement of a minimum level of spa- tial uniformity in a given lot area; and • Protocols for data analysis and reporting such that the con- struction process is field controlled in an efficient manner to ensure the final product meets design assumptions. This second specification may not be ready for immedi- ate implementation on a construction project because of training needs and limitations in technology, data analysis/ software, and endorsed test methods/standards. Neverthe- less, it presents an approach for establishing target values for acceptance based on engineering parameters that relate to design assumptions. Roller-integrated Compaction Monitoring (RiCM) proof Mapping performance Specification for Subgrade Commentary: The goal of this guide specification is to describe a new construction quality control (QC) and quality assurance (QA) approach to verify that pavement subgrade support con- ditions are satisfactory. The specification includes a provision to replace traditional forms of proof rolling with roller- integrated compaction monitoring (RICM) proof mapping. Compared with proof rolling, proof mapping has the advan- tages of (1) providing geospatially referenced documentation of an RICM measurement value (MV), (2) providing real- time information to the contractor during the construction process, and (3) being correlated to subgrade support values such as bearing capacity and stiffness. By incorporating proof mapping capability into rollers, the results can be used as part of the contractor’s process control operations. Through agency verification performance testing, the RICM measurement records are intended to be used in the agency’s acceptance decision. For practical reasons, the verification test Performance Specifications for Earthwork/Pavement Foundation

56 results in this situation cannot be independent RICM mea- surements; so it is recommended that verification tests involve in situ testing conducted by the agency and correlated to the RICM MV (e.g., LWD, DCP, PLT). This specification was drafted as part of the SHRP 2 R07 research effort to develop guide performance specifications for rapid highway renewal. The Missouri Department of Transportation (MoDOT) provided guidance in the develop- ment and field testing of this guide specification. An example of the proof mapping output is provided with this document. The MoDOT field results demonstrate an effective application of RICM proof mapping as an alternative to traditional proof rolling via a loaded, tandem-axle dump truck. Implementation of this specification is not envisioned in the short term because of limitations in technology, data analysis/ software, endorsed test/method standards (e.g., AASHTO), and training. A well-planned program will need to be devel- oped to overcome these obstacles. As part of this research, a demonstration project was organized to provide field data to validate parts of this specification. The project report sum- marizes key findings from the demonstration project. 1 DESCRIPTION This work shall consist of testing the support conditions of the prepared roadbed subgrade by proof mapping with a roller- integrated compaction monitoring (RICM)–equipped com- pactor before paving. Perform RICM proof mapping on all prepared subgrade, including main line, outer roadways, ramps, and all side streets. The department will establish tar- get values for proof mapping through on-site RICM verifica- tion testing. Record and document all RICM measurements obtained as part of compaction process control operations. Submit process control results to the department on request. Submit RICM proof mapping passes intended for inclusion in the depart- ment’s acceptance decision on completion of mapping opera- tions. RICM deliverables shall be current for each payment period. Commentary: As an alternative to traditional nuclear mois- ture density testing and moisture content testing, drive core sampling (ASTM 2937), dynamic cone penetration testing (ASTM 6951), plate load testing (ASTM D1196), light weight deflectometer testing (ASTM E2583 or ASTM E2835), and other tests can be considered. A description of target value determination for these alternative methods is beyond the scope of this guide specification. Motivations to use alterna- tives to nuclear gauges include elimination of the nuclear compliancy and safety training issues and the understand- ing that current RICM measurements are better correlated to strength and stiffness measurements than to volumetric/ gravimetric measurements. 2 TERMS AND DEFINITIONS For the purpose of this specification, the following defini- tions shall apply. A. Roller-integrated compaction monitoring (RICM): RICM for earthwork and pavement foundation materials is defined as the generic gathering of data from roller sys- tems involved with the measurement and recording of roller position, date/time, speed, vibration frequency, vibration amplitude, pass count, travel direction, and a compaction measurement value (MV). The RICM system is supplied by either the roller manufacturer or a third party. The RICM monitoring system shall include calibra- tion records of the sensor systems. B. Measurement value (MV): Measurement values are cal- culated from calibrated sensors integrated into rollers that provide information on machine-ground interaction(s). Machine-ground interaction measurements are typically derived from vibration analysis of accelerometers, sensor systems that monitor machine drive power inputs, or direct measures of sinkage/rutting. C. Target value (TV): Target values are the established mini- mum MVs based on in situ correlation analysis to in situ performance point measurements. Correlation analysis requires statistical analysis of geospatially paired indepen- dent point measurement values (PMVs) linked to MVs using global navigation satellite system (GNSS) position- ing information. D. Subgrade bearing capacity is the plate load test contact pressure required to induce 1 in. of plate deflection (25.4 mm) for a 12-in. (300-mm) diameter plate. E. Real-time kinematic (RTK)–based GNSS with base sta- tion corrections is used for determining the position of the roller and correlation spot tests. Results from the RICM shall be displayed to the roller operator on a color- coded computer screen in real time during roller opera- tions, and the data shall be saved for transfer and viewing by the engineer. Commentary: Additional terms and definitions may be needed for modified versions of this specification. The focus on subgrade bearing capacity for this specification is based on MoDOT’s current proof rolling specification. Also note that the incorporation of moisture content measurement into the suite of RICM measurements is not commercially available; but it is an ongoing area of research and industry develop- ment, and it is expected to be incorporated in the near term. 3 EQUIPMENT/TEST CAPABILITIES A. Provide RICM-equipped compactor(s) that have the capability to near continuously measure and record a

57 roller-ground interaction measurement value (MV) that correlates to the subgrade bearing capacity as deter- mined from a static plate load test performed in accor- dance with ASTM 1196. Commentary: The RICM system requirement of “near con- tinuous measurement” is intended to provide a requirement for reporting the measurement value. Reporting an RICM MV in distance increments ≤12 in. (300 mm) traveled is desirable but is not a set requirement at this point. An alternative to defining subgrade bearing capacity based on 1 in. of plate deflection is to use a target minimum modulus of subgrade reaction (e.g., k-value used for pavement design purposes) at a defined plate contact stress. In brief, modulus of subgrade reaction is defined as the plate contact stress divided by the average plate deflection (see ASTM D1196 or AASHTO T222). Common plate contact stress values used to define modulus of subgrade reaction are 10 pounds per square inch (psi) (69 kPa) for subgrade and 30 psi (207 kPa) for sta- bilized subgrade and aggregate base. Although a 12-in. diam- eter plate is listed above, a plate diameter of 30 in. is normally the reference standard. For plate diameters smaller than 30 in. (762 mm), perimeter to surface area corrections are typically required so that the reported values are equivalent to the stan- dard 30-in. diameter plate. B. Provide an RTK GNSS to acquire northing, easting, and elevation data for mapping of RICM measurements. Ensure the system has the capability to collect data in an established project coordinate system. Furnish a local base station for broadcasting differential correction data to the rollers with a tolerance less than 0.1 ft in the vertical and horizontal. Commentary: If a lower accuracy system is substituted for RTK GNSS, the quality of correlation analysis from verifica- tion testing is reduced and may require increased in situ test- ing frequencies and/or high minimum RICM target values to account for position induced measurement error. RTK GNSS position information is recommended. C. The RICM system shall have the capability to immediately display and provide a permanent electronic record of the proof mapping results and data as follows: 1. Integrated, color-coded, real-time computer display viewable by roller operator showing RICM measure- ment value (MV), RICM MV with reference to RICM target value (TV), and roller pass coverage. Provide dis- played results to the engineer for review on request. 2. Electronic data file in American Standard Code for Information Interchange (ASCII) format with time stamp, RTK global positioning system (GPS) position in state DOT standard coordinate system, roller operation parameters (speed, gear, and travel direction), the RICM measurement value (MV), and target value (TV). 4 CONSTRUCTION REQUIREMENTS 4.1 RICM Work Plan Submit to the engineer an RICM work plan at the time of the preconstruction conference. A. Describe in the RICM work plan the following: • Roller vendor, • Roller model, • Roller dimensions and weights, • Description of RICM measurement system(s), • Past independent verification of RICM correlations to in situ engineering measurements, • Roller data collection methods including sampling rates and intervals, • RTK GPS capabilities, • Minimum parameters for GPS calibration (required daily), • Validation process of RICM equipment and results (required daily), • Documentation system and data file types, • Software, • Roller operations per manufacturer recommendations, and • Proposed rolling patterns for each lift. B. Describe the process for RICM operations during the agency’s testing to establish RICM target values. C. Address quality management of the pavement foundation layers, including testing to be performed and coordination with the department’s efforts to verify that the contractor is meeting the minimum and/or maximum engineering parameter values. Commentary: Agencies are encouraged to consider require- ments for RICM operating training/certification when the data will be used as part of the acceptance decision. D. Describe how data will be acquired and transferred to the engineer, including method, timing, and personnel responsible. Data transfer shall occur at a minimum once per day or as directed by the engineer. Provide and export the following data in a comma, colon, or space delimited ASCII file format: • Machine model, type, and serial/machine number; • Roller drum dimensions (width and diameter); • Roller and drum weights; • File name; • Date stamp; • Time stamp;

58 • RTK-based GPS measurements showing northing, easting, and elevation (e.g., in local project coordinate system); • Roller travel direction (e.g., forward or reverse); • Roller speed; • Vibration setting (i.e., on or off); • Vibration amplitude; • Vibration frequency; • RICM MV; and • Pass count. 4.2 RICM Target Value Determination and Correlation Analysis A. For RICM verification and correlation analysis to estab- lish RICM target value, the department (or an indepen- dent third-party inspection firm) will conduct in situ testing. Perform RICM roller operations for correlation analysis in the presence of the engineer, unless approved otherwise. The engineer will review all results to set the RICM TV. B. The department (or its third-party inspection firm) will prepare reports containing the results of the plate bearing testing and assessment of the RICM TV determination within 24 hours of testing. The test report will include the following: • Test identification number, • Dates of testing, • Names of QC/QA field personnel conducting tests, • Description of tests, • Tables presenting all data, • Plots of plate bearing test results, • Summary of calculated engineering values, • Plot of RICM MV versus independent measurements, and • Plots of RICM proof maps. 4.3 Proof Mapping Roller Operation To allow comparison of successive roller passes, the roller operations should be consistent between passes. For static (e.g., nonvibratory) rolling operations, maintain relatively constant speed and operate within the manufacturers slope and pitch limits. For vibratory rolling operations, maintain relatively constant vibration frequency and amplitude during roller operations. Permitted variation in vibration frequency is ±2 Hz. Maintain rolling speed to provide a minimum of 10 impacts per linear foot and within ±0.5 mph during mea- surement passes. Record roller operations in forward and reverse directions. Check and validate, if necessary, RICM equipment at the beginning of each workday. Make GNSS calibration checks on a daily basis. Commentary: Changes in frequency and amplitude can influ- ence RICM MVs. However, the limits for vibration frequency and speed variation can be adjusted if the RICM technology is documented as providing reliable and repeatable measure- ments outside the noted ranges. Speed fluctuations can also influence the RICM MVs and should not be allowed outside of the specified range during measurement passes. It is anticipated that RICM MVs will be affected by rolling direction, and there- fore the output data fields shall indicate rolling direction. A. RICM proof mapping shall include two complete passes per lane and one complete pass in shoulder areas. Perform each pass so that a 0% to 10% overlap occurs between passes in the coverage area. The roller operations and roll- ing patterns for each lift shall be in accordance with the manufacturer guidelines and as proposed in the RICM work plan, subject to approval by the engineer. B. Protect completed work before the placement of the sub- sequent layers and until final acceptance of the project. At any time during construction of aggregate base pavement materials, the engineer may require the contractor to per- form RICM proof mapping according to this specifica- tion in areas on the project where unstable subgrade is observed. Make corrections to the subgrade even if the engineer previously accepted the areas before they became unstable. C. Provide the results of RICM proof mapping to the engi- neer in printed and electronic form on request or within at least 24 hours of measurement. On approval of the RICM proof mapping, place the subbase, base course, or initial pavement course within 48 hours. If the subbase, base coarse, or initial pavement course is not placed within 48 hours or the condition of the subgrade changes because of weather or other conditions, perform proof mapping and corrective work at the discretion of the engineer and at no expense to the department. 5 PERFORMANCE REQUIREMENTS The department will consider the roadbed to be unstable if the RICM measurement value is less than the established requirements for the mapping area based on the RICM target value (TV). To establish the RICM TV, the department will perform correlation analysis of the RICM MV to the sub- grade bearing capacity, as defined in Section 2. The depart- ment will use simple linear regression analysis to establish a correlation between the RICM MV and plate load test values. The department will use a minimum of eight plate load tests to establish the correlation. The department will set the RICM TV as the RICM MV that correlates to a 1-in. plate deflection at a contact pressure of 90 psi (10,178 lbf for 12-in. diameter plate).

59 Commentary: Simple linear regression analysis involves devel- oping a relationship between independent and dependent variables using an intercept and slope coefficient. This analy- sis is simple enough to be performed on a hand calculator. For each linear, univariate regression model, the coefficient of determination R2 provides a measure of how well the regres- sion model describes the data. In this specification the cor- relation is considered acceptable if R2 ≥ 0.5. The regression relationships will be developed by considering the “true” independent variables (in this specification, plate bearing test measurements or modulus of subgrade reaction) and the RICM MV as the dependent variable using the model shown in Equation 1. = + αiRICM MV b b (1)0 1 where b0 = intercept, b1 = slope, and a = independent variable. As an alternative to on-site calibration using simple linear regression analysis, suitable evidence of RICM MV correla- tions with the selected in situ point measurements (e.g., plate load tests) may be used. Suitable evidence would be unbiased third-party measurements describing and verifying the sta- tistical significance of the determined correlations. The cor- relations would need to be derived from the same roller machine configuration, operating conditions, and similar soil types. Note: Relationships between RICM to in situ point measure- ments can be nonlinear, in which case simple linear regression is not recommended. There are many nonlinear models that can be used to develop correlations. An example of a hyper- bolic relationship is provided in Figure C.1. 6 ACCEPTANCE REQUIREMENTS The department will base acceptance of the RICM proof mapping area on achievement of the RICM TV in the proof mapping area with a minimum of 80% of the RICM MV ≥ TV and no contiguous, isolated areas that are larger than 25 ft in length. When proof mapping identifies unacceptable areas in the roadbed, the contractor shall rework the area by scarifying and moisture conditioning the soils as necessary. Reshape and compact the disturbed areas. The engineer may not require retesting of that area by RICM proof mapping if the engineer is satisfied that the corrective actions taken have eliminated the cause of the instability as evidenced by testing and/or visual inspection. Commentary: The 80% minimum criterion is a suggested value and is expected to vary from about 70% to 90% depend- ing on the desired quality conditions and uniformity. Further, the 25-ft maximum for unstable areas may be adjusted from 3 ft to 50 ft contiguous length. An alternative to the maximum continuous length is to use a maximum area such as the roller footprint (about 150 ft2). Currently, limited information is available to fully understand the impacts of the size of non- conforming areas, and the engineer should use judgment in setting these limits. Areas requiring corrective work, as deter- mined from proof mapping, because of unforeseen condi- tions may require extra work, in which case the engineer may need to identify the needed remediation. Proof mapping areas are generally on the order of the project width by 200 ft to 1,000 ft in length, but that will depend on the project conditions. In addition to the RICM mapping described, it may be desirable for the agency to conduct quality assurance plate bearing tests. The number of tests and test locations will be based on assessment of the RICM MVs. In areas of high RICM variability (e.g., coefficient of variation, COV >20%), the test frequency will be about one test per 500 ft. In areas of low RICM variability (e.g., COV <20%), the test fre- quency will be about one test every 1,000 ft. The test loca- tions could be randomly selected or by inspection of the RICM proof map to identify soft spots. The target numbers for quality assurance testing and RICM variability are related to the materials being tested and the type of RICM measurement technology. Engineering judgment should be used when selecting these limits. Typical values are pre- sented in NCHRP Report 676. 7 BASIS OF PAYMENT All RICM proof mapping operations are considered inciden- tal to the grading and earthwork. No direct payment will be made to the contractor for RICM proof mapping or correc- tive work required as a result of the proof mapping. Commentary: An alternative basis of payment language is as follows: Payment for RICM will be the lump sum contract price. Payment is full compensation for all work associated with providing RICM equipped rollers, transmission of elec- tronic data files, two copies of RICM roller manufacturer soft- ware, and training. Delays resulting from GPS satellite reception of signals to operate the RICM equipment or RICM roller breakdowns will not be considered justification for con- tract modifications or contract extensions. In the event of RICM roller breakdowns, system malfunctions, or GPS prob- lems, the contractor may operate with conventional rolling operations; but RICM proof mapping shall be provided for a minimum 90% of the project surface. If, because of unforeseen ground conditions and as deter- mined from proof mapping, the engineer determines that cor- rective construction work is necessary, such corrective work could be paid at the applicable contract unit price or as extra work.

60 Test Area #1 - QC Proof Map: 88% ≥ RICM-TV = 123 Test Area #2 - QC Proof Map: 0% ≥ RICM-TV = 123 CBR (800 mm Weighted Average) 1 10 100 M D P 80 90 100 110 120 130 140 150 f = if(x>0, y0+a*ln(abs(x)), 0) y0 = 78.1790 a = 20.0339 R2adj = 0.87 @ MDP = 123 CBR = 10 Rut Depth (mm) (note 1 inch = 25.4 mm) 0 20 40 60 80 100 120 140 160 180 M D P 80 90 100 110 120 130 140 f = y0+a*x a = -0.4180 y0 = 135.4280 R2adj = 0.91 MDP Target value = 125 Modulus of Subgrade Reaction (psi/in) @ 90 psi for 1 inch deflection 0 200 600 800 1000 M D P 80 90 100 110 120 130 140 f = a*(1-exp(-b*x))+c*(1-exp(-d*x)) a=104.7487 b=0.0858 c=31.7822 d=0.0095 MDP Target value = 123 R2adj = 0.93 Figure C.1. Example RICM proof maps and calibration plots.

61 performance Specification for embankment and pavement Foundation Construction Commentary: This guide specification, developed under the SHRP 2 R07 project, provides a template from which a state highway agency can develop a detailed performance specifica- tion for quality control (QC) and quality assurance (QA) of embankment and pavement foundation materials. Imple- mentation of this specification will require investment in new technologies, training, and data management solutions. Tra- ditionally, earthwork specifications are prescriptive, require relatively low test frequency, and/or do not use acceptance testing methods that directly evaluate performance character- istics during construction. To overcome these limitations, this guide specification includes the following key features: • Acceptance and verification testing using performance mea- sures and parameters—such as elastic modulus testing, mod- ulus of subgrade reaction, and shear strength—that relate to design assumptions; • Use of real-time roller-integrated compaction monitoring (RICM) technology [i.e., intelligent compaction (IC), contin- uous compaction control (CCC), compaction documentation system (CDS)] or instrumented proof rolling technology to provide nearly 100% coverage to identify areas needing fur- ther work, geospatially referenced data for uniformity analysis, and information to select verification testing locations; • Protocols for establishing target values for acceptance based on the required engineering parameter values consistent with the design methodology used for the project; • Quality statements and assessment methods that require achievement of at least some overall minimal value during construction, achievement of a minimum level of uniformity, and identification of contiguous areas of noncompliance that exceed the maximum allowable; • Protocols for data analysis and reporting such that the con- struction process is field controlled in an efficient manner to ensure the final product meets design assumptions; • Assignments of responsibility for field QC/QA, data report- ing, and verification testing, and guidance on data interpre- tation and remediation; and • A few options for pay adjustments that provide incentives/ disincentives to promote achievement of the specific perfor- mance criteria and maximize coverage of the performance verification assessment. A distinguishing factor for this guide specification, compared with other components of civil infrastructure, is the subter- ranean nature of the earthworks and pavement foundation projects. If such projects are not built to achieve the intended performance criteria to begin with, maintenance and repair can be costly and difficult, if not impossible. The need to pro- vide technologies and specification guidelines to improve pro- cess control and verify as-constructed conditions remains high. A companion performance guide specification was developed separately from this document and titled, Roller- Integrated Compaction Monitoring (RICM) Proof Mapping Performance Specification for Subgrade. The proof mapping guide specification is a simpler alternative to this specification and achieves many of the key performance criteria. Implementation of this specification is not envisioned in the short term because of limitations in technology, data analysis/ software, endorsed test/method standards (e.g., AASHTO), and training. A well-planned program needs to be developed to overcome these obstacles. As part of this research, demon- stration projects were organized to provide field data to vali- date parts of this specification. A project report summarizes key findings from the demonstration. 1 GENERAL This specification presents details on how to evaluate and accept the placement of embankment and pavement founda- tion materials in terms of performance measures and perfor- mance quality statements. A. Materials: This specification is applicable to a range of unbound granular and nongranular earth materials, including general embankment fill materials, pavement subgrade materials, unbound aggregate base materials, and chemically and mechanically stabilized materials. B. Technologies: Testing technologies that provide rapid measures for increased test frequency are required for quality control (QC) and quality assurance (QA) test- ing. Many of these technologies are standardized with existing test protocols while some are not standardized and require special protocols for their use as described in this specification. C. Performance criteria and assessment: The goal of the specification is to provide a mechanism to ensure that the compacted materials are satisfactory for the intended design purpose. Performance quality assessment is based on achievement of the following quality criteria: 1. Critical design property value(s) over the entire site achieves the specified minimum value; 2. Nonuniformity of the critical design property value(s) over the entire site are no more than the specified max- imum amount; 3. Contiguous noncompliance areas are not larger than the specified maximum value; and 4. Moisture contents are greater than the specified mini- mum values to eliminate postconstruction saturation induced volume and stiffness changes to the acceptable level. Commentary: Traditional end-result earthwork specifications normally address item (1) through infrequent random point

62 measurements. The point measurements have traditionally been moisture content and density determined from nuclear density tests. The test frequency is such that less than 0.1% of the soil volume is typically tested, making statistical analysis of the data difficult. Geospatially referenced RICM and proof rolling technologies provide the opportunity to address items (2) and (3). Options for enforcing these quality criteria are presented in this guide specification. Generally, moisture con- trol is critical for effective and efficient soil compaction. The specification options address the influence of moisture con- trol through an option to include moisture content as a sig- nificant variable in the correlation analysis with stiffness and strength performance criteria and by requiring laboratory testing to select minimum moisture contents to limit post- construction wetting-induced design property changes to within acceptable limits. D. Responsibilities and reporting: As part of this specifica- tion, the contractor shall develop, implement, and main- tain a quality management plan (QMP). The plan shall address selection of the measurement technologies, methods for test strip construction to establish site- and material-specific target values, and electronic data collec- tion and transfer. 2 TERMS AND DEFINITIONS For the purpose of this specification, the following definitions shall apply: A. Roller-integrated compaction monitoring (RICM): RICM for earthwork and pavement foundation materials is defined as the generic gathering of data from roller sys- tems involved with the measurement and recording of roller position, date/time, speed, vibration frequency, vibration amplitude, pass count, travel direction, and a compaction measurement value (MV). The RICM system is supplied by either the roller manufacturer or a third party. The RICM monitoring system shall include calibra- tion records of the sensor systems. B. Measurement value (MV): Measurement values are cal- culated from calibrated sensors integrated into rollers that provide information on machine-ground interaction(s). Machine-ground interaction measurements are typically derived from vibration analysis of accelerometers, sensor systems that monitor machine drive power inputs, or direct measures of sinkage/rutting. C. Target value (TV): Target values are the established mini- mum MVs based on in situ correlation analysis to in situ performance point measurements. Correlation analysis requires statistical analysis of geospatially paired indepen- dent point measurement values (PMV) linked to MVs using global navigation satellite system (GNSS) position- ing information. D. In situ performance point measurement value (PMV): Point measurement values are in situ measurements used to set TVs for RICM MVs. PMVs suitable for per- formance measurements include measures of strength and stiffness. E. Real-time kinematic (RTK)–based GNSS with base sta- tion corrections is used for determining the position of the roller and correlation spot tests. Results from the RICM shall be displayed to the roller operator on a color- coded computer screen in real-time during roller opera- tions, and the data shall be saved for transfer and viewing by the engineer. F. RICM repeatability refers to variation observed in the measurement values (also referred to as measurement error) obtained over a test area from consecutive passes under identical operating conditions (i.e., using same operator, amplitude, speed, direction of travel, etc.). G. RICM reproducibility refers to the variation in measure- ments obtained from consecutive passes under changing conditions. The changing conditions may be due to differ- ent measurement methods, machines used, operators, or speed and amplitude settings. 3 TEST EQUIPMENT AND METHODS Commentary: This section should list and describe suitable test equipment and methods to be used in the performance quality assessments. Some of the test methods may not have established AASHTO or ASTM standards and will require list- ing of state agency standards and/or reference to accepted user manuals. There are many details here, including special focus on RICM and proof rolling/mapping equipment as it is rela- tively new and not well described in current specifications. The devices for which AASHTO/ASTM standards exist are not described. 3.1 Roller Provide RICM rollers that comply with the standard speci- fications for self-propelled vibratory rollers, static rollers, or pneumatic roller. Ensure that RICM equipment can mea- sure roller position, date/time, speed, vibration frequency, vibration amplitude, pass count, travel direction, and a compaction measurement value (MV) with known repeat- ability and reproducibility. Provide a computer screen in the roller cab for viewing measured results. Ensure that results are stored for transfer to the engineer for viewing on a lap- top computer. Provide the engineer with a copy of the RICM data analysis software for viewing results. Ensure that results are displayed as color-coded spatial maps based on GNSS coordinates.

63 3.1.1 Data Collection, Export, and Onboard Display Provide and export the following data in a comma, colon, or space delimited ASCII file format: 1. Machine model, type, and serial/machine number; 2. Roller drum dimensions (width and diameter); 3. Roller and drum weights; 4. File name; 5. Date stamp; 6. Time stamp; 7. RTK-based global positioning system (GPS) measure- ments showing northing, easting, and elevation [±76 mm in the horizontal and vertical directions (RTK GPS)]; 8. Roller travel direction (e.g., forward or reverse); 9. Roller speed (±0.5 km/h); 10. Vibration setting (i.e., on or off); 11. Machine gear; 12. Vibration amplitude (±0.2 mm); 13. Vibration frequency (±2 Hz); 14. Compaction measurement value (MV); and 15. Pass count. Ensure that the roller onboard display will furnish color- coded GNSS-based mapping showing number of roller passes, vibration frequency, vibration amplitude, and the MV on a computer screen in the roller operator’s cab. Provide dis- played results to the engineer for review upon request. 3.1.2 Local GNSS Base Station Provide an RTK GNSS to acquire northing, easting, and ele- vation data for use in mapping of RICM measurements. Ensure the system has the capability to collect data in an established project coordinate system. Furnish a local base station for broadcasting differential correction data to the rollers with a tolerance less than 25 mm in the vertical and horizontal. Commentary: If a less accurate system is substituted for RTK GNSS, the quality of correlation analysis from verification testing is reduced and may require increases in the number of in situ tests and/or a higher minimum RICM target value to account for position-induced measurement error. RTK-GNSS position information is recommended to minimize this error. 3.1.3 Roller Operations Conduct roller operations according to the manufacturer’s recommendations to provide reliable and repeatable RICM measurements. To allow comparison of successive roller passes, the roller operations should be consistent between passes. For static (e.g., nonvibratory) rolling operations, maintain relatively constant speed and operate within the manufacturer’s slope and pitch limits. For vibratory rolling operations, maintain relatively constant vibration frequency and amplitude during roller operations. Permitted variation in vibration frequency is ±2 Hz. Maintain rolling speed to provide a minimum of 10 impacts per linear foot and within ±0.5 mph during measurement passes. Record roller opera- tions in forward and reverse directions. If necessary, check and validate RICM equipment at the beginning of each work- day. Make GNSS calibration checks on a daily basis. Commentary: Changes in frequency and amplitude can influ- ence RICM MVs. However, the limits for vibration frequency and speed variation can be adjusted if the RICM technology is documented as providing reliable and repeatable measure- ments outside the noted ranges. Speed fluctuations can also influence the RICM MVs and should not be allowed outside of the specified range during measurement passes. RICM MVs will likely be affected by rolling direction, and therefore the output data fields shall indicate rolling direction. 3.1.4 Repeatability and Reproducibility Analysis RICM measurements determined from repeated passes must exhibit reproducible and repeatable results for well-compacted materials. If the results are not repeatable, a test section should be constructed to evaluate the influence of roller operating and changing ground conditions. The procedure for calculating reproducibility and repeatability errors is pre- sented in Attachment A: Repeatability and Reproducibility Analysis Using Two-Way Analysis of Variance (ANOVA). Commentary: Currently, there are no published acceptable limits of measurement error for roller MVs. However, it is an important element of this specification for evaluating the use- fulness of a machine before its use or even periodically during the course of project; this will help build confidence in the measurements. As with any quality assessment device, the measurement values should be both repeatable and reproduc- ible. Variability in roller MVs is one source of scatter in rela- tionships compared with in situ point measurements. The measurement variability is quantified in this specification in a repeatability and reproducibility context. Repeatability refers to variation observed in the measurement values (also referred to as measurement error) obtained over a test area from con- secutive passes under identical operating conditions (i.e., using same operator, amplitude, speed, direction of travel, etc.). Reproducibility refers to the variation in measurements obtained from consecutive passes under changing conditions. The changing conditions may result from different measure- ment methods, machines used, operators, or speed and ampli- tude settings. The repeatability and reproducibility analysis procedure described is applicable for any RICM technology,

64 although the magnitude of measurement error (for the range of MVs) is expected to be different for different RICM tech- nologies. This is important from a specification standpoint as it affects the regression relationships, minimum TVs, and anticipated variability in MVs. 3.2 Test Devices for In Situ Performance Point Measurement Values The department will establish target values (TVs) for RICM MVs based on material and RICM machine-specific param- eters. Select appropriate in situ PMVs from Table C.1. Maintain current records of calibration and inspection records for the in situ test devices. Submit records to the engi- neer, on request, before initiating testing. Commentary: The in situ test technologies listed were selected with the goal of linking design with the as-constructed condi- tions. Ideally, these measurement technologies will (1) mea- sure characteristics that significantly affect performance, (2) assess quality compaction characteristics that are under the direct control of the contractor, and (3) provide a mea- surement at or near the time of construction. In some cases no suitable testing technology is available to measure the various Table C.1. In Situ Point Measurements Property Measurement Test Methods/References Measurement Parameter Modulus of subgrade reaction (k-value) AASHTO T222: Nonrepetitive Static Plate Load Test of Soils and Flexible Pavement Components for Use in Evaluation and Design of Airport and Highway Pavements k-value Dynamic modulus ASTM E2583: Standard Test Method for Mea- suring Deflections with a Light Weight Deflectometer (LWD); ASTM WK25932: New Test Method for Measuring Deflections Using a Portable Impulse Plate Load Test Device ELWD Dynamic cone penetration (DCP) resistance ASTM D6951: Standard Test Method for Use of the Dynamic Cone Penetrometer in Shal- low Pavement Applications DCP Index, California bearing ratio (CBR) Falling weight deflectometer (FWD) modulus ASTM D4694–09: Standard Test Method for Deflections with a Falling-Weight-Type Impulse Load Device EFWD Clegg impact hammer (CIH) value ASTM D 5874: Standard Test Method for Determination of the Impact Value (IV) of a Soil Clegg impact value (CIV) Rolling wheel deflectometer (RWD) value ARA. 2005. Rolling Wheel Deflectometer. Bro- chure. Applied Research Associates, Inc., Albuquerque, N.M. http://www.ara.com/ Projects/RWD_brochure.pdf. Accessed November 9, 2009. d Seismic pavement analyzer (SPA) value Nazarian, S., M. Baker, and K. Crain. 1995. Use of Seismic Pavement Analyzer in Pave- ment Evaluation. In Transportation Research Record 1505, TRB, National Research Council, Washington, D.C., pp. 1–8. ESPA Borehole shear test (BST) shear strength parameters Handy, R. L. 2002. Borehole Shear Test Instruction Manual. Handy Geotechnical Instruments, Inc., Madrid, Iowa. c′, f′ Vane shear test (VST) peak and residual shear strength ASTM D2573: Standard Test Method for Field Vane Shear Test in Cohesive Soil Su, Su-r Moisture content Numerous devices can be used to determine moisture content. w% Other* To be determined* To be determined* Note: *Other test devices may provide desired performance assessments that are not listed here, and many new technologies are being developed that will serve this purpose.

65 functional design properties (e.g., measures that reflect long- term repetitive loading conditions). In addition to these cur- rent technology gaps, analysis gaps exist for which there is no known way to collect and process the desired information. Many recent studies (e.g., NCHRP 626) have focused on iden- tifying improved measurement technologies. 4 DESIGN AND PERFORMANCE CRITERIA Design parameter values for the materials subject to perfor- mance quality assessment in this specification were developed on the basis of the procedures identified in Table C.2. The design values establish the performance quality target values to be evaluated in the quality control and quality assessment testing. Table C.2 also lists the project-specific performance criteria. Commentary: This section lists the project design procedure(s) and elements of the geotechnical system and engineering parameters and mechanisms that control performance attri- butes. By providing this information, the link is established between the design phase and construction quality assessment phase of the project. The performance parameters determined from laboratory measurements and the field investigation should be provided. 5 CONSTRUCTION REQUIREMENTS Commentary: In exchange for providing the contractor flex- ibility with regard to construction operations to meet the design and performance criteria for embankment and foun- dation construction, the agency should require the contractor to describe in its QMP how it intends to perform the work and meet the performance requirements. A well-developed plan should help assure the agency that the contractor understands how its own actions (e.g., scheduling, hauling, spreading, fin- ishing, and compaction) will affect the in-place properties and performance of the work and that the contractor has planned the work and allocated its resources accordingly. 6 QUALITY MANAGEMENT Commentary: The requirements included in this section assume the contract includes a separate provision related to development and implementation of a quality management plan (QMP) that defines general requirements related to the Table C.2. Example Design and Performance Criteria Material Components Design Procedure1 Example Performance Criteria2 Embankment fill (>3 ft below bottom of pave- ment layer) Limit equilibrium slope instability analysis at (failure surface) FS ≥ 1.5 Total settlement criteria ≤ 2% of fill height Differential settlement criteria ≤ 1 in. Effective cohesion, c′ = 500 psf Effective friction angle, f′ = 25 degrees (accounting for geometric factors and ground water table, etc.) k-value ≥ 200 pci w% ≥ strain softening condition for post- saturation and ≤ required to achieve strength/stiffness criteria Pavement foundation layers (subgrade, stabi- lized subgrade, unbound base and fill ≤3 ft below bottom of pavement layer) 1993 AASHTO Guide for Design of Pavement Structures/MEPDG Determine resilient modulus (Mr) per AASHTO T307 and estimate k-value = Mr /19.4 Subgrade k-value = 160 pci Stabilized subgrade, k-value = 300 pci or achievement of 50 psi unconfined com- pressive strength Unbound k-value = 400 pci (composite k-value based on 30-in. diameter plate load test) In situ Mr = 30,000 psi w% ≥ strain softening condition for post- saturation and ≤ required to achieve strength/stiffness criteria Fill materials at identified critical areas (e.g., structural foundations, box culverts) Total settlement criteria ≤ 1% of fill height Differential settlement criteria ≤ 0.5 in. k-value = 500 pci w% ≥ strain softening condition for post- saturation and ≤ required to achieve strength/stiffness criteria 1 Agency to update design references with applicable FHWA design or agency procedures. 2 Parameters and values provided as examples only. Actual values are project specific and based on the project design requirements.

66 contractor’s quality management personnel and organiza- tional structure, documentation and reporting requirements, and procedures related to nonconforming work, corrective action, and similar matters. In case such requirements are not otherwise addressed in the contract’s general conditions, a sample general provision addressing quality management is included among the guide specifications developed under the SHRP 2 R07 project. 6.1 Contractor’s Quality Management Plan (QMP) Develop and submit a project-specific QMP at the time of the preconstruction meeting that addresses • Quality control of the compaction materials, including RICM equipment, operations, and coordination with the department’s on-site calibration testing. QC may be based on assessment of the RICM MVs according to Section 6 of this specification. • Process for performing compaction operations during the agency’s verification testing to establish RICM tar- get values. • Data acquisition methods and methods of transmit- ting data to the engineer. • Corrective actions to bring areas of noncompliance into compliance per the performance assessment crite- ria described in Section 6 of this guide specification. • Development of daily quality compaction report sub- mittals to the engineer. 6.2 RICM Repeatability/Reproducibility Analysis Perform a repeatability/reproducibility analysis accord- ing to the procedures described in Attachment A. Conduct repeatability/reproducibility analyses at the beginning of the project and thereafter as directed by the engineer. 6.3 Correlation Analysis For correlation analysis, the agency will conduct the in situ PMV testing. Perform RICM roller operations for calibration testing in the presence of the engineer, unless approved other- wise. Conduct roller operations to ensure the results are repeatable and reproducible. The engineer will evaluate all MV and PMV results to set the RICM TV. The analysis details for correlation analysis are described in Attachment B: Correlation Analysis Between RICM Measurement Values and QA/QC Point Measure- ments. A test report will be prepared within 24 hours of com- pleting the testing and will include the following: • Test identification number; • Dates of testing; • Names of QC field personnel conducting tests; • Description of tests; • Tables presenting all data; • Plots of test results; • Summary of calculated engineering values; • Plot of RICM MV versus in situ PMV measurements; and • Geospatially referenced plots of RICM results (see Attachment C: Geospatial Uniformity Analysis). 7 PERFORMANCE EVALUATION AND ACCEPTANCE CRITERIA The department will base performance compaction accep- tance on four primary quality factors for compacted materi- als and Type I or Type II performance compaction quality assessment options. 7.1 Primary Quality Factors The four primary quality factors for compacted materials are as follows: 1. The RICM TV (in correlation with the PMV) over the entire site is achieved to at least some specified minimal value during construction (e.g., 80% of the lot area). 2. The variability of the RICM MV (in correlation with the PMV) over the entire site is no more than some specified maximum amount [e.g., the coefficient of variation (COV) <30%, distribution of 90% of 90% RICM TV, or geospatial statistical analysis parameters]. 3. Contiguous areas (“blobs”) not achieving the RICM TV (in correlation with the PMV) are no larger than some maximum specified value (e.g., 25 yd2 of area, depending on the severity of noncompliance). 4. The moisture content is not less that the critical moisture content to ensure postsaturation placement volumetric stability (e.g., prevent collapse/swell, strain softening). Assessment of these factors is described in Section 7.2, Quality Compaction Performance Acceptance Options. Commentary: The quality assessment program should provide the ability to measure the design parameters in the field to assess compliance with the design, and to facilitate the setting of suit- able target values for in situ measurements that will provide assurance of the quality and performance of the final product. The four primary quality factors in Section 7.1 form the basis of requirements for testing to establish the target values and define responsibilities for the contractor’s process control and the agency’s verification and acceptance testing. The specification should require that the contractor report the QC from RICM MVs while the agency (or independent agent) performs the in situ performance QA testing. The RICM MVs will be part of the overall data used to inform the agency’s acceptance decision.

67 7.2 Quality Compaction Performance Acceptance Options The department will assess the four primary quality factors using one of the two options described in the following: Commentary: Refer to Figure C.2 and Table C.3 for additional explanation of the two options. Performance compaction Type I: For this option, the depart- ment will use the calibrated RICM-MV maps to target loca- tions for QA PMV testing. The department will use the RICM-MV proof maps to identify areas of possible non- compliance (e.g., too dry/wet, undercompacted, low stabi- lizer content) to focus QA point measurements. Use the compaction history of the RICM MVs to control the compaction process. Follow and document proper QC procedures (e.g., controlling moisture content, lift thickness) during compaction operations. Provide the RICM-MV proof maps to the engineer for evaluation and selection of QA test locations. The proof maps are to be assessed in terms of the four primary quality factors described in Section 7.1. The engineer (or the department’s independent QA agent) will select the number of tests and test locations on the basis of the RICM proof maps. The department will base acceptance on achievement of the RICM-TV requirements and in situ PMVs. If quality criteria are not met, perform additional compaction passes and/or adjust construction operations (e.g., moisture, lift thickness), after which the engineer will retest the area. Performance compaction Type II: The department will establish RICM TVs from on-site calibration of RICM MVs to QA point measurements. This specification option requires detailed calibration of RICM MVs to in situ QA PMVs from a representative calibration test strip before performing pro- duction QA testing. The department will establish the RICM TV from project QA criteria through regression analysis and application of prediction intervals. Correlation test strip con- struction and testing for this option are discussed in Attach- ment B: Correlation Analysis Between RICM Measurement Values and QC/QA Point Measurements. The department will base acceptance of the production area on achievement of MV-TV at the selected prediction interval (e.g., 80%) and achievement of target QA PMVs in the areas with MVs < MV-TV. If quality criteria are not met, perform additional compaction passes and/or adjust construction operations (e.g., moisture, lift thickness), after which the engi- neer will retest the area. Low MV High MV In-situ QAx x Perform production compaction Map production area with constant roller operation settings (a, f, v) Adjust MV scale to find “weak” areas Perform additional compaction and/or adjust process control operations: material type, moisture, lift thickness, etc. NO Retest failed areas YES Production area Accepted Production area Map x Ty pe I Minimum QA-TV MV -TV Prediction limits associated with % confidence Perform calibration to determine target MV-TV In-situ QA Test R ol le r M V Production Area MVs > MV-TV over 80% of the lot area NO Perform additional compaction and/or adjust process control material type, moisture, lift thickness, etc. In-situ QA tests in “weak” areas > QA-TV YES* NO Production area Accepted Retest failed areas Roller operation settings (a, f, and v) are constant during calibration Fail Pass In-situ QAx x x x Production area Map Roller operation: a, f, v are similar to calibration x x x Ty pe II Minimum QA-TV MV -TV Measurements that do not meet the QA criteria Ro lle r M V + Production QA tests + + + + + + Contiguous areas not achieving the RICM-TV are no larger than maximum specified value YES* *Perform QC testing and maintain adequate process control operations (i.e., lift thickness, moisture, etc). Compaction history documents with roller passes and can be monitored to identify problematic areas. For example, if ∆MV ≤ 5%, it can identified as an area with no compaction change, which can be because the material is compacted or the material is too wet or too thick. MV ≤ 5% Av e ra ge Ro lle r M V Pass Count Co m pa ct io n H is to ry Establish RICM-TV based on Compaction History In-situ QA tests in “weak” areas > QA-TV Ty pe I operations:Ty pe II ∆MV Co m pa ct io n H is to ry Figure C.2. Illustrations of the specification process for performance compaction Types I and II.

68 Commentary: For modulus/strength measurements simple linear regression analysis is generally suitable, while for cor- relation to dry unit weight/relative compaction measurements, multiple regression analysis including moisture content as a variable may be needed. If underlying layer support condi- tions are heterogeneous, relationships are likely improved by performing multiple regression analysis with RICM MV or point measurement data from underlying layers. Details of regression analysis are described in Attachment B: Correlation Analysis Between RICM Measurement Values and QC/QA Point Measurements. Assessment of the required moisture content on the basis of per- formance parameters values (e.g., strength, stiffness, volumetric stability) has been described in the literature and continues to be part of ongoing research efforts. An example of a method to adjust plate load test k-values is described in AASHTO T222. In that test standard, a saturation correction factor is developed on the basis of the ratio of the deformation of a test speci- men at the natural moisture content to the deformation in a saturated specimen under loading. Two specimens of the un disturbed material are placed in a consolidometer or triaxial chamber. One specimen is tested at the in situ moisture content and the other is saturated after the seating load has been applied. Each specimen is then subjected to the same seating load that was used for the field test (or to account for the desired embankment loading). The seating load is allowed to remain on the in situ moisture content specimen until all deformation occurs, at which time a zero reading is taken on the vertical deformation dial. Without releasing the seating load, additional load is applied to the specimen and allowed to remain until all deformation has occurred. A final reading is then taken on the vertical deformation dial. The other speci- men is allowed to soak in the consolidometer or trial cell under the seating load. After the specimen is saturated, a zero dial reading is obtained; then without releasing the seating load, an additional load is applied. The load is allowed to remain on the specimen until all vertical deformation has occurred, and after that a final reading on the dial is obtained. A correction for saturation is then applied. Determine the target stiffness values as described in ASTM D5874: Standard Test Method for Determination of the Impact Value (IV) of a Soil. The test method involves Table C.3. QC/QA Test Guidelines for Performance Compaction Types I and II Description Type I Type II Subgrade, subbase/base layers, stabilized layers <– 3ft below the bottom of the pavement Acceptance criteria QC RICM TV is achieved in at least 90% of the lot area; QC TV is achieved in RICM-identified “weak” areas; COV < 30%, or 90% of RICM values fall within 90% of RICM TV or of meeting geostatistical target parameters; and RICM noncompliance areas (“blobs”) not achieving the RICM-TV are no larger than 15m2. QA QA TV is achieved in RICM-identified weak areas. RICM-TV determination RICM TV is established by contractor, on the basis of machine-soil specific operations and monitoring compaction curves (e.g., DMV ≤ 5%). RICM TV is established from calibration test strips on the basis of a QA-TV point measurement and a desired percentage prediction interval (e.g., 80%). Testing frequency QC RICM-MV Quality Compaction Reports: Lift thickness, roller pass count, RICM compaction curves QA 1 per 4000 yd2/layer 1 per 8000 yd2/layer QA/QC test methods QC RICM MV QA Plate load test (PLT), DCP (for nongranular soils), LWD (for granular and stabilized soils), FWD Embankment fill > 3 ft below the bottom of the pavement Acceptance criteria QC RICM TV is achieved in at least 80% of the test area; QC TV is achieved in RICM-identified weak areas; COV < 40%, or 80% of RICM values fall within 90% of RICM-TV or of meeting geostatistical target parameters; and RICM contiguous noncompliance areas (“blobs”) not achieving the RICM TV are no larger than 25m2. QA QA TV(s) are achieved in RICM-identified weak areas. RICM-TV determination RICM TV is established by contractor, on the basis of machine-soil specific operations and monitoring compaction curves (e.g., DMV ≤ 5%). RICM TV is established from calibration test strips on the basis of a QA-TV point measurement and a desired percentage prediction interval (e.g., 80%). Testing frequency QC RICM-MV Quality Compaction Reports: Lift thickness, roller pass count, RICM compaction curves QA 1 per 5000 yd3 (1 per 2000 yd3 in designated critical areas) 1 per 10,000 yd3 (1 per 5000 yd3 in designated critical areas) QA/QC test methods QC RICM MV QA PLT, DCP (for nongranular soils), LWD (for granular and stabilized soils), BST, VST

69 preparation of test specimens and selected moisture contents and compaction energies. Tests are then performed to estab- lish the CIV versus moisture content. In this standard test method a target value for the CIV is determined from the correlation curve at the point at which an increase in water content results in a corresponding loss of strength. Similar procedures can be used to set strength and stiffness–based tar- get values. 8 METHOD OF MEASUREMENT Measurement for embankment materials furnished and placed in accepted portions of work will be in cubic yards of placed material. Measurement for subgrade materials, stabi- lized materials, and unbound base material furnished and placed in accepted portions of work will be in square yards for the specified design thickness. The measured area will be based on plan dimensions for the finished surface but will exclude fillets. The department will verify design thickness of the placed materials with spot checks of the grade. 9 BASIS OF PAYMENT AND PAYMENT ADJUSTMENTS This section describes relationships between payment, pay factors, and performance measurement values. A. Option 1: The contractor will be paid the contract unit price per square yard for each specified design thickness of sub- grade materials, stabilized materials, and unbound base as measured above. This payment shall be full compensation for furnishing all materials, water, preparation of subgrade, and for doing all work necessary to complete the material placement in compliance with the contract documents. B. Option 2: Payment for RICM will be the lump sum con- tract price. Payment is full compensation for all work associated with providing RICM-equipped rollers, trans- mission of electronic data files, two copies of RICM roller manufacturer software, and training. Delays resulting from GPS satellite reception of signals to operate the RICM equipment or RICM roller breakdowns will not be considered justification for contract modifications or con- tract extensions. In the event of RICM roller breakdowns or system malfunctions/GPS problems, the contractor may operate with conventional rolling operations; but RICM proof mapping shall be provided for a minimum 90% of the project surface. If corrective construction work is necessary, as determined from proof mapping, because of unforeseen ground conditions, the department may pay for the corrective work required at the applicable con- tract unit price or as extra work. C. Option 3: The contractor will be paid according to a pay adjustment to the final quantities on the basis of the final proof map RICM MVs according to the following relationships: Range of RICM MV >– TV Pay Factor 80 1.00 85 1.04 95 1.08 100 1.10

70 Attachment A: Repeatability and Reproducibility Analysis Using Two-Way Analysis of Variance (AnOVA) For roller measurement values m: number of passes on a test strip; I: number of data points across the test strip; and J: change in operator, amplitude, speed, direction, etc. For LWD measurement values m: number of measurements at a location; I: number of test locations; and J: change in operator, device, material tested, etc. The two-way random effects model and the three quantities of interest are provided here: = µ + α + γ + αγ + ε σ = σ σ = σ + σ σ = σ + σ γ αγ2 2 & 2 2 yijk i j ij ijk repeatability reproducibility R R reproducibility repeatability Estimates of these from two-way ANOVA results are shown here, and the parameters of the equations are shown in Table C.A.1 with ANOVA results. MSErepeatabilityσ = σ = For LWD measurements, srepeatability is simply the standard deviation of repeated measurements obtained at a given loca- tion. To calculate, sR&R and sreproducibility, Condition (i.e., opera- tor, device, material tested, etc.) variables are considered as nominal variables in two-way ANOVA. A typical ANOVA table is provided (Table C.A.1). For roller measurements, srepeatability is computed by consid- ering Pass and Location as nominal variables in two-way ANOVA—accounting for the systematic pass effect. To calcu- late, sR&R and sreproducibility, Condition (i.e., amplitude, speed, direction, etc.), and Location variables are considered as nominal variables in two-way ANOVA. A typical ANOVA table is provided (Table C.A.1). Pass effect on the measurement val- ues in this case should be statistically insignificant (as assessed by student’s t-ratio and p-value). (As a rule-of-thumb, in a simple linear regression analysis between pass and roller mea- surement values, if t-ratio is < -2 or > 2 and p-value is < 0.05, the effect of pass can be considered statistically significant.) To conclude that there is no effect of change in Condition or Loca- tion, the reproducibility standard deviation should be similar or less than the repeatability standard deviation. Requirements for Reproducibility and Repeatability Analy- sis: Currently, there are no published acceptable limits of mea- surement error for the roller measurement values. However, it is an important element of this specification for evaluating the usefulness of a machine before its use or even periodically dur- ing the course of the project, and it will help build confidence in the measurements. Variability in RICM MVs is one source of scatter in relationships with in situ point measurements. The measurement variability is quantified in this specification in a repeatability and reproducibility context. Repeatability refers to variation observed in the measurement values (also referred to as measurement error) obtained over a test area from consecu- tive passes under identical operating conditions (i.e., using same operator, amplitude, speed, direction of travel). Repro- ducibility refers to the variation in measurements obtained from consecutive passes under changing conditions. The changing conditions may result from different measurement methods, machines used, operators, or speed and amplitude settings. The repeatability and reproducibility analysis proce- dure described is applicable for any IC technology, although the magnitude of measurement error (for the range of RICM MVs) is expected to be different for different RICM technologies. This is of consequence in a specification context as it affects the regression relationships and anticipated variability in MVs. The procedure for calculating reproducibility and repeatabil- ity errors is presented in the attachment. Generally, a 250-ft long well-compacted test section representative of the pro- duction area is suitable for conducting the repeatability test- ing. At least four roller passes are recommended for a given roller operation parameter (speed, theoretical vibration amplitude, vibration frequency, and travel direction). The roller passes should be performed to capture the planned operating conditions on the project. The total number of passes can be determined as follows: Number of passes = 4 × machine operation variables to be used during production (e.g., amplitude, speed, direction, frequency). For example, the total number of passes required to evaluate just the influence of speed at two different settings, then the total number of passes required = 4 × 2 = 8 passes. It should be noted that the measurement error should be expected to increase with an increasing number of variables in the analysis. Variants of this process can also provide acceptable results and depend on the desired roller operating conditions. As discussed later, the RICM roller measurement error is an input parameter that is required as part of statistical QA/QC assessment. Analysis Methodology: Consider a data set consisting of m repeated measurements at a test location at I different loca- tions under each condition of operation J.

71 σreproducibility MSC ml ml MSE = + −( ) −max ,0 1I MSAC m R R reproducibility repeatabili     = +σ σ σ& 2 ty2 A two-way ANOVA Table such as indicated in Table C.A.1 can be generated using any standard statistical analysis software (e.g., JMP, SPSS) or using add-ins in Excel. An example step- by-step procedure of repeatability and reproducibility analy- sis using JMP statistical analysis software for roller and ELWD measurement values follows. Example Calculation of Repeatability and Reproducibility Analysis for Roller Measurements [Outputs from JMP Sta- tistical Analysis Software]: The following analysis is for roller measurements (MDP*) obtained over a 50-m long compacted test strip with variable stiffness in two different speeds (nominal 3.2 km/h and 6.4 km/h) at a constant amplitude setting (a = 0.9 mm). The data is analyzed for repeatability of MDP* at constant speed settings and repro- ducibility of MDP* with change in speed. • For this data set 44 m: number of passes on the test strip in each setting = 5; 44 I: number of data points across the test strip = 164; and 44 J: total number of speed settings = 2. • First, the repeatability (srepeatability) of MDP* at each speed setting is computed. As explained earlier, number of Passes and Location are considered as nominal variables and a two- way ANOVA is performed, accounting for any systematic pass effect, to compute srepeatability. The data must be orga- nized into columns of Pass, Location [location represents data points across the test strip], and Measurement Values as shown in Figure C.A.1. One challenge with organizing the Location column is that the data points obtained from dif- ferent passes are not collected at the exact same location. To overcome this problem, the data should be processed in such a way that an average data is assigned to a preset grid point (e.g., 0.3 m as used in this report) along the roller path. The grid point along the roller path represents an average of RICM MVs that falls within a window of size that is half the size of the grid length (in this case it is 0.15 m) in forward and backward directions. • The Pass and Location columns have to be selected as Nomi- nal (highlighted as histograms, see Figure C.A.1) while the measurement values (in this case MDP*) have to be selected as Continuous (highlighted as the triangle, see Figure C.A.1) variables. • Then select “Fit Model” as shown in Figure C.A.2 which opens a “Model Specification” window. Select the measure- ment value as “Y”, and add Pass and Location number as “Construct Model Effects” as shown in Figure C.A.4. Then select “Run Model.” The two-way ANOVA table and MSE repeatability= σ results are shown in Figure C.A.2. • For reproducibility analysis, select at least three passes data that have statistically negligible effect of pass. Organize the data in columns of Pass, Location, Measurement Value (in this case MDP*), and Speed. The Pass, Location, and Speed columns have to be selected as Nominal, while the Mea- surement Value column has to be selected as Continuous (see Figure C.A.3). • Then select “Fit Model” and select the measurement value as “Y”, and add Location (I), Speed (J), and Location * Speed (I*J) interaction terms as “Construct Model Effects” as shown in Figure C.A.4. Then select “Run Model.” • The two-way ANOVA Table and MSE reproducibility= σ results are shown in Figure C.A.3. Using the SSC, SSAC, and cor- responding degree of freedom numbers calculate )( )(σ = + − − σ = σ + σ max 0, I 1 MSAC & 2 2 MSC mI mI MSE m reproducibility R R reproducibility repeatability • Using data in Figure C.A.3 and the above equations (for MDP*), the srepeatability = 5.9, sreproducibility = 18.2 mm, and sR&R = 19.1 mm. • Results indicate that the contribution of sreproducibility to the overall variability sR&R is greater than the contribution of srepeatability. For this data set, the impact of change in speed on MDP* is considered statistically significant. Table C.A.1. Typical Two-Way ANOVA Table Source SS (sum of square) DOF (degree of freedom) MS (mean square) Location (I) SSA I - 1 MSA = SSA/(I - 1) Operating condition (J) SSC J - 1 MSC = SSA/(J - 1) I × J (interaction term) SSAC (I - 1) (J - 1) MSAC = SSAC/(I - 1)(J - 1) Error SSC IJ (m - 1) MSE = SSE/IJ(m - 1) Total SSTot IJm - 1 —

72 Nominal Continuous Multiple pass data Figure C.A.1. Data organization in JMP for repeatability analysis of roller measurement values.

73 MSE repeatability= σ Figure C.A.2. Repeatability analysis procedure in JMP.

74 Nominal Continuous Multiple pass data Corresponding Speed setting Figure C.A.3. Data organization in JMP for reproducibility analysis.

75 SSC SSAC (J-1)*(I-1) J-1 Two-Way ANOVA Table MSE repeatability= σ Figure C.A.4. Results of two-way ANOVA for roller measurement reproducibility analysis.

76 Portions of this attachment are reprinted from NCHRP 2009b, with permission from the Transportation Research Board. Implementation of RICM technologies into earthwork speci- fications requires an understanding of relationships between roller MVs and soil compaction measurements. Simple linear correlations between MVs and compaction layer in situ point measurements are possible for a compaction layer underlain by relatively homogenous and stiff/stable supporting layer. Heterogeneous conditions in the underlying layers, however, can adversely affect the relationships. In some cases regres- sion coefficients can be improved using multiple regression analysis that includes parameter values to represent underly- ing layer conditions when statistically significant, to improve the correlations. ELWD, EV1, EV2, and EFWD measurements gen- erally capture the variation in roller MVs better than dry unit weight measurements. DCP tests are effective in detecting deeper weak areas (at depths > 300 mm) which are com- monly identified by the roller MVs and not by compaction layer point measurements. High variability in soil properties across the drum width and soil moisture content contribute to scatter in relationships. Averaging measurements across the drum width and incorporating moisture content into multiple regression analysis, when statistically significant, can help mitigate the scatter to some extent. Relatively constant machine operation settings are critical for calibration strips (i.e., constant amplitude, frequency, and speed), and correla- tions are generally better for low amplitude settings (e.g., 0.7 mm to 1.1 mm) for vibratory rollers. A field testing protocol to obtain reliable correlations during implementation/roller calibration testing and establishing target values from simple and multiple regression relationships is described in this attachment. Requirements for Correlation Test Strips Construction and In Situ Testing: The calibration test area should be prepared and constructed with the same methods and conditions (e.g., material type, moisture conditioning, and lift thickness) as in the production area. Roller MVs are influenced by lift thick- ness, material type, moisture content, and the underlying layer support conditions. Plan dimensions required for the calibration area depend on the spatial heterogeneity of the support conditions and variability in moisture content of the material. As a guide, for areas with relatively homogenous support conditions and uniform moisture content, a repre- sentative calibration test area with minimum dimensions of 5 m wide by 50 m long should be identified. The test area should be relatively consistent in structure (e.g., cut/fill sec- tion) to a depth of about 1 m. If heterogeneous support condi- tions are evident over the production area, the plan dimensions should be increased up to 7.5 m wide by 100 m long. A roller MV map of the underlying layer and/or MV map of the first roller pass over the production area are helpful in selection of an appropriate area for calibration. Judgment is involved in selecting the location and size of the calibration test area. The 50 to 75 percentile variation can be used to target the size and location of the calibration area on the basis of MVs from an initial roller pass of the area. Compaction operations in the calibration area should be performed at constant amplitude (if not static), frequency, and speed. A low amplitude vibration setting (~0.7 mm to 1.1 mm) is preferred for vibratory operations. High amplitude settings can cause “jumping” as compaction increases, which affects some roller MVs and reduces correlations to QA point measurements. Point test measurements as required by the project QA criteria (e.g., target dry unit weight, ELWD) should be performed in parallel with roller compaction operations. At each test location, at least three test measurements should be obtained across the drum width and averaged to generate one regression point. Regression relationships improve by averaging measurements across the drum width. Test mea- surements should be obtained at several locations across the calibration area, for at least three intermediate passes (e.g., 1, 2, 4, 8, or 12) until target compaction is achieved. As the range of regression data increases, the correlations are improved and likely more representative of variability in the production areas. For a 50-m long test strip, five test points per pass along the centerline of the roller lane would be the minimum, and 10 test points per pass with three measurements across the drum width at each test point would be about the maximum. The contractor and/or owner will benefit from investing in more testing up front as part of the calibration to improve reliability of the correlations and selected MV-TVs. Calibra- tion analysis of roller MVs to in situ point measurements is described later in the attachment. Simple linear regression relationships are developed from calibration analysis with prediction intervals using in situ point measurements averaged over the width of the drum(s) and roller MV data corresponding to the spatially nearest point. Generally, the least-square regression relationship should achieve an R2 value of at least 0.50. Typically, the R2 values do not exceed 0.80. Obtaining reliable correlations between com- paction layer point measurements (e.g., dry unit weight) and roller MVs with soft and heterogeneous support conditions (especially in the case of a soft underlying layer) can be difficult. Variation in roller MVs are generally better captured by stiff- ness/modulus measurements compared with dry unit weight measurements, especially with heterogeneous support condi- tions at shallow depths (<300 mm). In situ point measurements Attachment B: Correlation Analysis between RiCM Measurement Values and QC/QA point Measurements

77 (e.g., DCP, PLT, EFWD/ELWD) that provide information deeper than the compaction layer can help improve confidence in cor- relations for such conditions. Regardless, scatter in regression relationships is to be expected. Major factors that influence the regression relationships include (a) differences in measurement influence depths, (b) range over which measurements were obtained, (c) influence of moisture content on point measure- ments, (d) intrinsic measurement errors associated with the roller MVs and in situ point test measurements, (e) position error from pairing point test measurements and roller MV data, and (f) soil variability. Multiple regression analysis can be performed by incor- porating underlying layer properties (i.e., roller MVs or in situ point measurements of the underlying layer) for hetero- geneous support conditions to obtain improved correlations with compaction layer point measurements. Selection of tar- get values using multiple regression relationships should be based on applying prediction intervals to the predicted roller MV and mean squared error of the estimate. Moisture con- tent can also be included in multiple regression analysis to better relate dry unit weight to roller MVs. MV TVs for that case should be based on multiple regression relation- ships. Regression analysis between roller MVs and in situ stiffness based point measurements (e.g., ELWD, EFWD) gener- ally do not require multiple regression analysis with mois- ture as a variable. Simple Linear Regression Analysis: Simple linear regression analysis involves developing a relationship between indepen- dent and dependent variables using an intercept and slope coefficient. This analysis has the advantage of being simple enough to perform on a hand calculator. For each linear, uni- variate regression model the coefficient of determination R2 provides a measure of how well the regression model describes the data. For reference, correlations considered acceptable per the European specification options meet the requirement of R2 ≥ 0.5. Although simple linear regression analysis is relatively straightforward, many factors can affect the quality of the cor- relation between MVs and the various point measurement val- ues. A list of these factors is provided in this section to aid the reader in interpretation of the results. Multiple regression analysis was identified as one approach to overcome some of the factors that affect the simple liner regression relationships and is discussed later. Analysis Approach: Simple linear regression relationships were developed by considering in situ point measurements as “true” independent variables and roller MVs as dependent variables using the model shown in Equation C.B.1. Statistical significance of the independent variable was assessed based on p- and t-values. The selected criteria for identifying the signifi- cance of a parameter included p-value < 0.05 = significant, p-value < 0.10 = possibly significant, p-value > 0.10 = not sig- nificant, and t-value < -2 or > +2 = significant. Roller MV b b i (C.B.1)0 1= + α where b0 = intercept, b1 = slope, and a = point measurement value. Calibration analysis of roller MVs to in situ point measure- ments is performed using the inverse regression method (Ott and Longnecker 2001) to establish an MV TV for a target QA measurement value (QA TV). This procedure is illustrated in Figure C.B.1 with MV as a dependent variable (y) and the in situ point measurement as an independent true measurement variable (x). As a measure of uncertainty in the regression relationship, prediction limits at the selected percent confi- dence can be applied to estimate the limits of in situ test mea- surement values for an observed roller MV (prediction limits should not be confused with confidence intervals). From this procedure, roller MV TV to achieve a minimum QA TV corresponding to a percent confidence can be estab- lished using the upper prediction limits as shown in Fig- ure C.B.1. The greater the percent confidence needed in the predictions, the higher the MV TV. Factors Affecting Quality of Regression Relationships: As with any regression analysis, it is important to identify factors that affect the quality of the regressions. Factors affecting regression relationships are broadly identified in Table C.B.1 for the purpose of linking some of these factors to various test bed (TB) conditions. This list was derived from linking TB conditions with correlation analysis but also from experi- ences gained from field tests as part of this study. Five exam- ples described in the next section illustrate some of the TB conditions that led to development of Table C.B.1. Hetero- geneity in support conditions of layers underlying the com- paction layer is one of the major factors that affect correlations between MVs and point measurements. This is largely due to differences in measurement depths between the roller and the point measurements. Roller MVs from 11- to 15-ton vibra- tory rollers can be representative of conditions to depths of 1.0 to 1.2 m (3.3 to 3.9 ft). Use of underlying layer MVs and use of point measurements with comparable measurement influence depths are ways to overcome this obstacle. This approach is discussed in detail in the multiple regression analysis section. Multiple Linear Regression Analysis: Use of multiple regres- sion analysis to statistically assess the influence of variability in underlying layer soil conditions and variability in machine operation conditions is presented in this section. Multiple regression analysis is performed by incorporating variables of interest as independent variables into a general multiple

78 linear regression model, as shown in Equation C.B.2. The sta- tistical significance of each variable is assessed based on p- and t-values. The selected criteria for identifying the sig- nificance of a parameter included p-value < 0.05 = signifi- cant, < 0.10 = possibly significant, > 0.10 = not significant, and t-value < -2 or > +2 = significant. The p-value indicates the significance of a parameter, and the t-ratio value indicates the relative importance (i.e., the higher the absolute value, the greater the significance). (C.B.2) 0 1 2 3 4 5 6 2 7 8 Roller MV b b b w b A b b b w b f b vi i i i i i i i = + α + + + β + γ + + + where b0 = intercept; b1, b2, b3, b4, b5, b6, b7, b8 = regression coefficients, A = amplitude (mm), a = point measurement value (gd, ELWD, etc.); b = underlying layer roller MV or point measurement; g = lift thickness (mm); f = vibration frequency (Hz); and v = velocity (km/h). For the multiple regression analysis, the reported R2 values have been adjusted for the number of regression parameters, as shown in Equation C.B.3, where n = the number of data points and p = the number of regression parameters. The adjusted coefficient of determination R2adj from multiple regression analysis may be compared with R2 from simple linear regression analysis to assess which regression model best captures variation in the data. R adjusted R n n p 1 1 1 (C.B.3)2 2( ) ( )= − − − − Complications with collinearity should be avoided when performing multiple regression analysis. Collinearity refers to inclusion of two or more strongly related independent vari- ables into a model to predict a dependent variable, which may result in misleading R2adj values (Ott and Longnecker 2001). This is possible in the above-described model if, for example, underlying layer MV and point measurement values are included together. Collinearity in a model can be detected using variance inflation factors (VIF). VIF of ith independent variable is defined as 1/(1 - R2i), where R 2 i is the coefficient of determination for the regression of the ith independent vari- able on all other independent variables. Although there are no formal criteria on the acceptable magnitude of VIF, a common rule of thumb is that if VIF of the ith independent variable is < 1/(1 - R2), where R2 is the coefficient of determination of the univariate model), then it can be concluded that the variable is not contributing to collinearity (Freund et al. 2003). Figure C.B.1. (a) Illustration of inverse regression method and (b) application of prediction limits to establish roller MV target values. y = 0 + 1x Distributions of y for various x x y Linear regression model is y = 0 + 1x + for a normal error with mean 0 and standard deviation ( describes how much y’s vary for a fixed x) Mean value of y x y Prediction limits associated with % confidence 0 1y x Least squares best-fit equation: Limits of x with a % confidence in the measured y Minimum QA-TV MV -TV In-situ measurement ( d, ELWD, EFWD, EV1, CBR, etc) R ol le r M V Measurements during calibration (a) (b) Table C.B.1. Summary of Factors Affecting Correlations Between MVs and In Situ Point Measurements No. Factors Affecting Correlations 1 Heterogeneity in underlying layer support conditions 2 High moisture content variation 3 Narrow range of measurements 4 Machine operation setting variation (e.g., amplitude, frequency, speed) and roller “jumping” 5 Nonuniform drum/soil contact conditions 6 Uncertainty in spatial pairing of point measurements and roller MVs 7 Limited number of measurements 8 Not enough information to interpret the results 9 Intrinsic measurement errors associated with the roller MVs and in situ point test measurements Source: NCHRP 2009b.

79 The section of this attachment on uniformity criteria is reprinted from NCHRP 2009b, with permission from the Transportation Research Board. Uniformity Criteria Uniformity is recognized as an important component of quality compaction (e.g., Davis 1953; Sherman et al. 1966). Results from numerical studies indicate that considering average values in design may not capture actual performance (e.g., White et al. 2004; Griffiths et al. 2006). With the ability of real-time viewing of compaction data, roller-integrated measurement technology offers an opportunity to construct more uniform earthwork layers. Current CCC specifications address uniformity using percentage limits based on an MV-TV. The International Society of Soil Mechanics and Geotechnical Engineers (ISSMGE 2005)/Austrian CCC earthwork specifications, for example, require that roller MVs in the production area should fall within 0.8 to 1.5 MIN-TV with a coefficient of variation < 20% (MIN-TV cor- responds to the MV at 0.95 QA-TV established from calibra- tion). Using a slightly different approach, the Minnesota Department of Transportation (MnDOT) implemented a predetermined target percentage limits distribution criterion (MnDOT 2007) on a full-scale earthwork project in the state (White et al. 2007, 2008a, 2008b). The acceptance require- ment was that 90% of roller MV data in the production area should fall within 90% to 120% of the MV-TV; none should be below 80% of the MV-TV; and if any are above 120%, a new MV-TV should be established. If uniformity criteria are desired as part of the specification, the ISSMGE and MnDOT approaches described above can be implemented [for some specification options]. However, it must be realized that these approaches are limited to condi- tions where Evaluation Sections have similar spatial heteroge- neity in compaction layer properties and support conditions to the Calibration Area. If not, achieving these uniformity tar- gets is challenging. For such cases, information of underlying support conditions may help in evaluating compaction layer data and selecting representative Calibration Areas. Further, these approaches do not address uniformity from a spatial standpoint. More research is needed in relating uniformity to performance for a better understanding of the level of unifor- mity desired and how field operations can be improved to control nonuniformity. An alternate approach to quantify uniformity is to use spatial statistics in combination with univariate statistics (mean and standard deviation; Brandl 2001; Vennapusa et al. 2010; Facas et al. 2010). Using spatial statistics requires developing semi- variogram models using spatially referenced GPS coordinate measurements, which describe the spatial relationship in the measured roller MVs. The three main characteristics by which a semivariogram is often summarized are range, sill, and nugget (Isaaks and Srivastava 1989). Comparatively, a semivariogram with a lower sill and longer range represents reduced nonunifor- mity and improved spatial continuity. Vennapusa et al. (2009) describe an approach for using spatial statistics to target areas for compaction that results in improved spatial continuity and reduced nonuniformity. Geostatistical Analysis The Geostatistics section of this attachment is reprinted from Vennapusa et al. 2010, with permission from the American Society of Civil Engineers. Geostatistics characterize and quantify spatial variability. The semivariogram g(h) is a common analysis tool to describe spatial relationships in many earth science applications and is defined as one-half of the average squared differences between data values that are separated at a distance h (Isaaks and Srivastava 1989). If this calculation is repeated for as many different values of h as the sample data will support, the result can be graphically presented as shown in Figure C.C.1 (shown as circles), which constitutes the experimental semivario- gram plot. The mathematical expression to estimate the experimental semivariogram is h n h z x h z xi i i n h ˆ 1 2 (C.C.1)2 1 ∑[ ]( ) ( ) ( ) ( )γ = + − ( ) = where z(xi) = a measurement taken at location xi; n(h) = the number of data pairs h units apart in the direction of the vector, and gˆ = an experimental estimate of the underlying variogram function g (Olea 2006). The three main characteristics by which a semivariogram plot is often summarized include the following (Isaaks and Srivastava 1989): Range (a): As the separation distance between pairs increases, the corresponding semivariogram value will also generally increase. Eventually, however, an increase in the distance no longer causes a corresponding increase in the semivariogram, and the semivariogram reaches a plateau. The distance at which the semivariogram reaches this plateau is called the range. Longer range values suggest greater spatial continuity or relatively larger (more spatially coherent) “hot spots”; Sill (C0 + C): The plateau that the semivariogram reaches at the range is called the sill. A semivariogram (which is one-half of the variogram) generally has a sill that is approximately equal to the variance of the data (Srivastava 1996); and Attachment C: Geospatial Uniformity Analysis

80 Nugget effect (C0): Though the value of the semivariogram at h = 0 is strictly zero, several factors, such as sampling error and very short scale variability, may cause sample values separated by extremely short distances to be quite dissimilar. This causes a discontinuity at the origin of the semivariogram called the nugget effect. Some important points to note are that a semivariogram model is stable only if the measurement values are stationary over an aerial extent. If the data values are nonstationary, spatial variability should be modeled only after appropriate transformation of the data (Clark and Harper 2002). If the values show a systematic trend, the trend must be modeled and removed prior to modeling a semivariogram (Gringarten and Deutsch 2001). In addition to quantifying spatial variability, geostatistics can be used as a spatial prediction technique, i.e., for predict- ing a value at unsampled locations based on values at sam- pled locations. Kriging is a stochastic interpolation procedure (Krige 1951) by which the variance of the difference between the predicted and “true” values is minimized using a semi- variogram model. Kriging was used to create “smoothed” contour maps of RICM point data for analysis of non-unifor- mity and comparison to maps of different in situ spot test measurement values. Fitting a Theoretical Model The major purpose of fitting a theoretical model to the exper- imental semivariogram is to give an algebraic formula for the relationship between values at specified distances. There are many possible models to fit an experimental semivariogram. Some commonly used models include linear, spherical, exponential, and Gaussian models. Mathematical expres- sions for these models are presented in Table C.C.1. Detailed descriptions of these theoretical models can be found else- where in the literature (e.g., Isaaks and Srivastava 1989; Clark and Harper 2002). The range in a spherical model is well defined because it has a definitive sill. This is not true for exponential or Gauss- ian models that have asymptotic sills. The approximate range for those models is three to five times larger than the range values obtained for closely matched spherical models (Clark and Harper 2002). Some researchers have used 3a as an effec- tive range for the exponential semivariogram (e.g., Erickson et al. 2005). Range (R) Scale, C Nugget, C0 Sill C + C0 Range, R: As the separation distance between pairs increase, the corresponding semivariogram value will also generally increase. Eventually, however, an increase in the distance no longer causes a corresponding increase in the semivariogram, i.e., where the semivariogram reaches a plateau. The distance at which the semivariogram reaches this plateau is called as range. Longer range values suggest greater spatial continuity or relatively larger (more spatially coherent) “hot spots”. Sill, C+C0: The plateau that the semivariogram reaches at the range is called the sill. A semivariogram generally has a sill that is approximately equal to the variance of the data. Nugget, C0: Though the value of the semivariogram at h = 0 is strictly zero, several factors, such as sampling error and very short scale variability, may cause sample values separated by extremely short distances to be quite dissimilar. This causes a discontinuity at the origin of the semivariogram and is described as nugget effect. (Isaaks and Srivastava, 1989) Spherical Semivariogram Experimental Semivariogram (circles) RhCC)h( Rh0 R2 h R2 h3CC)h( 0)0( 0 3 3 0 Se m iv a rio gr am , (h) Separation Distance, h Figure C.C.1. Description of a typical experimental and spherical semivariogram and its parameters. Table C.C.1. Commonly Used Theoretical Semivariogram Models Model Name Mathematical Expression Linear g (0) = 0 g (h) = nC0 + ph, when h > 0 Spherical g (0) = 0 g (h) = C0 + C −   3 2 2 3 3 h a h a when 0 < h < a g (h) = g (h) = C0 + C when h > a Exponential g (0) = 0 g (h) = C0 + C − −  1 exp h a when h > 0 Gaussian g (0) = 0 g (h) = C0 + C 1 2 2 exp h a − −    when h > 0 Note: p = slope of the line, a = range, C0 = nugget effect, and C + C0 = sill.

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