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Construction of the California Precast Concrete Pavement Demonstration Project
Chapter 4. Design
There are several factors which must be considered for the design of a precast prestressed concrete pavement. A detailed discussion of these design considerations is beyond the scope of this report, but the primary factors are summarized below. For more information on design considerations, the reader is referred to CTR Reports 1517-1(1) and 1517-1-IMP.(2)
Traffic loading is a factor in the design of all pavements. Wheel loads induce a bending action in concrete pavements that generates tensile stresses in the bottom of the slab and compressive stresses in the top. Pavement designs are generally governed by the expected number of 80-kN (18 kip) equivalent single-axle loads (ESALs) that the pavement will experience over its intended design life. The repetition of these wheel loads over time will fatigue the concrete, eventually leading to pavement failure. Accurate prediction of the number of ESALs a pavement will experience will help ensure that the pavement is adequately designed.
As discussed previously, one of the advantages of prestressed concrete pavement is that the tensile stresses generated by wheel loads can be counteracted through prestressing. This allows for a thinner pavement slab to be designed with a fatigue life that is equivalent to a much thicker slab.
Temperature and Moisture Effects
Temperature has a significant effect on all concrete pavements, but the effect is particularly pronounced in prestressed concrete pavements. Daily and seasonal temperature cycles cause concrete pavements to expand, contract, and curl. Because prestressed pavement slabs are generally very long (between expansion joints), a significant amount of horizontal movement (expansion and contraction) can be expected at the ends of the slab. If this movement is restrained fully or partially by friction between the bottom of the pavement and the base material, stresses will develop in the slab. Because it is impossible to construct a pavement that is completely unrestrained, temperature effects will always generate stresses in prestressed concrete pavements that must be accounted for in design.
Slab curling also generates stresses in concrete pavements. Concrete pavement slabs rarely have a uniform temperature throughout the depth of the slab. The resulting temperature gradients cause the ends of the slab to curl upward or downward. As the sun heats the surface of the pavement in the morning, for example, it causes the ends slab to curl downward. However, because of the weight of the slab resisting this movement, tensile stresses also develop in the bottom of the slab. Due to the length of most prestressed slabs, this effect is even more pronounced and must be accounted for in design.
Moisture has a similar effect as temperature in that moisture gradients cause warping of the concrete slab. In general, moisture gradients are such that the bottom of the slab has a higher moisture content than the top of the slab due to the ease with which moisture can evaporate from the top surface. This moisture gradient will cause upward warping of the ends of the slab, resulting in tensile stresses in the top of the slab and compressive stresses in the bottom of the slab. In conventional cast-in-place pavements, this moisture gradient can become "built in" as the fresh concrete sets. This is one advantage of precast concrete pavements: so-called built-in temperature and moisture gradients are essentially eliminated.
The interaction at the slab-support interface essentially consists of four components: friction, interlock, adhesion, and cohesion.(11) Friction is the result of the rubbing together of the two materials, interlock is the restraint caused by the macrotexture of the two surfaces in contact, adhesion is the attraction or "sticking" together of the two materials, and cohesion is related to the internal deformability capacity of the base layer. It is possible for the combined forces of these four components to be such that the restraint at the interface exceeds the internal strength of the base layer, resulting in failure of the base.(12)
It is essential to minimize restraint between the slab and base to reduce the magnitude of stresses that develop in the slab (and base) during horizontal slab movements. In general, compressive stresses will develop when the slab expands, while tensile stresses will develop when the slab contracts. The latter situation is more critical, as these tensile stresses may be additive to those tensile stresses caused by wheel loads and curling to such an extent that the slab may crack.(13) For the sake of simplicity in design, the stresses generated during slab expansion and contraction are generally assumed to be constant over the depth of the slab. Fortunately, precast panels tend to be fairly smooth on the bottom, which helps to reduce friction and interlock between the slab and base but still requires a friction-reducing material, such as polyethylene sheeting, to further reduce frictional restraint while also preventing adhesion.
Prestress losses are another important design consideration for prestressed concrete pavements. In general, losses of 15 to 20 percent of the applied prestressing force can be expected for a carefully constructed post-tensioned concrete pavement.(10) Some of the factors that contribute to prestress losses include the following:
- Elastic shortening of the concrete.
- Creep of the concrete (shrinkage is not a factor for precast pavements).
- Relaxation of the stressing tendons.
- Slippage of the stressing tendons in the anchorage.
- Friction between the stressing tendons and ducts.
- Horizontal restraint between the slab and support.
Fortunately, most of the factors are fairly well understood and can be estimated with reasonable accuracy. A more detailed discussion of each of these factors can be found elsewhere.(10)
The design procedure for the California precast pavement is similar to that used for the design of the Georgetown, Texas, precast pavement(2) and will only be briefly summarized here. The design procedure is based on the principle of equivalent thickness design, meaning that the precast pavement is designed for an equivalent design life (fatigue life) to that of a thicker pavement. The first step in the design procedure is to determine the minimum prestressing required to achieve the equivalent thickness. This is accomplished through a layered elastic analysis of pavement stresses.
The second step is to adjust the prestressing requirements for the precast pavement slab to account for environmental effects. At this stage, the slab-support interaction, prestress losses, and temperature and moisture effects are accounted for. The result is the actual prestressing that must be applied to the pavement (during post-tensioning) to meet the equivalent thickness design requirements.
The final step in the design procedure is to check maximum horizontal slab movement (expansion and contraction) to ensure that the maximum permissible expansion joint width is not exceeded. At this stage, the slab length (between expansion joints) can be adjusted if necessary.
Design for Fatigue
The first step in the design procedure is to determine the required prestressing for a precast pavement with an equivalent fatigue life (design life) to that of a thicker conventional cast-in-place pavement. The basic premise of equivalent fatigue design is that the same bottom fiber tensile stress in slabs of different thickness will produce pavements with the same fatigue life.
The original pavement design for widening I-10 in El Monte called for a 250-mm (10 in.) JPCP. While it would have been possible to design a 150-mm (6 in.) or 200-mm (8 in.) precast pavement with an equivalent thickness to the 250-mm (10 in.) JPCP, for constructability reasons it was decided that a 250-mm (10 in.) precast concrete pavement would be constructed. However, for the sake of comparison, the precast concrete pavement was actually designed to be equivalent to a JPCP that is 355 mm (14 in.) thick.
Support Structure and Prestress Requirements
The support structure for the El Monte precast pavement consists of 150 mm (6 in.) of LCB over 220 mm (8.5 in.) of aggregate base (Class 3) over the existing subgrade, as shown in figure 11. This support structure was used to determine the tensile stresses in the bottom of the equivalent 355-mm (14 in.) JPCP under the loading shown in figure 11. This loading condition represents the typical theoretical wheel load from dual wheels on a single-axle truck. The properties of the different layers of the support structure were estimated based upon Caltrans Standard Specifications.(14) The resilient modulus values for the aggregate base and subgrade were determined from the R-value requirements given in the Special Provisions for this project. The minimum R-value given was 50, corresponding to a resilient modulus of 75.8 MPa (11,000 lbf/in²).
Figure 11. Illustration. Support structure for equivalent pavement design (subgrade, class 3 aggregate base, and lean concrete base), topped by either jointed concrete pavement or precast prestressed concrete pavement.
Using the support structure and loading condition shown above, the tensile stress (T) at the bottom of the equivalent JPCP control pavement was determined using layered elastic analysis. The computer program BISAR (Bitumen Structures Analysis in Roads)(15) was used for the layered elastic analysis. Stresses were computed beneath the loads and between the loads to determine the worst condition.
Table 1 summarizes the stresses for the two pavement thicknesses (250 mm and 355 mm). The highest tensile stresses occurred at the midpoint between loads, but the largest difference in bottom fiber stress occurred beneath the load. The difference in bottom fiber tensile stress of 92 kPa (13.3 lbf/in²) is the magnitude of prestressing required in the 250-mm (10 in.) precast concrete pavement to achieve an equivalent JPCP thickness of 355 mm (14 in.).
|Pavement Thickness||Bottom Tensile Stress, sT, kPa|
|Beneath Load||Midpoint Between Loads|
1 kPa = 0.145 lbf/in2
Fatigue Life Implications
The benefit of a thicker equivalent pavement will be realized through the increase in fatigue life of the pavement. Fatigue life can be predicted using pavement fatigue equations such as that given in figure 12, developed by Taute et al.(16) This fatigue equation predicts the number of 80-kN (18 kip) ESAL repetitions to serviceability failure.
Figure 12. Equation. Fatigue life prediction based on number of 80-kN (18 kip) ESALs experienced by the pavement.
- N18 = Number of 80-kN (18 kip) ESALs to serviceability failure
- f = Concrete flexural strength (MPa)
- T = Bottom fiber tensile stress from wheel loading (MPa)
Using the equation given in figure 12 and the stresses computed in table 1 (worst case: midpoint between loads), the predicted fatigue life, in terms of 80-kN (18 kip) ESALs, of the original 250-mm (10 in.) pavement and the "equivalent" 355-mm (14 in.) pavement were calculated as shown in table 2. Concrete flexural strength was calculated from the American Concrete Institute's modulus of rupture equation for 41.4 MPa (6,000 lbf/in²) compressive strength concrete to be 4 MPa (580 lbf/in²). It is evident from this analysis that the reduction in bottom fiber tensile stress of only 27 percent will significantly increase the fatigue life of the pavement.
|Pavement Thickness||Bottom Fiber Tensile Stress (kPa)||Predicted ESALs to Serviceability Failure|
|250-mm prestressed pavement
(equivalent to 355-mm JPCP)
1 kPa = 0.145 lbf/in2
To calculate the effect of this increase in fatigue life in terms of years, traffic data for I-10 in El Monte were obtained from Caltrans and used to predict the number of ESALs in the design lane, assuming a constant growth rate of 2 percent. As table 3 shows, the 250-mm (10 in.) pavement is adequate for a 30-year design life. However, a 250-mm (10 in.) precast, prestressed pavement (equivalent to a 355-mm JPCP), will have a design life just over 57 years. It should be noted that if a 3 percent growth rate were used, the design life of the. 250-mm (10 in) pavement would be only 27 years, while that of the 350-mm (14 in.) pavement would be 48 years.
|Prediction||Design Period (years)|
|Growth factor (%)||2||2|
|ESAL volume, 1st year||4,579,451||4,579,451|
|% ESALs in design lane||40||40|
|Total predicted ESALs||185,779,515||478,962,126|
|Total design lane ESALs||74,311,806||191,584,850|
Although long-term traffic volumes are difficult to predict with a great deal of certainty, and actual pavement performance is also difficult to predict due to the many variables that affect pavement performance, this analysis demonstrates the relative benefit of prestressed pavement in terms of design life.
Design for Environmental Effects
In the previous section, the fatigue design revealed that a prestress force of 92 kPa (13.3 lbf/in²) was required to produce a 250-mm (10 in.) precast, prestressed pavement with a design life equivalent to a 350-mm (14 in.) JPCP pavement. Therefore, at every point along the length of the slab, a minimum compressive stress of 92 kPa (13.3 lbf/in²) must be maintained under varying environmental conditions to meet the fatigue requirements. This is the residual pavement stress caused by environmental conditions (i.e., slab expansion and contraction, curling, etc.) and does not include wheel loads, which were accounted for in the fatigue design.
PSCP2 Design Program
A very powerful tool for analyzing the effects of environmental conditions on precast, prestressed pavement is the computer program PSCP2. This program was originally developed at CTR as a design and analysis tool for cast-in-place post-tensioned pavements, but can also be used to analyze precast, prestressed pavements by adjusting the inputs to the program. A full description of the PSCP2 program is beyond the scope of this report, but the reader is referred to Mandel et al.(5) and Merritt et al.(1) for a more detailed discussion of the PSCP2 program and its application to precast pavement design.
To summarize the functionality of the PSCP2, the program calculates horizontal slab movement, frictional restraint stresses, prestress losses, curling stresses, and curling movement at a specified number of points along the length of the slab for any number of days (or years) after construction. The user inputs slab geometry, material properties (concrete and prestressing steel), slab-support frictional characteristics, prestress application, and expected slab temperatures into the program. After running the program, the user can evaluate total slab stress and movement at any point in the pavement's design life.
The inputs used for the PSCP2 analysis for the California precast pavement are summarized below.
- Slab thickness: 250 mm (10 in.).
- Slab width: 11.2 m (37 ft).
- Slab length: 38.1 m (125 ft) (76.2 m was also evaluated).
- Compressive strength: 41.4 MPa (6,000 lbf/in²).
- Ultimate shrinkage strain: 0.00019 mm/mm (for precast concrete).
- Coefficient of thermal expansion: 9 x 10-6 mm/mm/°C (5 x 10-6 in/in/°F)-from PCI Design Handbook(3) for granitic coarse aggregate.
- Unit weight: 2,322 kg/m³ (145 lb/ft3).
- Poisson's ratio: 0.15.
- Creep coefficient: 2.1.
Post-Tensioning Steel Properties
- Strand diameter: 15 mm (0.6 in.).
- Cross-sectional area: 140 mm² (0.217 in2).
- Yield strength: 1,675 MPa (243,000 lbf/in²).
- Elastic modulus: 19.7 x 104 MPa (28.5 x 106 lbf/in²).
- Thermal coefficient: 12.6 x 10-6 mm/mm/°C (7 x 10-6 in/in/°F).
The pavement was assumed to be post-tensioned in the longitudinal direction, in one stage, 6 hours after panel installation, although the timing of post-tensioning is irrelevant for this analysis. The strands were assumed to be stressed to 80 percent (1,490 MPa) of their ultimate strength. Strand spacing was initially set at 0.9 m (36 in.) as this is deemed to be the maximum permissible strand spacing for a prestressed pavement with monostrand tendons. This spacing was adjusted during the PSCP2 analysis as needed to meet the fatigue requirements.
A k-value of 135.7 kPa/mm (500 lbf/in²/in) was specified for the slab support, although this input has essentially no effect on the analysis. The friction-displacement relationship was assumed to be a linear relationship with a maximum coefficient of friction of 0.2 and corresponding displacement of 0.5 mm (0.02 in.) at sliding.
The pavement was analyzed at 90 days, 1 year, 5 years, and 30 years to determine the worst-case condition for slab movement and stress. The 30-year analysis proved to be the controlling design for both slab movement and stresses.
Temperature data were specified for the first 24-hour period after placement and for a 24-hour period at each of the analysis periods (90 days, 1 year, 5 years, 30 years). Both mid-slab temperature and top-bottom slab temperature differential were specified. Ambient temperature data were obtained from the National Weather Service for El Monte, California. Daily temperature distributions for a typical summer day and a typical winter day were generated from the temperature history for El Monte. Concrete temperatures were estimated from ambient temperature using the empirical formula shown in figure 13.(17) Top-bottom temperature differentials were estimated from previous prestressed pavement measurements.(18) Table 4 summarizes the temperatures used for the PSCP2 design.
Figure 13. Equation. Prediction of concrete temperature based on ambient temperature.
TC = 20.2 + 0.758TA
- TC = concrete temperature (°F)
- TA = ambient temperature (°F)
|Time of Day||Summer Temperatures (°C)||Winter Temperatures (°C)|
|Ambient Temperature||Concrete Temperature||Top-Bottom Differential||Ambient Temperature||Concrete Temperature||Top-Bottom Differential|
Longitudinal Prestress Requirements
Previous precast pavement analyses have revealed that the controlling case for design of longitudinal prestress occurs when the pavement is placed under summer temperature conditions and evaluated under winter conditions. In other words, the worst-case stress condition will occur when a pavement constructed under summer climatic conditions is evaluated under winter climatic conditions. Therefore, the summer/winter PSCP2 analysis was considered the controlling design case.
When analyzing longitudinal prestress, the spacing of the post-tensioning strands is adjusted in a "trial and error" analysis until the longitudinal prestress requirements are met. For this project, 92 kPa (13.3 lbf/in²) was the minimum longitudinal prestress requirement. As mentioned previously, a "rule of thumb" maximum strand spacing for post-tensioned pavements is 0.9 m (36 in.). Based on the PSCP2 analysis for the summer/winter condition and 0.9 m (36 in.) strand spacing, the maximum bottom fiber stress was calculated as 685 kPa (99.3 lbf/in²) (compressive), which is well above the required 92 kPa (13.3 lbf/in²) (compressive). Therefore, longitudinal strand spacing was specified as 0.9 m (36 in.).
Transverse Prestress Requirements
While transverse prestressing is essential for the long-term performance of prestressed pavements, transverse prestress requirements are generally governed by handling stresses for precast panels. Transverse prestressing is specified such that no cracking will occur during handling of the panels. As a "rule of thumb" from the Texas pilot project, a minimum of 1.4 MPa (200 lbf/in²) prestressing is recommended to counteract both handling stresses and long-term in situ pavement stresses. To check the adequacy of 1.4 MPa (200 lbf/in²) for handling, stresses were calculated in accordance with Section 5.2 of the PCI Design Handbook.(3) Removal of the panels from the forms is generally the critical design case, as the panels have not reached their full 28-day design strength. The modulus of rupture at removal was computed to be 2.18 MPa (316 lbf/in²) using the following equation from the PCI Design Handbook (Eq. 5.2.1):
Figure 14. Equation. Equation for estimation of modulus of rupture from compressive strength.
- f'r = Modulus of rupture.
- K = Constant prescribed by ACI as 7.5, reduced by a factor of safety of 1.5 to 5 as per PCI Design Handbook recommendation.
- = 1.0 for normal-weight concrete.
- f'ci = Concrete compressive strength at release of prestress, 27.6 MPa, (4,000 lbf/in²) for the California demonstration project.
Lifting stresses were computed using moments calculated for a two-point pick-up (four lifting points located approximately 0.2L from each edge of the panel) as recommended by the PCI Design Handbook. An equivalent static-load multiplier of 1.3 was added to the unit weight of the concrete to account for stripping and dynamic forces as the panels are removed from the forms. Based upon these design parameters, the maximum lifting stress for 11.2 m x 2.4 m x 290 mm (average thickness) panels was computed to be 2.2 MPa (320 lbf/in²). This stress is slightly higher than the modulus of rupture (2.18 MPa [316 lbf/in²]), but is counteracted by 1.4 MPa (200 lbf/in²) of compression from pretensioning. Assuming that 13-mm (0.5 in.), 1,860 MPa (270,000 lbf/in2) prestressing strand (stressed to 80 percent of ultimate strength) will be used, six strands were required to achieve the 1.4 MPa (200 lbf/in²) transverse prestress requirement.
Expansion Joint Limitations
The last step in the design process is to check horizontal slab movement under varying temperature conditions to ensure that the expansion joints limitations are satisfied. Expansion joint widths should be checked to ensure they will never fully close and never open excessively. In the case of the California demonstration project, the maximum expansion joint width was limited to 25 mm (1 in.).
The PSCP2 computer program was used to predict long-term slab movement for estimation of expansion joint widths. Horizontal slab movement was examined for two worst-case scenarios: placement of the pavement under summer climatic conditions and evaluation in winter (summer/winter), and placement under winter climatic conditions and evaluation in the summer (winter/summer). The summer/winter condition generally governs for determining maximum expansion joint width (i.e., how wide the joint will open over time), while the winter/summer condition generally governs for determining the minimum required expansion joint width (i.e., the minimum width that must be provided to allow for slab expansion). Based on the PSCP2 analysis, the maximum amount of slab contraction predicted was 7.5 mm (0.3 in.) for the 38.1-m (125 ft) slab length. For the expansion joints, this translates to 15 mm (0.6 in.) of total movement (7.5 mm [0.3 in.] on either side of the expansion joint). The maximum amount of slab expansion predicted was 2.5 mm (0.1 in.), or 5 mm (0.2 in.) of total expansion joint movement (closure). It should be noted that these are long-term predictions, with the maximum (15-mm) joint contraction movement anticipated at 30 years after construction.
While these predicted slab movements were within the expansion joint limitations (maximum width of 25 mm), it was necessary to develop recommendations for the width of the expansion joints during construction. The expansion joint widths (at the level of the dowels) after completion of post-tensioning were given in the project plans to ensure the joints will never fully close and never open more than 25 mm (1 in.). The contractor adjusted the width of the expansion joints to meet these requirements after post-tensioning. Table 5 shows the expansion joint width requirements. The width was specified based upon the approximate ambient temperature after post-tensioning. It should be noted that these recommendations were based upon the climatic conditions and climatic history in El Monte, California. Different regions of the country will have different requirements.
|Approximate Ambient Temperature (°C)||Joint Width (at height of the dowels)|
|T < 16°||13 mm|
|16º ≥ T ≤ 32°||6 mm|
|T > 32°||0 mm|
1 mm = 0.039 in.
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