PROJECT

I.HeaderNovember 29, 2015To: Professor John HarveyUniversity of California, DavisOne Shields Ave. Davis, CA 95616From: Samuel Ray 999576030Subject: Pavement Analysis and Design,Bogota International Airport

I am submitting a report on the design of a newly reconstructed takeoff taxiway. The taxiway will only carry the loads of the following aircraft: Boeing 777-300 ER (B777) Airbus A350-900 (WV001) (A350)

II.Purpose:The Bogota International Airport is considering expanding a terminal in order to accommodate new flights by the above mentioned aircraft B777 and A350. The Mechanistic-Empirical design method was used to create alternate pavement designs. Both asphalt concrete and Portland cement concrete were used. The results were acquired by using both openpave and EverFe for each new design. Openpave was used for the design of the asphalt concrete (AC) and EverFe was used for the design of the Portland cement concrete (PCC).III. Summary of Data:Flexible:It is expected that 3 B777 and 4 A350 will use the terminal every day. The main speed on the taxiways is 25 km/hour. It will be used 365 days per year and will be evenly divided between winter and summer, and between day and night. Expected pavement temperatures at the site are 20ºC during summer days, 15ºC during summer nights and winter days, and 4ºC during winter nights, all at 1/3 depth in the asphalt concrete.The following two tables were provided by Consultant John Harvey.Table S1: Proposed Pavement Structure:Existing Layer Thickness DescriptionAsphalt Concrete 150 mm Dense graded AC, badly crackedAggregate Base 300 mm Imported aggregate base, compacted to 98 percent modified ProctorSubgrade Very thick fill. Original design CBR values of 4-6Table S2: Deflections of existing taxiwaysSensor location (mm) 0 200 300 600 900 1200 1500Deflection (m) 777 704 649 499 385 302 242

Table 1 specifies the existing layers (Asphalt Concrete, Aggregate base, and subgrade) and their thicknesses. The shear strengths of the unbound layers are

100 kPa for the subgrade, and 420 kPa or 350 kPa for the aggregate base. The design life for this pavement is 20 years. A Heavyweight Deflectometer was used to test the deflections in the existing runway. The load was 100kN on the 150 mm radius plate. The results are shown above in Table 2. PCC Design:For the alternative concrete design we assumed a doweled (50 mm diameter) plain slab with dimensions of 4m by 4m, with the PCC having a stiffness of 28 GPa and a MR of 5 MPa. The nighttime temperature gradient is -5ºC for summer and -3 ºC for winter, and daytime temperature gradients of +4 ºC for both seasons. The slab would also have a constant equivalent temperature of -2 ºC from moisture.IV. Summary of MethodsAsphalt ConcreteUsing the deflections in table 2, the stiffness of the subgrade and aggregate base were obtained by back calculation in openpave. Given values of viscosity and penetration (Viscosity at 60 C is 18,000 poises and penetration at 25 C is 45 dmm) The Shell method was used to calculate the Asphalt Stiffness. Intermediate steps of finding loading time, diameter at 1/3 depth, percent by volume of aggregate and bitumen were needed to complete the shell method. Stiffness was found for all 4 season conditions for both air craft.Given dimensions/positions of tires and their given loads and pressures were put into openpave. Critical points were determined and analyzed to find max tensile strains and vertical stresses. 4 open paves for each season condition were created. With the max tensile strains, for each plane, for each season condition, fatigue life (Nf) was found for each pass of each wheel. Expected number of repetitions for each plane for each season condition (n) was found with the given information. Miner’s law was used to check if the pavement failed due to fatigue. The pavement does fail due to fatigue under the tires of both the B777 and the A350. Simultaneously at the critical points determined, vertical stress was obtained from each openpave created. The thickness of the aggregate base (AB) was to be designed to protect the subgrade (SG) from rutting. Iterations in open pave were used to find this thickness based on the criteria of .4saturated shear strength >.5 vertical stress. The thickness found that satisfies this criteria is 1225 mm. Same procedure was done for rutting of the AB but, it seems that the AB will rut regardless of any changes made. PCC k-value was found using the funky chart and previously back calculated subgrade stiffness modulus. Overall temperature gradient was found for each season temperature. The dimensions of the wheels were placed into EverFe along with the configurations of the wheel with its corresponding loads.

Four iterations were made for each plane and for each season temperature making a total of 12 iterations. The max tensile stresses and the deflections at the corners were recorded for each iteration. Flexural Strength (MR) was equal to 5 meaning the acceptable max tensile stress would be 2.75.The design thickness was found to be 605.5 mm with a deflection of 2.848 mm and a maximum stress approximately 2.75 MPa. The critical plane was A350 during summer/winter day because this combination had the largest max stresses. Plots were then made to show the relationship between thickness of PCC and deflection as well as max tensile stress.*All calculations, tables and figures are in the Attachments section with step by step methods.V. Final RecommendationFlexibleMy final recommendation would be to design the AB to a thickness of 1225 mm to protect the SB from rutting. Due to the large loads and the thin required AC thickness, the AB will rut regardless of thickness. I’d recommend using the AB with a saturated shear strength of 420 kPa because it will rut less than the alternative. The pavement also fatigues due to the large loads of the tires and the slow velocity as well. Because minors law for the max critical point was around 6 the pavement cannot be expected to last 20 years but around 6 times less than 20 years. The pavement will fatigue after 3-4 years so preventive maintenance before these years could be an option. The thin asphalt, heavy loads and slow speeds of the planes will cause the AB to rut and the AC to fatigue. Changing one of those variables could greatly increase the life of this pavement.RigidMy final recommendation would be to design the PCC to a thickness of 605.5 mm to achieve allowable tensile stresses. Rigid pavement design would be better to handle the heavy loads of the aircraft however, it is more expensive and a considerable large thickness would be required. If the money is there I’d suggest using PCC instead of the thin asphalt.

VI. ClosureThere are many issues with the Asphalt pavement such as fatigue and rutting of the AB. The PC however when designed correctly did not fail. The PCC however, costs more and more of it is used. The PCC would be a better option because the AC will fail and a reliable expensive pavement is better than a failing inexpensive one.

VII. AttachmentsPart 1Table 1Sensor location (mm) 0 200 300 600 900 1200 1500Deflection (m) 777 704 649 499 385 302 242

Using the sensor and deflection measurements stiffness can be found using open pave. Stiffness of asphalt concrete is given for this back calculation as 10500 MPa. Thickness of aggregate base (AB), radius and load were also given. When you enter in the load and radius openpave calculates the pressure.Table 2Location X (mm) Y (mm) Load (kN) Pressure (kPa) Radius (mm)

1 0 0 100 1414.7106 150           Using the given information and iterations the stiffness of the AB and the subgrade (SG) can be found.Table 3

Layer Thickness (mm) Elastic Modulus (MPa) Poisson's Ratio Friction1 150 10500 0.35 12 300 280 0.35 13 0 80 0.35 1

*Poisson’s ratio and Friction are assumedTable 4

Point 1 2 3 4 5 6 7X (mm) 0 200 300 600 900 1200 1500Y (mm) 0 0 0 0 0 0 0Z(mm) 0 0 0 0 0 0 0Layer 1 1 1 1 1 1 1Table 5

z (mm) 0.7776996 0.7035079 0.6491723 0.4994464 0.3846662 0.301618 0.2421815Therefore the elastic modulus of AB=280 MPa and SG=80 MPaStep 2: Find stiffness of ACWe must find the Stiffness of the asphalt concrete (AC). First Plot Viscosity at 60 C: 18,000 poisesPenetration at 25 C: 45 dmmOn the Bitumen Test Data Chart

Figure 1¿chart

T r∧b=62° C

T 1=25 °C

Penetration@T 1=45dmm

PI calculation

20−PI10+PI

=log (800 )−log (Penetration@T 1 )

Tr∧b−T 1

20−PI10+PI

=log (800 )−log (45 )

62−25

PI=1.16

Find area of tire cross-section on the surface LoadB777=288120N

Pressur eB777=1520550Pa

A= LoadPressure

= 2881521

= .189m2

Find the Diamter of tire cross-section on the surfaceA=

dsurface2 π4

.189=d surface2 ∗π4

dsurface=.49mFind Diameter at 1/3 depth13thickess=.058m

d 13 depth

=dsurface+2∗13

thickness

d 13depth

=.49+2∗.058=.608m

Find loading time (t)velocity (v )=6.9m

s

t=d 13depth

v

t= .6086.9

=.09 sec

Table 6max tire Mass (kg) P/g (kg/m^2) Area (m^2) diameter (m) thickness (m)

B777 29370 155000 0.18948387 0.491180575 0.175A350 34112.5 169381.9735 0.20139392 0.506381976 0.175

Table 7 (N) (Pa)1/3 thickness (m) diameter @ 1/3 depth (m) V (m/s) Loading time (s) Load Pressure

0.058333333 0.607847242 6.944444444 0.087530003 288119.7 1520550 B7770.058333333 0.623048643 6.944444444 0.089719005 334643.6 1661637.16 A350

*same procedure is followed for the A350. Loading times are very similar so we will use .09 sec

Use given temperatures, calculated loading times and PI to find stiffness of bitumen.Plot these values on nomograph for determining the stiffness modulus of bitumen.Table 8difference in temperature © load time (s) PI42 0.087530003 1.1547 0.087530003  47 0.087530003  58 0.087530003  

Figure 2From nomograph

Table 9

E1 (Pa)  9000000 day/summer

20000000 night/summer20000000 day/winter70000000 night/winter

Find percent volume of bitumen and aggregate

Figure 3From Sample CalculationsTable 10Vb % Vg %10.7 84

With calculated values of stiffness modulus of bitumen, volume of bitumen and volume of aggregate we can find stiffness modulus of bituminous mix.Plot these values on nomograph for mixed stiffness.

Table 11Vb % Vg %0.107 0.84E1 (Pa)  

9000000 day/summer20000000 night/summer20000000 day/winter70000000 night/winter

Figure 4From nomograph

Table 12  Stiffness of AC (Pa)day/summer 1900000000night/summer 3200000000day/winter 3200000000night/winter 8000000000

Step 3: Find position of wheels on open paveDetermine vertical StressSet up openpave with loads for B777 and A350Only one side of the plane is needed to be evaluated due to symmetry.Loads and Pressures were calculated before.Table 13Load (N) Pressure (Pa)  288119.7 1520550 B777334643.6 1661637.16 A350Positions of wheels and critical points with loads were calculated and put in openpave for the A350 and B777Table 14: Wheel LoadsA350          Location X (mm) Y (mm) Load (kN) Pressure (kPa) Radius (mm)

1 4432.5 0 335 1662 253.298112 4432.5 2040 335 1662 253.298113 6167.5 0 335 1662 253.298114 6167.5 2040 335 1662 253.29811

Table 15: Wheel LoadsB777          Location X (mm) Y (mm) Load (kN) Pressure (kPa) Radius (mm)

1 4790 0 288 1521 245.502942 4790 1450 288 1521 245.502943 4790 2930 288 1521 245.502944 6190 0 288 1521 245.502945 6190 1450 288 1521 245.502946 6190 2930 288 1521 245.50294Table 16: Critical Points

A350Point 1 2 3 4 5 6 7 8 9 10 11 12

X (mm) 4790 5490 4432.5 5300 4432.5 5300 4432.5 5300 4432.5 5300 4432.5 5300Y (mm) 0 0 0 0 0 0 1020 1020 0 0 1020 1020Z(mm) 175 175 175 175 1400 1400 1400 1400 175 175 175 175Layer 1 1 1 1 2 2 2 2 2 2 2 2Table 17: Critical Points

B777Point 1 2 3 4 5 6 7 8 9 10 11 12

X (mm) 4790 5490 4432.5 5300 4790 5490 4790 5490 4790 5490 4790 5490Y (mm) 1450 1450 1450 1450 1450 1450 725 725 1450 1450 725 725Z(mm) 175 175 175 175 1400 1400 1400 1400 175 175 175 175Layer 2 2 2 2 3 3 3 3 2 2 2 2

4200 4400 4600 4800 5000 5200 5400 56000

200

400

600

800

1000

1200

1400

1600

Coordinate Axis for B777 and A350

A350 loadB777 LoadCritical points fatigueCritical Points Rutting

x (mm)

y (m

m)

Figure 5Step 4: Find Thickness of AB to protect SG from rutting.*we only have to check for rutting for Summer Day because that is the time that is most susceptible to rutting.find desiredmax value for σ zz (vertical stress )

.4∗shear strength>.5σ zz

s sSG=100 kPa

σ zz<80 kPaVarying the depths we got these values*note through observation using openpave the B777 caused more vertical stress therefore this was the plane used to determine if there will be rutting in the SG.Table 18SG SG SG SG AB AB AB AB

point 5 6 7 8 9 10 11 12AB 300 mm szz (kPa) -224.96 -120.33 -106.76 -92.067 -733.281 -55.4613 -47.90628 -31.0746AB 1200 mm szz (kPa) -77.337 -81.076 -71.932 -76.151 -799.741 -39.2644 -32.40267 -0.77226AB 1300 mm szz (kPa) -72.208 -76.598 -67.948 -72.508 -799.998 -39.449 -32.64279 -0.94547

Looking at AB 1200 mm and AB 1300mm we have just above and below 80 kPa respectively, when looking at the max vertical stress.

200 300 400 500 600 700 800 900 10000

50

100

150

200

250

A350 AB thickness to protect Subgrade

Stress vs ThicknessDesign thickness

Thickness of AB (mm)

verti

cal S

tres

s (k

Pa)

Figure 6: AB thickness vs rutting in subgrade A350

200 400 600 800 1000 1200 14000

20

40

60

80

100

120

B777 Actual Design Thickness

(vertical stress)/2 vs depthDesign thickness

thickness of AB (mm)

(ver

tical

str

ess)

/2 k

Pa

Figure 7: AB thickness vs rutting in subgrade B777Through interpolation we get a design thickness of 1225 mmTable 19

SG SG SG SG AB AB AB ABpoint 5 6 7 8 9 10 11 12

AB 1225 mm szz (kPa) -75.987 -79.928 -70.912 -75.237 -799.811 -39.3083 -32.46416 -0.80931

B) Determine if Subgrade ruts Find desired σ zz

samemethodas before

σ zz<336 kPaBy looking at point 9, on table 19, it shows a vertical stress of 800 kPa therefore, the AB will rut. Changing any thickness of the AB will not protect the AB.

0 200 400 600 800 1000 1200 14000

100

200

300

400

500

600

700

800

900

1000

Check for Rutting in AB1 & AB2

A-350

B777

Saturated Shear Stress for AB1

Saturated Shear Stress for AB2

Thickness (mm)

Verti

cal S

tres

s (kP

a)

Figure 8: Rutting in AB vs Thickness of ABC) Determine if the AC fails due to fatigueStep 1: find the tensile strains due to passing of planesUsing open Pave the following micro strains were calculated at the bottom of the asphalt layer.

Table 20  B777 wheel  

A350 wheel  critcal point A B C DA350 summer day (micro strain) 358 124 797 125A350 summer night (micro strain) 327 90.4 659 95.9A350 winter day (micro strain) 327 90.4 659 95.9A350 winter night (micro strain) 244 102 421 83.9B777 summer day (micro strain) 677 168 269 137B777 summer night (micro strain) 568 76.9 479 125B777 winter day (micro strain) 568 76.9 479 125B777 winter night (micro strain) 370 88.2 364 116Step 2: find allowed number of repetitions

for A 350 summer day point A

ϵ tension=358∗10−6

N field=SF∗e−23.63−4.2913∗ln (ϵ tension)

N field=5∗e−23.63−4.2913 ln(358∗10−6)=167847allowed repititions

Table 21wheel B777 wheel A350

critcal point NA NB NC NDA350 summer day (micro strain) 167846.8382 15881478.1 5412.06872 15343394.73A350 summer night (micro strain) 247578.3282 61643290.2 12237.9428 47842427.57A350 winter day (micro strain) 247578.3282 61643290.2 12237.9428 47842427.57A350 winter night (micro strain) 869731.9717 36718546.4 83716.2255 84908602.8B777 summer day (micro strain) 10901.4996 4314412.61 572262.698 10353386.51B777 summer night (micro strain) 23155.6184 123400152 48113.5729 15343394.73B777 winter day (micro strain) 23155.6184 123400152 48113.5729 15343394.73B777 winter night (micro strain) 145702.6124 68517586.6 156292.101 21143789.56

Step 3: find actual repetitionsnactual for each season forB777=

365∗20∗3∗32

2=16425

*n will only change between the different planesTable 22 

n (repetitions)A350 14600B777 16425Step 3: use minors law to find whether pavement fails due to fatigue

nN

for A350 summer day at critical point A

nN

= 14600167847

=.087

*same process for each minor law calculationTable 23

wheel B777 wheel A350critcal point minors A minors B minors C minors DA350 summer day (micro strain) 0.086984063 0.00091931 2.69767454 0.00095155A350 summer night (micro strain) 0.058971236 0.00023685 1.19301097 0.000305168A350 winter day (micro strain) 0.058971236 0.00023685 1.19301097 0.000305168A350 winter night (micro strain) 0.016786781 0.00039762 0.17439869 0.00017195B777 summer day (micro strain) 1.506673449 0.00380701 0.02870185 0.001586437B777 summer night (micro strain) 0.709331088 0.0001331 0.34137976 0.001070493B777 winter day (micro strain) 0.709331088 0.0001331 0.34137976 0.001070493B777 winter night (micro strain) 0.112729619 0.00023972 0.10509168 0.000776824

Now sum up n/N at each critical pointsum A sum B sum C sum D

3.259778561 0.006104 6.074648 0.006238AC fails due to fatigue at A and C

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

1

2

3

4

5

6

7

Minors Law for design thickness

Path AMinors Law Failure linePath BPath CPath D

Path

n/N

sum

Figure 9

0 500 1000 1500 2000 25000

0.2

0.4

0.6

0.8

1

1.2

Minors Law vs AB thickness for A350 & B777

1225mm

300mm

2000mm

Max Strain before Fatigue

Thickness (mm)

Σn/N

Figure 10: Minors Law vs AB thicknessAs you can see here the AC will rut no matter what even if you change the thickness of the AB. It levels off. AB cannot protect the AC.Part 2A) Find k-value

¿ funky chart

Figure 11: funky chart@stiffness=80MPaBearing value=42 psi

deflection=.2∈¿

k−value=42.2

=210 psi¿Using the funky chart and the back calculated stiffness modulus of SG, we can find the k-value. K-value=210 psi/in

210 psi¿ =.0543 MPa

mm=k−value

B) Find design thickness of asphaltStep 1: Find wheel dimensions

Area B777=.189m2

¿ B777 infowebsite we found thewidthW of thewheel¿ be .53m

L= AW

=. 189.53

=.357m

*same procedure for A350Table 24:wheel dimentions

  W (m) L (m)B777 0.53 0.357516738A350 0.53 0.379988533

Step 2: set up wheel configuration.

Figure 12:B777 configuration in EverFe

Figure13: A350 configuration in EverFeStep 3: Find Changes of Temperature

Figure 14Step 4: iterate to find design thicknessDo 4 iterations for each temperature gradient and for each plane.Check the deflections and the max stress by using visualize for pointsHere is a table of all the iterations of PCC thickness and corresponding plane/season/thickness/deflection and Max tensile stress.

Table25:Thickness and respective stresses and deflectionsthickness (mm) Max (Mpa) Displacement (mm)

B777 summerday 250 7.25 4.203500 2.77 3.608600 2.72 3.482400 3.74 3.893

summernight 250 6.32 3.907500 2.346 3.58400 3.3469 3.665450 2.787 3.618

winternight 250 6.468 4.055500 2.4 3.651400 3.425 3.753450 2.84 3.713

A350 winternight 250 7.23 3.652500 2.5454 3.057400 3.63 3.231450 3.01 3.134

Summernight 250 6.997 3.628400 3.497 3.201450 2.9 3.113500 2.655 3.077

summerday 250 7.9565 3.868500 3.1277 3.065600 2.768 2.868615 2.718 2.83

Looking at chart we can see that the design thickness would be for the A350 summer day between 600 and 615Step 5: find design thicknessHere is the criteria for Max stressstress<.55∗MR=.55∗5MPa=2.75MPaThrough interpolation of A350 between 600 and 615 mmm.Design thickness will be 605.5mm

Table 26 Design Thicknessthickness (mm) Max (Mpa) Displacement (mm)

605.5 2.75 2.848

Figure 15: results for points

Figure 16: results for stressesC) Plots of deflections and Max stress vs thickness for each season and each plane.

0 100 200 300 400 500 600 700 8000

1

2

3

4

5

6

7

8

B777 Stress vs Thickness

B777 Max Stress Summer/Winter DayB777 Max Stress Summer NightB777 Max Stress Winter NightMax allowable stress

thickness (mm)

stre

ss (M

Pa)

Figure 17

200 250 300 350 400 450 500 550 600 6500

0.51

1.52

2.53

3.54

4.5

B777 Deflections vs Thickness

B777 Defliction Summer/Winter DayB777 Deflection Summer NightB777 Deflection Winter Night

thickness (mm)

Defle

ction

s (m

m)

Figure 18

200 250 300 350 400 450 500 550 600 6500

0.5

1

1.5

2

2.5

3

3.5

4

4.5

A350 Deflections vs Thickness

A350 Deflections Winter NightA350 Deflections Summer NightA350 Deflections Summer/Winter Day

thickness (mm)

Defle

ction

s (m

m)

Figure 19

0 100 200 300 400 500 600 700 800 9000

1

2

3

4

5

6

7

8

9

A350 Max Stress vs Thickness

A350 Max Stress Winter NightA350 Max Stress Summer NightA350 Max Stresses Summer/Winter NightMax Allowable Stress

Thickess (mm)

Max

Str

ess (

MPa

)

Figure 20

Full openpaveTable 26: B777 summer day 1225 mm AB2 FALSE

Layer Thickness (mm)

Elastic Modulus

(MPa)

Poisson's Ratio Friction

v1.2 2013/11/01

1 175 1900 0.35 12 1225 280 0.35 13 0 80 0.35 1

B777

Location X (mm) Y (mm) Load (kN) Pressure (kPa)

Radius (mm)

1 4790 0 288 1521 245.502942 4790 1450 288 1521 245.502943 4790 2930 288 1521 245.502944 6190 0 288 1521 245.502945 6190 1450 288 1521 245.502946 6190 2930 288 1521 245.50294

Point 1 2 3 4 5 6 7 8 9 10 11 12X (mm) 4790 5490 4432.5 5300 4790 5490 4790 5490 4790 5490 4790 5490Y (mm) 1450 1450 1450 1450 1450 1450 725 725 1450 1450 725 725Z(mm) 175 175 175 175 1400 1400 1400 1400 175 175 175 175Layer 1 1 1 1 3 3 3 3 2 2 2 2

dx (mm) 0.0460238 1.992E-18 -0.05336 0.0747688 -0.243002 -7.04E-18 -0.233207 4.198E-18 0.0460238 -6.8E-19 0.0452378 -1.14E-19dy (mm) 0.0008441 0.000804 0.0007438 0.0008143 0.0004765 0.0005956 -0.153576 -0.163099 0.0008441 0.000804 0.0436325 0.0450907dz (mm) 4.5261254 3.9575179 3.8190628 4.0204931 3.4648562 3.607807 3.3682408 3.5069249 4.5261254 3.9575179 3.6766042 3.7262018sxx (kPa) 1545.6535 -819.3785 -541.8694 -842.018 -3.015868 -3.973741 -2.972402 -3.670139 -139.4201 -138.7973 -43.08247 -63.8778syy (kPa) 1539.367 -208.9041 244.07669 -118.1604 -9.130115 -9.92306 -10.50235 -11.04529 -140.3465 -48.83269 -123.2224 -63.24715szz (kPa) -799.8108 -39.30833 -222.9388 -83.07334 -75.98734 -79.92796 -70.91174 -75.23658 -799.8108 -39.30833 -32.46416 -0.809315txy (kPa) 0.1603383 8.164E-17 0.5752276 -0.14223 0.0263584 5.117E-17 -1.569139 1.843E-18 0.0236288 1.77E-17 0.8342597 4.715E-16txz (kPa) 19.51558 -1.91E-15 192.03055 -66.34295 14.867919 -2.21E-15 14.221205 8.036E-16 19.51558 -3.02E-15 18.359115 1.583E-15tyz (kPa) -0.336668 -0.323698 -0.266036 -0.32895 -0.184633 -0.199808 7.1726342 7.7371278 -0.336668 -0.323698 8.2023736 8.9988087exx (me) 677.26782 -385.5285 -289.0882 -406.098 334.69054 343.42644 319.03162 331.60642 677.26782 -385.5285 40.742224 -148.0644eyy (me) 672.80109 48.229606 269.34713 108.22185 231.51262 243.03168 191.96381 207.15083 672.80109 48.229606 -345.6467 -145.0238ezz (me) -989.2463 168.73189 -62.47965 133.15216 -896.7031 -938.301 -827.4448 -876.0773 -2506.759 94.150647 91.937646 156.01577gxy (me) 0.2278492 1.16E-16 0.8174287 -0.202116 0.8895962 1.727E-15 -52.95845 6.221E-17 0.2278492 1.707E-16 8.044647 4.546E-15gxz (me) 27.732666 -2.72E-15 272.88552 -94.27683 501.79225 -7.46E-14 479.96568 2.712E-14 188.18595 -2.91E-14 177.03432 1.526E-14gyz (me) -0.478423 -0.459992 -0.37805 -0.467455 -6.231353 -6.743522 242.0764 261.12806 -3.24644 -3.121371 79.094317 86.774227s1 (kPa) -799.9732 -819.3785 -632.0141 -847.7737 -78.90089 -79.92853 -74.60912 -76.15599 -800.3872 -138.7973 -123.9662 -64.51822s2 (kPa) 1539.3632 -208.9048 -132.7946 -118.1628 -9.129628 -9.92249 -9.663307 -10.12588 -140.3465 -48.84368 -56.61721 -63.8778s3 (kPa) 1545.8198 -39.30771 244.07715 -77.3152 -0.102813 -3.973741 -0.114068 -3.670139 -138.8437 -39.29734 -18.18561 0.4617567t1 (kPa) 3.2282593 84.798523 188.43585 20.423816 4.5134076 2.9743746 4.7746194 3.2278705 0.7513613 4.7731706 19.215801 0.320209t2 (kPa) 1169.6682 305.23687 249.60976 364.80544 34.885629 35.003019 32.472906 33.015053 330.02037 44.976827 33.674488 32.169778t3 (kPa) 1172.8965 390.0354 438.04561 385.22926 39.399037 37.977393 37.247525 36.242923 330.77173 49.749998 52.890288 32.489987e1 (me) -989.3617 -385.5285 -353.1384 -410.1876 -945.8692 -938.3106 -889.838 -891.5922 -2509.538 -385.5285 -349.2329 -151.1522e2 (me) 672.7984 48.229167 1.5701941 108.22015 231.52084 243.0413 206.12261 222.6658 672.80132 48.176626 -24.51458 -148.0644e3 (me) 677.38592 168.73233 269.34746 137.24347 383.84834 343.42644 367.26601 331.60642 680.04659 94.203628 160.78064 162.14415g1 (me) 4.5875264 120.50316 267.77726 29.023317 152.32751 100.38514 161.1434 108.94063 7.2452694 46.027003 185.29522 3.08773g2 (me) 1662.1601 433.75766 354.70861 518.40773 1177.39 1181.3519 1095.9606 1114.258 3182.3393 433.70512 324.71828 310.20858g3 (me) 1666.7476 554.26083 622.48587 547.43105 1329.7175 1281.737 1257.104 1223.1987 3189.5846 479.73212 510.0135 313.29631

Vertical Deflection Only

ExactDefaultFast

Quick and DirtyBoussinesq METNumerical MET

Table 27:A350 summer day 1225mm AB2 FALSE

Layer Thickness (mm)

Elastic Modulus

(MPa)

Poisson's Ratio Friction

v1.2 2013/11/01

1 175 1900 0.35 12 1225 280 0.35 13 0 80 0.35 1

A350

Location X (mm) Y (mm) Load (kN) Pressure (kPa)

Radius (mm)

1 4432.5 0 335 1662 253.298112 4432.5 2040 335 1662 253.298113 6167.5 0 335 1662 253.298114 6167.5 2040 335 1662 253.29811

Point 1 2 3 4 5 6 7 8 9 10 11 12X (mm) 4790 5490 4432.5 5300 4432.5 5300 4432.5 5300 4432.5 5300 4432.5 5300Y (mm) 0 0 0 0 0 0 1020 1020 0 0 1020 1020Z(mm) 175 175 175 175 1400 1400 1400 1400 175 175 175 175Layer 1 1 1 1 3 3 3 3 2 2 2 2

dx (mm) 0.1637382 -0.052345 0.0416707 -1.19E-16 -0.176907 2.092E-17 -0.190746 3.748E-17 0.0416707 -9.58E-17 0.0450648 -1.67E-17dy (mm) 0.0491543 0.0499137 0.0476136 0.0500403 -0.175714 -0.189668 6.446E-17 5.971E-17 0.0476136 0.0500403 2.894E-18 8.202E-18dz (mm) 3.2297521 2.8893916 3.7025542 2.8447482 2.5414658 2.6382765 2.6208574 2.7413959 3.7025542 2.8447482 2.7555075 2.8423382sxx (kPa) -557.579 -619.7042 1820.4093 -557.0478 -2.545508 -7.449442 -3.095809 -5.9641 -146.1233 -86.831 -24.75767 -34.16275syy (kPa) 393.59285 -120.7942 1830.7434 -150.3555 -2.397556 -2.884479 -10.55528 -10.33015 -144.6004 -26.8974 -58.14795 -36.85543szz (kPa) -262.4988 -28.32028 -902.6045 -10.32378 -58.95866 -56.2899 -51.04972 -52.49747 -902.6045 -10.32378 -0.386484 3.3447316txy (kPa) 4.7333056 -1.866369 7.279715 -8.85E-17 -1.923359 5.931E-17 2.327E-15 -5.82E-16 1.0728001 3.263E-17 -4.91E-15 1.606E-14txz (kPa) -184.8637 36.822078 11.85226 8.32E-14 9.6219619 7.762E-16 10.136517 3.691E-16 11.85226 7.678E-14 12.600875 -3.37E-15tyz (kPa) 10.750672 11.052177 10.029906 11.098495 8.5564156 9.313915 -4.22E-15 -6.99E-15 10.029906 11.098495 -6.01E-15 -7.89E-15exx (me) -317.6115 -298.6917 787.13724 -263.5842 236.61457 165.7699 230.82428 200.31958 787.13724 -263.5842 -15.2522 -80.12146eyy (me) 358.22108 55.797047 794.47985 25.381327 239.11126 242.80365 104.94571 126.64253 794.47985 25.381327 -176.2411 -93.104ezz (me) -107.9493 121.5022 -1147.636 124.87757 -715.3573 -658.4129 -578.398 -584.931 -2860.183 105.28987 102.25173 100.71819gxy (me) 6.7262764 -2.652209 10.344858 -1.26E-16 -64.91337 2.002E-15 7.853E-14 -1.97E-14 10.344858 3.147E-16 -4.73E-14 1.549E-13gxz (me) -262.7011 52.32611 16.842685 1.182E-13 324.74121 2.62E-14 342.10745 1.246E-14 114.28965 7.404E-13 121.50843 -3.25E-14gyz (me) 15.27727 15.705725 14.253025 15.771545 288.77903 314.34463 -1.42E-13 -2.36E-13 96.716955 107.0212 -5.8E-14 -7.61E-14s1 (kPa) -646.6376 -622.0011 -902.6927 -557.0478 -61.84436 -57.86764 -53.10435 -52.49747 -902.9224 -86.831 -58.14795 -36.85543s2 (kPa) -173.6195 -122.0225 1816.6622 -151.2297 -1.527025 -7.449442 -10.55528 -10.33015 -146.6354 -32.4615 -30.10122 -34.16275s3 (kPa) 393.77219 -24.79513 1834.5787 -9.449599 -0.530331 -1.306741 -1.04118 -5.9641 -143.7705 -4.759673 4.9570618 3.3447316t1 (kPa) 236.50901 48.61369 8.9582716 70.890054 0.4983466 3.0713505 4.7570496 2.1830237 1.4324286 13.850914 14.023368 1.3463369t2 (kPa) 283.69586 249.98928 1359.6774 202.90905 30.158669 25.209099 21.274536 21.083662 378.14351 27.184748 17.529139 18.753742t3 (kPa) 520.20487 298.60297 1368.6357 273.7991 30.657016 28.28045 26.031586 23.266685 379.57594 41.035662 31.552508 20.100079e1 (me) -380.89 -300.3236 -1147.698 -263.5842 -764.0536 -685.0372 -613.0699 -584.931 -2861.715 -263.5842 -176.2411 -93.104e2 (me) -44.79824 54.924295 784.47477 24.760201 253.80148 165.7699 104.94571 126.64253 784.6684 -1.445597 -41.01573 -80.12146e3 (me) 358.34851 124.00691 797.20495 125.4987 270.62068 269.42797 265.49613 200.31958 798.4811 132.11679 128.01525 100.71819g1 (me) 336.09176 69.082612 12.730175 100.7385 16.819199 103.65808 160.55043 73.67705 13.812704 133.56239 135.22534 12.982534g2 (me) 403.14675 355.24793 1932.1732 288.34444 1017.8551 850.8071 718.01559 711.57358 3646.3839 262.13864 169.03098 180.83966g3 (me) 739.2385 424.33054 1944.9034 389.08293 1034.6743 954.46518 878.56601 785.25063 3660.1966 395.70103 304.25632 193.82219

Vertical Deflection Only

ExactDefaultFast

Quick and DirtyBoussinesq METNumerical MET