What is FWD Deflection Analysis and Back-Calculation?

FWD analysis is the process that finds the stiffness of each pavement layer from the surface deflections that a falling weight deflectometer (FWD) measures. The FWD drops a weight on a load plate and records the deflection with sensors. The engineer then turns the readings into layer moduli, joint and void checks, and design inputs.

What an FWD measures

An FWD is an impulse load device. A weight falls on rubber springs and pushes the load plate on the pavement. The load depends on the mass of the weight and the drop height. The operator can match it to a wheel load of the aircraft. The force pulse typically lasts 20 to 60 milliseconds. For pavements that serve commercial air carrier aircraft, the FAA gives an impulse load between 20 and 55 kips (90 and 250 kN). The heavy weight deflectometer (HWD) works the same way with loads near 70 kips. The light weight deflectometer (LWD) is a portable version for unbound layers.

The FAA recommends sensors at the center of the plate and at 12 in (30 cm) steps out to 72 in (180 cm). Other agencies use other layouts, for example the SHRP 4-sensor layout at 0, 12, 24 and 36 in. AC 150/5370-11B says a 12 in (30 cm) plate is normal for bound surfaces. An 18 in (45 cm) plate suits unbound base, subbase or subgrade. Use of AC 150/5370-11B is mandatory for projects that AIP or PFC funds pay for.

The deflection basin

The load makes a bowl-shaped dip in the surface. This is the deflection basin. The deflection is largest under the plate and falls with distance. The deflection under the plate (d0) shows the stiffness of the whole structure. The deflection at the outermost sensor shows the stiffness of the subgrade. A weaker pavement deflects more under the same load. The shape of the basin depends on all the layers, so two pavements can have the same d0 and still have different bases and subgrades. Asphalt temperature, moisture and concrete slab curling also change the basin.

FWD formulas

FWD analysis uses a few short formulas, and one long calculation:

• Impulse stiffness modulus (ISM). ISM = L / d0, where L is the applied load and d0 is the maximum deflection under the plate. The unit is kips/in. A higher ISM means a stiffer pavement for the same load.
• Load normalization. The normalized deflection is d0n = (Lnorm / Lapplied) x d0. It adjusts deflections from different drop loads to one standard load, for example a 40,000 lb (180 kN) wheel load.
• Subgrade resilient modulus. AC 150/5370-11B gives Mr = 0.24 P / (dr x r) for a closed-form subgrade value. P is the load in pounds, dr is the deflection at the distance r, and r is the distance in inches. For AASHTO 1993 work, the result needs a correction factor, typically 0.33, to match a laboratory resilient modulus.
• Deflection load transfer efficiency (LTE). LTE = deflection of the unloaded slab / deflection of the loaded slab x 100%.
• ISM ratio. ISM ratio = ISM at the slab center / ISM at the slab corner or joint.
• Layer moduli. No single formula gives them. They come from back-calculation.

Plots of ISM or normalized deflection along a runway show strong and weak locations. The engineer uses the plot to find where one pavement section ends and the next begins. A section is an area that should perform uniformly.

Back-calculation

Back-calculation finds the elastic modulus of each layer from the basin. The engineer assumes the layer thicknesses and solves for the stiffness. The FAA names two types of static-linear method. The closed-form method computes the modulus of each layer directly from the thicknesses and from one or more sensors. The iterative method uses elastic layer theory and needs deflections from at least four sensors.

The iterative method runs in a loop:

1. Set an initial modulus (a seed value) and a modulus range for each layer.
2. Compute the basin that those moduli give under the FWD load.
3. Compare the computed basin with the measured basin.
4. Adjust the moduli, and repeat until the match error is acceptable.

FHWA says that an error (RMS) under 2 percent is reasonable, and a value over 3 percent is questionable. The engineer must also compare the moduli with typical values for the material.

The engineer first removes basins that have errors. A Type I basin has an outer sensor that reads more than the center sensor, and it produces the largest error. A Type II basin has an unusually large drop between two neighbouring sensors. A Type III basin has a sensor that reads more than the sensor next to it on the inside. Causes include a crack near the plate, a dead sensor, a calibration error, a void, or slab curling.

The result is not unique. The FAA lists the factors that change it. They include the number of layers, layer thickness, layer interface condition and asphalt temperature. Seed values, a stiff layer below, cracks and sensor errors also change it. The FAA warns that static back-calculation models can overestimate the modulus of base, subbase and subgrade. Layer thickness comes from cores or ground-penetrating radar, not from the FWD.

Back-calculation software

BAKFAA is the FAA software for back-calculation. It uses the LEAF calculation routine, it takes up to 10 layers, and it back-calculates asphalt, concrete and asphalt-overlaid concrete moduli. AC 150/5370-11B also lists MODULUS (Texas Transportation Institute, a database method), WESDEF, BISDEF, CHEVDEF, ELSDEF and MICHBAK. FHWA lists EVERCALC as well. EVERCALC uses the Levenberg-Marquardt method and can normalize the asphalt modulus to a standard temperature.

The software choice depends on what comes next. The FAA says the back-calculation method must match the method of the evaluation or design program. FAARFIELD uses elastic layer theory, so the elastic modulus from BAKFAA goes straight into it. For a CBR-based study, the engineer converts the elastic modulus to a CBR value. A backcalculated k-value is a dynamic value. The FAA cites NCHRP Report 372, which found the static k-value equal to one half of the dynamic one.

Joints, voids and slab durability

On concrete pavement, the FWD tests joints and corners as well as the slab center. Corner tests put the plate within 6 in (15 cm) of the joints.

Load transfer. The load transfer efficiency shows how much load passes to the next slab. More load transfer lowers the flexural stress in the loaded slab. The FAA design method assumes that load transfer cuts the free edge stress in the slab by 25 percent. For a 12 in plate, that needs an LTE of 70 percent when the radius of relative stiffness is 20 in. It needs 90 percent when the radius is 130 in. AC 150/5370-11B rates a joint with a table. The rating also depends on the radius of relative stiffness of the slab. At a radius of 20 in, an LTE of 70 to 100 percent is acceptable. A value of 50 to 70 percent is fair, and below 50 percent is poor. At a radius of 130 in, 90 to 100 percent is acceptable and 70 to 90 percent is fair. Below 70 percent is poor.

Voids. Back-calculation assumes full contact between the slab and the foundation. Corner breaks, faulting or slab cracks suggest a loss of support. Erosion, settlement and curling can cause it. The void test uses three load levels at the corner or mid-joint. A deflection intercept above 3 mils indicates a void. The FAA says to check the result with cores, ground-penetrating radar or infrared thermography. Curling changes the result during the day, so the FAA advises testing when the temperature is steady.

Durability. An ISM ratio above 3 may indicate poor concrete durability at the corner or joint. A ratio from 1.5 to 3 is questionable. Below 1.5 the pavement is probably in good condition.

Testing on an airfield

An FWD test can run while a runway stays in use. The FAA gives up to 250 test locations a day, and AC 150/5370-11B gives 150 to 250 per 8-hour shift. Center tests on a runway run along the wheel path, 100 to 400 ft (30 to 120 m) apart. The spacing depends on the pavement type and on project or network level. Each pavement section needs at least two tests. The operator records the pavement temperature during the test. Very hot weather can make an asphalt surface compress, so the FAA says to postpone the test. Results change with the season, and the thaw or a dry spell can give results that do not represent the subgrade.

What engineers do with the results

• Design inputs. The FAA says a backcalculated modulus or k-value can go straight into FAARFIELD. For a more conservative approach, use the mean minus one standard deviation. Remove outliers first if the coefficient of variation is above 20 percent, and split the section if the result is still too low.
• Remaining life and overlay design. Table 7 of AC 150/5370-11B shows which FAA programs do remaining life and overlay design from FWD data.
• Pavement strength reporting. Network-level NDT supplements PCI data. Together they generate Pavement Classification Ratings (PCR) for each airside facility under AC 150/5335-5.

Relation to a visual survey

The FWD shows structural condition. The FAA says other methods must assess the functional condition, for example the visual condition, roughness and friction. A PCI survey to ASTM D5340 rates the visual condition, and it gives only an indirect measure of structure. With both results, the engineer can assign an overall pavement condition rating.