Implications of the 4th Power Law
Implications of the 4th Power Law Information Sheet IS-06 September 2017 Information Sheet Purpose This Information Sheet provides relevant information to assist road planners in understanding the design aspects of pavements particularly the implication of heavy vehicle traffic on roads designed for low traffic volumes. Damage to pavements steeply increases with axle loading. Asset managers and road designers must take this into account when planning and designing the loading capacity of road pavements. The information in this information sheet gives an overview of the 4th Power Law and its implications for pavement design and maintenance policies.
Issues covered
• • • • • • • •
Overview Definitions Legislative background for heavy vehicle loading (Australia/NSW) Vehicle Loads and Pavement Wear The 4th Power Law Mass Limits for Heavy Vehicles Principles of assessing damage References
Overview Asset managers are tasked with the responsibility of maximising the service life of road assets and providing local communities with value for money infrastructure services. Traffic-induced wear of road pavements is mostly a result of the wheel loading imposed by heavy vehicles. One of the challenges road managers face is how to effectively balance the growing efficiency of trucking operations and efforts to extend the service life of road pavements.
Definitions Axle – One or more shafts, positioned in a line across a vehicle, on which one or more wheels intended to support the vehicle turn. Axle load – That portion of the total vehicle load transmitted to the road through single axle. Standard Axle Load – Single access with dual wheels loaded to a total mass of 8.2 tonne (80kN) General Mass Limits (GML) – The heavy vehicle axle mass limits that apply to public roads in Australia unless otherwise limited by load restriction signs. Concessional Mass Limits (CML) – The mass exception allows tandem and tri-axle groups to be 5% above general mass limits (GML), with a maximum gross mass increase of 1.0 tonne for a vehicle up to 55.0 tonnes gross mass and 2.0 tonnes for a vehicle exceeding 55.0 tonnes gross mass. Higher Mass Limits (HML) – A mass exception under the Heavy Vehicle National Law which allows higher mass limits on approved routes for particular vehicles or vehicle combinations dependent on other conditions being met (e.g. Intelligent Access Program (IAP) and/or road friendly suspension may need to be fitted to the vehicle). Load Equivalency Factors – The ratio of the number of repetitions of a specified axle load (termed the standard load) which the pavement can sustain to the number of repetitions of another axle load which the same pavement can sustain for given damage criteria. Legislative Background for Heavy Vehicle Loading (NSW/Australia) Australia has experienced the influx of heavier vehicles following advancements in heavy vehicle design, new tyre varieties and international experience. This, coupled with the increasing efficiency in trucking operations has benefitted the trucking companies but at the same time, has resulted in the reduced service life of pavements and increased maintenance costs. As a solution, road authorities have adopted a two-pronged strategy by applying stricter control of load limits and introducing additional road charges. Arrangements for weighing heavy vehicles, known as Measurement Adjustment (MA), were introduced nationally from 1 July 2006. More information can be found in https://www.nhvr.gov.au/safety-accreditationcompliance/chain-ofresponsibility/measurement-adjustment
Vehicle Loads and Pavement Wear It is common understanding that the traffic-induced wear of road pavements is largely due to the wheel loading brought about by commercial heavy vehicles. Damage caused to pavements sharply increases with the axle loading. Addis (1992) contends that while traditionally it has been held that static axle loads of heavy vehicles is the primary determinant of pavement deterioration, other factors can likewise contribute to deterioration such as: • • • •
Type of Axle (number of wheels and type of tyres) Axle arrangement Surface contact pressure of tyre Suspension system
On its own or in combination, these factors alter the basic structural wear mechanism functioning in the pavement thus influencing the static axle load-wear relationship (Addis 1992). Thus a rule that emphasizes that pavement damage is proportional to the axle weight of a vehicle, known as the 4th power rule, was developed. This rule is what is widely used by road authorities worldwide. The 4th Power Law The 4th power law traces back to extensive testing undertaken by the American Association of State Highway Officials (AASHO) between 1958 and 1961 (TRB 1962 as cited in Addis 1992) which equated pavement deterioration with reduced/loss of pavement serviceability. In this experiment, road pavements were constructed in the form of loops with sections that had widely varying strengths. Different heavy vehicles with single axle weights ranging between 0.9 tonnes and 13.9 tonnes as well as tandem axles between 10.9 tonnes and 21.8 tonnes, were driven over the road sections in a continuous stream with each road accommodating vehicles of single axle configuration only. The deterioration of the road was monitored throughout the duration of the experiment after which a road test equation was derived which drew the connections between the given amount of physical wear of the pavement to the number of applications of a given axle load.
One consequence of the Road Test Equation is the fourth power law, which predicts that the change in pavement damage is proportional to the difference in vehicle’s axle weight to the fourth power. For example, a vehicle with an axle weight of 1000 kg is considered to cause 16 times the damage compared with a vehicle with an axle weight of 500 kg. Mass Limits for Heavy Vehicles In New South Wales, there are three tiers of mass limits for heavy vehicles: •
•
General Mass Limits (GML) – These vehicles have unrestricted access to the road system. No specific access restrictions apply and no other permits are required provided these vehicles are registered and operators pay the registration charge appropriate to the vehicle configuration. Concessional Mass Limits (CML) – allow increased mass limits for eligible vehicles. To be eligible for CML, vehicles must be accredited under the National Heavy Vehicle Accreditation Scheme (NHVAS). Companies who wish to be accredited under the CML are required to meet the eight standards of compliance in the National Heavy Vehicle Regulator’s (NHVR) Mass Management Accreditation Guide which can be downloaded at https://www.nhvr.gov.au/file s/0001mass_management_accredia tion_guide.pdf CML allows eligible vehicles to operate at increased mass limits compared to statutory limits. Mass limits for CML are set at 5% above the General Mass Limit (GML), subject to: •
•
a maximum of 1 tonne for a vehicle or vehicle combination with an allowable gross mass not exceeding 55 tonnes a maximum of 2 tonnes for vehicle combinations with an allowable gross mass exceeding 55 tonnes
IPWEA (NSW) Roads & Transport Directorate Level 12, 447 Kent Street SYDNEY NSW 2000
•
an upper limit on axle and axle group mass More information can be obtained from https://www.nhvr.gov.au/files/2014020112-concessional-mass-limits.pdf.
•
Higher Mass Limits (HML) – Represent the highest level of mass allowed to be carried on NSW roads (other than by permit, notice, or exemption). Access can be obtained in NSW by enrolling under the Intelligent Access Program (IAP) that introduces GPSbased tracking technology to manage access and compliance. This satellite-based technology remotely monitors where, when, and how vehicles are operated on the road network while providing the community with assurance that the proper vehicle types operate on the prescribed roads. More information can be obtained https://www.nhvr.gov.au/roadfrom access/access-management/intelligentaccess-program It is important to note that jurisdictions have the right to refuse access to their road network or to exclude vulnerable assets from a vehicle’s access if they have reasonable concern that the presence of such vehicles and intended operation would cause unacceptable pavement wear. These restrictions remain until such time as a pricing regime fully recovers the additional pavement wear costs of PBS. Currently, there is no agreed national process for assessing unacceptable wear. The absence of such a process introduces a degree of uncertainty for truck operators operating across jurisdictions. Principles of Assessing Damage While increased heavy vehicle loads continue to benefit trucking companies by providing increased productivity, some heavily loaded axle configurations have a tendency to inflict additional wear on pavements thus reducing their service lives and contributing to increased maintenance costs. The general mechanistic design procedure (Austroads 2012) is based on an ability to calculate critical stresses and strains in the pavement. The number of allowable repeated applications of the critical strains is calculated with transfer functions for the pavement materials. Further information can be obtained from Austroads (2012) for compressive upgrade strain and for tensile (fatigue) strains in bound materials.
The SAR is defined as the number of axle group repetitions causing the same amount of damage as the single passage of a standard axle group. This is Austroads method in determining a standardised wheel load and a correlation for different wheel load configurations using the material damage exponent theorem. The standard axle in the pavement design procedure is a single axle with dual tyres (SADT) applying an axle load of 80 kN on the pavement. This approach is based on the assumption that a given axle load (SAST, SADT, TAST, TADT, TRDT, QADT) produces an equal maximum deflection of the pavement surface, and also causes the same damage to the pavement structure. More information on the principles of assessing damage can be found in ROADguide Road Design and Performance, IPWEA NSW Roads & Transport Directorate, 2012. REFERENCES and FURTHER READING:
The information contained in this Information sheet has been summarized from a number of resources. More detailed information may be sourced from the references below: Addis, R.R. 1992 Vehicle Wheel Loads and Road Pavement Wear, London, UK Austroads, 2011, Pavement Wear Assessment Method for PBS vehicles, AP-R372/11, Austroads, Sydney, NSW Austroads, 2012, Guide to Pavement Technology; Part 2: Pavement Structural Design, AGPT02/12, Austroads, Sydney, NSW
National Heavy Vehicle Regulator (NHVR) 2013, Mass Management Accreditation Guide https://www.nhvr.gov.au/files/0001mass_management_accrediation_guide.pdf National Heavy Vehicle Regulator (NHVR) 2014, Concessional Limits Factsheet https://www.nhvr.gov.au/files/201402-0112concessional-mass-limits.pdf IPWEA (NSW) Roads & Transport Directorate 2012, ROADguide Road Design and Performance, Sydney NSW
Whilst the design calculations refer to a standard load, real traffic comprises a wide range of vehicles with different axle load configurations and loading, each causing a different degree of damage. To conduct pavement design or estimate the damage, the spectrum of traffic loading must be translated to standard axle repetition – the SAR.
(02) 8267 3000 (02) 8267 3070 [email protected]
Issues covered
• • • • • • • •
Overview Definitions Legislative background for heavy vehicle loading (Australia/NSW) Vehicle Loads and Pavement Wear The 4th Power Law Mass Limits for Heavy Vehicles Principles of assessing damage References
Overview Asset managers are tasked with the responsibility of maximising the service life of road assets and providing local communities with value for money infrastructure services. Traffic-induced wear of road pavements is mostly a result of the wheel loading imposed by heavy vehicles. One of the challenges road managers face is how to effectively balance the growing efficiency of trucking operations and efforts to extend the service life of road pavements.
Definitions Axle – One or more shafts, positioned in a line across a vehicle, on which one or more wheels intended to support the vehicle turn. Axle load – That portion of the total vehicle load transmitted to the road through single axle. Standard Axle Load – Single access with dual wheels loaded to a total mass of 8.2 tonne (80kN) General Mass Limits (GML) – The heavy vehicle axle mass limits that apply to public roads in Australia unless otherwise limited by load restriction signs. Concessional Mass Limits (CML) – The mass exception allows tandem and tri-axle groups to be 5% above general mass limits (GML), with a maximum gross mass increase of 1.0 tonne for a vehicle up to 55.0 tonnes gross mass and 2.0 tonnes for a vehicle exceeding 55.0 tonnes gross mass. Higher Mass Limits (HML) – A mass exception under the Heavy Vehicle National Law which allows higher mass limits on approved routes for particular vehicles or vehicle combinations dependent on other conditions being met (e.g. Intelligent Access Program (IAP) and/or road friendly suspension may need to be fitted to the vehicle). Load Equivalency Factors – The ratio of the number of repetitions of a specified axle load (termed the standard load) which the pavement can sustain to the number of repetitions of another axle load which the same pavement can sustain for given damage criteria. Legislative Background for Heavy Vehicle Loading (NSW/Australia) Australia has experienced the influx of heavier vehicles following advancements in heavy vehicle design, new tyre varieties and international experience. This, coupled with the increasing efficiency in trucking operations has benefitted the trucking companies but at the same time, has resulted in the reduced service life of pavements and increased maintenance costs. As a solution, road authorities have adopted a two-pronged strategy by applying stricter control of load limits and introducing additional road charges. Arrangements for weighing heavy vehicles, known as Measurement Adjustment (MA), were introduced nationally from 1 July 2006. More information can be found in https://www.nhvr.gov.au/safety-accreditationcompliance/chain-ofresponsibility/measurement-adjustment
Vehicle Loads and Pavement Wear It is common understanding that the traffic-induced wear of road pavements is largely due to the wheel loading brought about by commercial heavy vehicles. Damage caused to pavements sharply increases with the axle loading. Addis (1992) contends that while traditionally it has been held that static axle loads of heavy vehicles is the primary determinant of pavement deterioration, other factors can likewise contribute to deterioration such as: • • • •
Type of Axle (number of wheels and type of tyres) Axle arrangement Surface contact pressure of tyre Suspension system
On its own or in combination, these factors alter the basic structural wear mechanism functioning in the pavement thus influencing the static axle load-wear relationship (Addis 1992). Thus a rule that emphasizes that pavement damage is proportional to the axle weight of a vehicle, known as the 4th power rule, was developed. This rule is what is widely used by road authorities worldwide. The 4th Power Law The 4th power law traces back to extensive testing undertaken by the American Association of State Highway Officials (AASHO) between 1958 and 1961 (TRB 1962 as cited in Addis 1992) which equated pavement deterioration with reduced/loss of pavement serviceability. In this experiment, road pavements were constructed in the form of loops with sections that had widely varying strengths. Different heavy vehicles with single axle weights ranging between 0.9 tonnes and 13.9 tonnes as well as tandem axles between 10.9 tonnes and 21.8 tonnes, were driven over the road sections in a continuous stream with each road accommodating vehicles of single axle configuration only. The deterioration of the road was monitored throughout the duration of the experiment after which a road test equation was derived which drew the connections between the given amount of physical wear of the pavement to the number of applications of a given axle load.
One consequence of the Road Test Equation is the fourth power law, which predicts that the change in pavement damage is proportional to the difference in vehicle’s axle weight to the fourth power. For example, a vehicle with an axle weight of 1000 kg is considered to cause 16 times the damage compared with a vehicle with an axle weight of 500 kg. Mass Limits for Heavy Vehicles In New South Wales, there are three tiers of mass limits for heavy vehicles: •
•
General Mass Limits (GML) – These vehicles have unrestricted access to the road system. No specific access restrictions apply and no other permits are required provided these vehicles are registered and operators pay the registration charge appropriate to the vehicle configuration. Concessional Mass Limits (CML) – allow increased mass limits for eligible vehicles. To be eligible for CML, vehicles must be accredited under the National Heavy Vehicle Accreditation Scheme (NHVAS). Companies who wish to be accredited under the CML are required to meet the eight standards of compliance in the National Heavy Vehicle Regulator’s (NHVR) Mass Management Accreditation Guide which can be downloaded at https://www.nhvr.gov.au/file s/0001mass_management_accredia tion_guide.pdf CML allows eligible vehicles to operate at increased mass limits compared to statutory limits. Mass limits for CML are set at 5% above the General Mass Limit (GML), subject to: •
•
a maximum of 1 tonne for a vehicle or vehicle combination with an allowable gross mass not exceeding 55 tonnes a maximum of 2 tonnes for vehicle combinations with an allowable gross mass exceeding 55 tonnes
IPWEA (NSW) Roads & Transport Directorate Level 12, 447 Kent Street SYDNEY NSW 2000
•
an upper limit on axle and axle group mass More information can be obtained from https://www.nhvr.gov.au/files/2014020112-concessional-mass-limits.pdf.
•
Higher Mass Limits (HML) – Represent the highest level of mass allowed to be carried on NSW roads (other than by permit, notice, or exemption). Access can be obtained in NSW by enrolling under the Intelligent Access Program (IAP) that introduces GPSbased tracking technology to manage access and compliance. This satellite-based technology remotely monitors where, when, and how vehicles are operated on the road network while providing the community with assurance that the proper vehicle types operate on the prescribed roads. More information can be obtained https://www.nhvr.gov.au/roadfrom access/access-management/intelligentaccess-program It is important to note that jurisdictions have the right to refuse access to their road network or to exclude vulnerable assets from a vehicle’s access if they have reasonable concern that the presence of such vehicles and intended operation would cause unacceptable pavement wear. These restrictions remain until such time as a pricing regime fully recovers the additional pavement wear costs of PBS. Currently, there is no agreed national process for assessing unacceptable wear. The absence of such a process introduces a degree of uncertainty for truck operators operating across jurisdictions. Principles of Assessing Damage While increased heavy vehicle loads continue to benefit trucking companies by providing increased productivity, some heavily loaded axle configurations have a tendency to inflict additional wear on pavements thus reducing their service lives and contributing to increased maintenance costs. The general mechanistic design procedure (Austroads 2012) is based on an ability to calculate critical stresses and strains in the pavement. The number of allowable repeated applications of the critical strains is calculated with transfer functions for the pavement materials. Further information can be obtained from Austroads (2012) for compressive upgrade strain and for tensile (fatigue) strains in bound materials.
The SAR is defined as the number of axle group repetitions causing the same amount of damage as the single passage of a standard axle group. This is Austroads method in determining a standardised wheel load and a correlation for different wheel load configurations using the material damage exponent theorem. The standard axle in the pavement design procedure is a single axle with dual tyres (SADT) applying an axle load of 80 kN on the pavement. This approach is based on the assumption that a given axle load (SAST, SADT, TAST, TADT, TRDT, QADT) produces an equal maximum deflection of the pavement surface, and also causes the same damage to the pavement structure. More information on the principles of assessing damage can be found in ROADguide Road Design and Performance, IPWEA NSW Roads & Transport Directorate, 2012. REFERENCES and FURTHER READING:
The information contained in this Information sheet has been summarized from a number of resources. More detailed information may be sourced from the references below: Addis, R.R. 1992 Vehicle Wheel Loads and Road Pavement Wear, London, UK Austroads, 2011, Pavement Wear Assessment Method for PBS vehicles, AP-R372/11, Austroads, Sydney, NSW Austroads, 2012, Guide to Pavement Technology; Part 2: Pavement Structural Design, AGPT02/12, Austroads, Sydney, NSW
National Heavy Vehicle Regulator (NHVR) 2013, Mass Management Accreditation Guide https://www.nhvr.gov.au/files/0001mass_management_accrediation_guide.pdf National Heavy Vehicle Regulator (NHVR) 2014, Concessional Limits Factsheet https://www.nhvr.gov.au/files/201402-0112concessional-mass-limits.pdf IPWEA (NSW) Roads & Transport Directorate 2012, ROADguide Road Design and Performance, Sydney NSW
Whilst the design calculations refer to a standard load, real traffic comprises a wide range of vehicles with different axle load configurations and loading, each causing a different degree of damage. To conduct pavement design or estimate the damage, the spectrum of traffic loading must be translated to standard axle repetition – the SAR.
(02) 8267 3000 (02) 8267 3070 [email protected]
