Introduction

Moisture Control Strategies Presently Employed

Proposed Moisture Control Strategy

Developing the Algorithms

Using the Algorithms

An Example

Comparison with Existing Methods

Conclusions/Future Work

References

The following procedures can be used to the predict moisture tolerance of a roofing system using these algorithms for the four quantifiable requirements for moisture control in low-slope roofing [1].

Determine the parameters listed below for the roofing system to be evaluated.

Type of insulation (fiberboard, foam or a composite of the two);
H = Heating degree days for the location;
h_r = Relative humidity of the indoor environment (40% = 0.4);
r = Membrane absorptance (0.7 for white and 0.1 for black);
P = Deck permeance (in English perms [See chart below]); and
T = insulation thickness (in inches).

Requirement 2: No condensation can occur under the roof membrane.
The flow rate of water into a roof occurs during the winter uptake period when the indoor vapor pressure is greater than the vapor pressure at the outer membrane of the roof. This creates a vapor pressure drive which forces moisture into the roofing system.

Calculate p_vm, (the average vapor pressure at the roof membrane during the winter uptake period, in psi) and t, (the length of time of winter uptake, in months):

pvm =

-0.93414+ 0.284hr + 4.850x10-4H - 7.995x10-8H2 + 4.215x10-12H3 - 2.053x10-5Hhr + 161.0/H + 0.002305P - 8.013x10-5P2 - 1.343x10-7HP - 0.008889r;

(Eqn. 1)

t =

-66.1 - 1.514hr + 0.03390H - 5.655x10-6H2 + 3.067x10-10H3 + 0.004424Hhr - 4.327x10-7hrH2 + 11430/H.

(Eqn. 2)

Compute p_vi, (the vapor pressure of the indoor air):

pvi =

hr pvsat ,

(Eqn. 3)

where p_vsat is the saturation vapor pressure, found in any standard saturated steam table at the indoor temperature. p_vsat at 68°F is 0.342 psi; at 70°F, it's 0.363 psi [8].

Now calculate m (the moisture accumulation in the roofing system, lb/ft²):

m =

0.215 x t (pvi - pvm)/(Rbl + Rd + Ri)

(Eqn. 4) [7]

where R_bl is the air boundary layer vapor resistance (0.211 reps) and R_d and R_i are the deck and insulation vapor resistances (in reps), respectively. Table 2 lists the vapor resistances for typical roofing materials.

Now compare m, the calculated moisture accumulation, with the appropriate failure threshold shown below. See Reference [9] for information regarding the derivation of these thresholds.

Insulation	Failure Threshold
	lb/ft	kg/m2
Fiberboard	0.20 lb/ft2	1.0 kg/m2
Foam	0.012 lb/ft2	0.06 kg/m2
Composite	0.14 lb/ft2	0.69 kg/m2

Requirement 3: If a leak occurs in the roofing system, no condensation can occur on the deck.
Condensation at the deck is most likely to occur during the summer, when the vapor pressure at the outer membrane of the deck is greater than the indoor vapor pressure. This is also the time when drying occurs, as water vapor is pushed into the indoor environment.

The analysis is separated by insulation type. Read the conditions listed in order for each insulation type. If a roofing system meets one of the conditions, pass or fail is decided. If not, the analysis must be continued.

Composite

All the composite roofing systems passed this requirement for all conditions tested. Therefore, any composite system, as described above, passes this requirement.

Fiberboard

1. If H is greater than or equal to 6151, T is less than or equal to 1 inch, and the indoor relative humidity, h_r, is less than or equal to 50%, the system fails.
2. All other fiberboard systems pass.

1. If the vapor resistance ratio, R_i/R_d is less than or equal to 1.5, the system fails.
2. If the above condition is not met, continue with the vapor pressure drive calculations shown below.

Calculate the deck vapor pressure, p_vd :

pvd =

-48.41 + 0.3261 hr - 0.02054P - 0.01661r - 0.0004427H - 0.01734Ri + 0.0005972P2 - 0.02675 hr 2 + 0.002402Ri2 +17322/H + 0.01288P hr + 0.002315Pa + 4.769x10-7PH + 0.01776/P - 2534135/H2 + 5.5574768*LN(H) + 5.626x10-8H/Ri

(Eqn. 5)

Calculate the vapor pressure drive, D_vp (the determination of p_vi is discussed in the previous section on requirement 2).

Dvp =

pvd - pvi

(Eqn. 6)

If the vapor pressure drive, D_vp, is greater than or equal to the failure threshold of 0.038 psi (0.19 kg/m²), then the system does not pass this requirement.

This method is also conservative, because it over predicts failure. The accuracy in predicting failures for the given database is over 99%, and for passes, it's 93%.

Requirement 4: If a leak occurs in the roofing system, drying time will be as short as possible.
Simulations were performed for each roofing system to determine the drying time after a leak of 10% by volume occurs. Separate correlations were developed for each insulation type: wood fiberboard, polyisocyanurate, and the composite of the two.

Calculate the relative time to dry. For a fiberboard system:

t =

-5.848+0.05641P + 5.6449r + 0.001264H + 7.463 hr + 0.4522r2 + 0.0002384rH + 7.7516x10-4 hr H + 3.75 hrr - 6.2 hr 2 - 7.83853x10-8 H2 - 0.05417T + 678.4/H - 0.5576/P - 0.00462rP - 1.627665x10-12H3 - 12.2547r3

(Eqn. 7)

For a foam system:

t =

-601.6 + 0.1774P + 4068r + 0.1309H - 67.88 hr - 5112r2 + 0.001416rH + 2.9644x10-3Hhr + 50.2083hrr +53.12hr 2 - 2.172x10-5H2 + 0.7542T + 44324/H + 2.037/P - 0.3933rP + 1.1374x10-9H3

(Eqn. 8)

For a composite system:

t =

18.74 + 0.02002P - 35.10r + 0.01328H + 0.6807 hr - 28.98r2 + 0.000255rH + 5.86x10-4Hhr + 2.083hrr + 1.25 hr2 - 2.0185x10-6H2 - 14.28T + 4702/H - 0.3850/P - 0.006140r + 9.866815x10-11 H3 + 102.4r3

(Eqn. 9)

It is recommended that the drying time should be less than one year. The "drying season" typically happens during the spring and summer months when the vapor drive pushes water vapor out of the roofing system and into the indoor environment. If the moisture is not removed during this time, it will remain in the roofing system until the next drying season. This method is also conservative and tends to slightly over predict drying time. For the given database, it predicts whether drying time is greater than 12 months with 100% accuracy. It predicts whether the drying time is 12 months or less with 97% accuracy.