Below are the first 10 and last 10 pages of uncorrected machineread text (when available) of this chapter, followed by the top 30 algorithmically extracted key phrases from the chapter as a whole.
Intended to provide our own search engines and external engines with highly rich, chapterrepresentative searchable text on the opening pages of each chapter.
Because it is UNCORRECTED material, please consider the following text as a useful but insufficient proxy for the authoritative book pages.
Do not use for reproduction, copying, pasting, or reading; exclusively for search engines.
OCR for page 203
APPENDIX D
MODEL EVALUATION
Sensitivity analyses were performed for PAVDRN and for the water film thickness and
hydroplaning speed models. The purpose of the sensitivity analysis was to determine ache
sensitivity of PAVDRN and the models to the various input parameters, to make certain that
the models behaved in a reasonable manner, and to establish the sensitivity of the response
variables (predicted values) to the input parameters (design parameters). The results of the
sensitivity analyses are given In this appendix.
ANALYSIS OF THE PAVDRN MODEL
The sensitivity analyses for the PAVDRN program were conducted by varying three
variables: cavemen" slope, S; rainfall intensity, i; and mean texture depth, MID. Each of
these input variables was assigned three valuesa low, an intermediate, and a high value as
given in table D~. The analyses were conducted by fixing two of the input variables (S and i,
S and MID, or i and MTD) at the intermediate value and allowing ache other two variables
(MID, i, and S. respectively) to assume their low, intermediate, and high values. The
calculations were conducted for the four pavement types: densegraded asphalt concrete, plain
Portland cement concrete, grooved Portland cement concrete, and opengraded porous asphalt
concrete. The values for the rainfall intensity, i, pavement slope, S. and mean texture depth,
MID, used In these calculations are given in table D~. Note that the values for rainfall
D1
OCR for page 203
intensity and pavement slope are the same for each of Me pavement types, but ache MID is
different for the opengraded asphalt concrete.
Table Dot. Values used In PAVDRN sensitivity analysis.
Variable
Minimum Intermediate Maximum
Rainfall' intensity' i 1.00 (25.4) 3.0 (76) 6.0 (152)
in/in (mm/h)
Slope' S 0.0050 (0.0050) 0.015 (0.015) 0.030 (0.030)
ft/ft (m/m)
Mean texture depth' MTD 0.01 (.25) 0.02 (0.51) 0.05 (1.14)
in (mm)3 DGAC and PCC(1)
1
`"DGAC =den segraced asphalt concrete, PCC = plain or grooved Portland cement concrete,
and OGAC opengraded asphalt concrete.
Values of water film thickness versus flow paw length for the four pavement types are
shown In figures D1 through Dot. The figures show how the water film thickness varies for
each of the variables when ache others are held at their extreme values.
D2
OCR for page 203
 rnPnC=~nr=H=H ~cr~h:~t ~nn~r=~`
5
4
~ 2 1 it, ~
O
0 5
a MTD = 0.254mm
~ MTD = 0.50Smm
 ·  MTD = 1.143mm
1
flow path distance, m

~ 3

2
1
O
0 5
10 15 20
Flow path distance, m
· Crosssiope = O.58/0
Crosssiope = 1.50/0
Crosssiooe = 3.0°/0
25 30

~ 3

2
o
~_
0 5
· RF] = 25.4 much
. RF! = 76.2 mmlh
* RF] = 152.4 mm~h
10 15 20
Flow oath distance. m
25 .. 30 ~
~ .
_·' ~_1 4~ _ =, a ~ __ ~ 1~__= ~it_ _ ~u 1
concrete pavement.
D3
OCR for page 203
E 3 ~
 (Portland cement concrete)
I MTD = 0~254mm
MID = O.508mm
MTD  1 ~ 143mm
Flow path distance' m 25 30
4
3

2
o
~ : :
10 15 20 25
Flow path distance, m
Crossslope = 0.5°/0
Crosssiope = 1.58/0
Crosssiope = 3.0%
0 5
30

~ 3

2
o
10 15 20
Flow path distances m
RFt = 25.4 mmfh
RFt = 76.2 mmlh
· RFi = 1 52 4 mmfh
25 . 30
Figure ~2. Values for water film thlc~ess versus flow path length for Portland cement
Dot
OCR for page 203
4
3
E 2

~ 1  .
O
o
Resee ~ concrete)
_ ~MTD=1.0mm
MTD = 2.5mm
~ MTD = 4.0mm
5 1015
Flow path distance, m
3
~ Crosssiope = 0.58XO
. Crosssiope = 1.S8/o

~ 2

~ 1
O
0 5 10
· Crossslope = 3.0%
____ it=

.
, .
_
15 20 25 30
Flow path distance, m
~ RF! = 25.4 mm/h
1
10 15 20
Flow path distance, m
. .
Figure D3. Values for water film thiclmess versus flow path length for opengraded asphalt
concrete pavement (no internal flow).
D5
OCR for page 203
4
3

~ 2

~ 1
o
_ _ _
(Open~raded aspha =
1 ~ 1
L
_~
MTD=1.0mm,
Permeability = O.75mmIs
· MTD = Grimm,
Per7neability = 2.1 mmJs
 MTD = 4.0mm,
Pe~eabili~ = 3.5mmIs
0 5 10 15 20 25 30
Flow path distance, m
~ 2

1
it
CrosssIope = O.5°/O
Crosssiope  1.5/
CrosssIope = 3.0%
it____ ~ __________________
, _~
, _
0 5 10 15
Flow path distance, m
!
I
20 25 30
3
~RFI= 25.4 much
~RFI= 76.2 mm~h
~I ~ RFI = 152 4 mmlh
0 5
10 15 20
Flow path distance, m
25 30
Figure >4. Values for water film thickness versus flow path length for ppeng~aded asphalt
concrete pavement (internal rioter).
D6
OCR for page 203
SENSITIVITY ANALYSIS OF THE WATER FILM THICKNESS MODEL
The following equation is used in PAVDRN to calculate the water film thickness:
y ~ 42.32 n q\06
~ s0.5
where
Y 
n
q 
S 
Flow depth (in)
Manning's roughness coefficient
Flow (ft3/s/ft)
Slope of the drainage path (ft/ft)
with Me values and coefficients In English units.
The water film thickness is predicted in PAVDRN using the following relationship:
(D~)
WFT = [ n L i s ]06 _ MID (D2)
where
n = Manning's roughness coefficient
~= Drainage path length (in)
i = Ra~nfaB rate (in/h)
D7
OCR for page 203
S = Slope of drainage path (mm/mm)
MTD = heart texture depth (in)
and the values and coefficients are In English units.
The sensitivity analyses were conducted using procedures outlined earlier. Low,
intermediate, and high values for n, q, and S are given In table D2, and the analyses were
conducted for several flow path lengths, as given In the table.
Table D2. Values used In kinematic wave equation sensitivity analysis.
Variable Minunum Intermediate Maximum
Manning's n 0.01 0.025 o.o5
Rainfall, intensity, i, 1.00 (25.4) 3.0 (76) 6.0 (152)
in/in (mm/h)
Slope, S. 0.0050 (0.0050) 0.015 (0.015) 0.030 (0.030)
ft/ft (m/m)
Drainage path length, L, 3.0 (0.92) 24 (7.3) 48 (14.6)
ft (m,
Flow, q, 6.94 x 10~5 3.37 x 10~3 6.67 x 10~3
ft3/s/ft~m3/h/myt~, (6.45 x106) (3.13x104) (6.20x104)
The values of the flow rate, q, are the result of multiplying the drainage path length, L, by
the rainfall ~tensi~9 i, and convening Me units as appropriate.
D8
OCR for page 203
SENSITIVITY OF THE: MODEL TO VARIATIONS IN N
The partial derivative of the kinematic wave equation witch respect to n is:
By 5.677 qO 6
= (D3)
On n04 S03
Using n 0.01, q 0.00000667 ft2/s, (0.00223m2/hr) aIld S 0.005 ft/ft (0.005
mm/mm) to obtain the highest By/On :
By 5.677 (0.006667~°6 = ~ figs in <220.6 mm) (D4)
fin (O 011° 4 (O 005~° 3
Multiplying this value by the highest n (= 0.05) yields the highest change In y _ 0.434 In
(~.0 my.
Using n 0.05, q 0.0000694 fF/s, (0.0232 in2/hr) and S  0.03 ft/ft (0.03
mm/mm) to obtain the lowest value of By/8n :
By 5.677 (0.00006944)°6 0 ~723 in (4 3~3 error) (D5)
an to 05~°4 LO 03~°3
Multiplying this value by the lowest n ~ 0.01) yields the lowest change in y0.001723 in
(0.0438 loamy.
D9
OCR for page 203
SENSITIVITY OF THE MODEL TO VARIATIONS IN Q
The partial derivative of the kinematic wave equation with respect to q is:
BY =
en
5.677 n06
q04 S03
Using n0.05, q0.0000694 ft2/s, (0.0232 huh) and S = 0.005 ft/ft (0.005
mm/mm) to obtain the highest Gy/6q :
BY =
~q
5.677 (o.oS)06
(0.00006944)° 4 (O.Oo5)o 3
= 212ft2/s/in
Multiplying this value by the highest value of q, 0.00666 ft2/s, (0.00223 iIl2/h) yields the
highest change in y per UIlit Bow.
(D6)
(D~
Using n = 0.01, q0.00000666 ft2/s, and S = 0.03 ft/ft to obtain the lowest Oy/6n
BY =
Be
5.677 (0.01)°6 _

(0.006667)o 4 (0 o3)o.3
7.61ft2/s/in
.
(D8)
Multiplying this value by the lowest q, 0.0000694 ft2/s, (0.0232 huh) yields the lowest change
in y per unit flow
. 
D10
OCR for page 203
SENSITIVITY OF THE: MODEL TO VARIATIONS IN S
The partial derivative of the ~nematic wave equation with respect to S is:
~Y _
~ _
~S
2~838 (n q)0 6
sl.3
(D9)
Us~ng n 0.05, q 0~00667 ft2/s~ and S0~005 ft/ft (0.005 m=/r~rn) to obtain the
highest By/6se
~y
~ =
~S
.
2e 838 [(0 05) (Oe0066697)]
(o.oo5)1 3
22 e 808
(D10)
Multiplying this value by the highest Se' OeO3 ftlft, yields the highest change in IYI = 0e684 1n
(17e4 mm) e
Us~ng n OeOl ~ q  OeO000694 ft2/s~ (OeO232 ~n2/h) and S = 0eO3 ft/fl (OeO3 rnmirurn)
to obtain the lowest dy/6n :
~y
~S
=
2 e 838 [(O e O 1) (0 ~ 00006944)]
I
(o.03)l 3
= ~ 0~0546
(D11)
Multiplying this value by the lowest S = 0.005 ft/ft (0.005 rnm/rr~m) yields the lowest change
in 1 Y 1 o e 000273 it1 (O e 00694 mm) ~
D11
OCR for page 203
ANALYSIS OF RESULTS
For the values of the highest change In the flow depth, y (see table D3), the order of
sensitivity is: q > S > n
Table D3. Variables affecting changes In flow depth.
Changes in y, in (mm)
Variable High Low
M~nning's n 0.434 (~.0) 0.00172 (0.0438)
Flow, q, (ft2/s) (cm3/s) 1.416 (36.0) 0.000528 (0.0134)
Slope, S (ft/ft) (mm/mm) 0.684 (17.4) 0.000273 (0.00694)
This shows that for high flows, the flow is the major factor that determines the flow depth. At
high rainfall rates and tong drainage path lengths, the quantity of the flow has the largest
effect on the depth.
For the lowest values of the change in y, the order is: n > q > S
This shows that at low flows, the resistance of the pavement, which is characterized by the
Manning roughness coefficient, is the most dominant factor affecting the depth of flow
D12
. 