Reliability theories
S = surface depression d
Analytical models formulated with derived probability distribution theory, for screening level analysis.
Reliability of detention systems
The probability density functions of rainfall characteristics are exponential:
f = ζe−ζhh
f = λe−λtt
f = ψe −ψbb
h = rainfall depth
t = rainfall duration
b = interstorm interval
Are independent random variables
The distribution parameters are: ζ = inverse of expected value of rainfall depth, λ = inverse of expected value of rainfall duration, ψ = inverse of expected value of rainfall inter-storm interval.
Detention: f = 0
Assuming as certain that the network can transfer water from the impervious sub-catchment to the tank, and that the overflow divider performs correctly, only the detention system is subject to failure.
Initial condition
In applying the analytical probabilistic approach to assess the efficiency of a stormwater detention system, it is important to obtain the storage facility’s initial condition, e.g., the available stormwater storage capacity of the facility.
Depending on the conditions preceding a random rainfall event, the storage facility may be completely or partly empty when the rainfall event starts.
Simplifying assumptions previously adopted in literature
- The storage facility is completely full at the end of the rainfall event preceding the random rainfall event under analysis. [Howard’s conservative assumption (Howard 1976)].
- The storage facility is completely empty when the analyzed random rainfall event starts.
Simplifying assumptions previously adopted in literature
- The storage facility is completely full at the end of the rainfall event preceding the random rainfall event under analysis. [Howard’s conservative assumption (Howard 1976)].
- The storage facility is completely empty when the analyzed random rainfall event starts.
Sd = storage depression = 0
Vasche di laminazione
Risk of overflow R is estimated, as the probability that either the rainfall volume is imp h > V or that two consecutive rainfall events occur in a short period of time. At the beginning of the second rainfall event, tank storage capacity is impQ b = V’ < V and rainfall volume is 0 s simp h > V’s.
Under the most conservative assumption that the reservoir is full at the end of the first of two consecutive rainfall events,
Rf = P[b≥Vs/Q imp]·P[h>Vs/imp] + P[b<Vs/Q imp]·P[h>Q b]0 0 0
Rf = P[b≥Vs/Q imp]·P[h>Vs/imp] + P[b<Vs/Q imp]·P[h>Q b]0 0 0
hp (h) eh bp (b) eb V sQ imp 0 b h b hR e e dh db e e dh dbf V V 0 bQs s 0Q imp imp0 V s Q imp Q 0R e 0f Q Q0 0
Se i volumi accumulati nella vasca di laminazione vengono riutilizzati per gli usi consentiti, è necessario valutare il rischio che i volumi risultino insufficienti alla laminazione e/o al riutilizzo.
Ursino, 2015
Dimensionless parameters
Rainfall model
ζ = inverse of expected value of rainfall depth and λ = inverse of expected inter-storm interval.
Dimensionless parameters
The storage facility is completely full at the end of the rainfall event preceding the random rainfall event under analysis. [Howard’s conservative assumption Risk of overflow
Dimensionless parameters
The storage facility is empty at the end of the dry period preceding the random rainfall event under analysis. [Howard’s conservative assumption Risk of water scarcity
Dimensionless parameters
Il volume della vasca V, influenza influenza piuttosto il peso relativo dei due addendi che compaiono nelle espressioni di rischio.
Risk analysis of rainwater harvesting systems around the world
Simplifying assumptions previously adopted in literature
- The storage facility is completely full at the end of the rainfall event preceding the random rainfall event under analysis. [Howard’s conservative assumption (Howard 1976)].
- The storage facility is completely empty when the analyzed random rainfall event starts.
Esempi di sistemi di riutilizzo
Efficiency is an increasingly good estimate of the system reliability as the number of years of observation increases.
- Jordan averaged monthly precipitation data Domestic use Abdulla et al., 2009.
- Brasilia (Brazil) Daily rainfall - 30 years washing vehicles Sanches Fernandes et al., 2015.
- South Africa data forecasted by 6 global circulation models household water requirements Mwenge Kahinda et al., 2010.
- Iran Daily rainfall - 50 years Reuse systems for residential buildings Mehrabadi et al, 2013.
- Italy Daily rainfall - 30 to 100 years Reuse systems for residential buildings Palla et al., 2011.
- Australia Monthly average rainfall - 80 years Reuse systems for residential buildings Zhang et al., 2009.
Design is usually performed with reference to tank efficiency.
In high demanding scenarios there will be a marked dependence of the RWH system efficiency on the water demand (Fernandes et al., 2015).
Non-dimensional analysis
Demand ratio: ratio between annual demand and annually collected rainwater.
Storage fraction: ratio between storage capacity of the system.
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