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Applications of Structural Fire Engineering, 9-11 June 2021, Ljubljana, Slovenia
AN IMPROVED RELIABILITY-BASED APPROACH TO SPECIFYING
FIRE RESISTANCE PERIODS FOR BUILDINGS IN ENGLAND
Ian Fua, Ieuan Rickardb & Danny Hopkina
a OFR Consultants, Oxford, United Kingdom
b OFR Consultants, Edinburgh, United Kingdom
Abstract
For common building situations in England, the contemporary fire safety design guidance
recommends structural fire resistance periods for elements based upon occupancy and building
height. Deterministic and probabilistic time equivalence methods in guidance documents and the
wider literature (Kirby et al., 2004; BSI, 2019, 2007) provide an alternative approach to assess the
required fire resistance rating for elements forming a specific building’s structure. This study revisits
the work of Kirby et al., resolving some key limitations and incorporating advancements in the field
to present a new approach to assessing the recommended fire resistance for structural elements. This
results in revised fire resistance recommendations for office, retail and residential type buildings in
England, linked to both the building Consequence Class and total floor area.
Keywords: Structural fire resistance, Probabilistic reliability assessment, Reliability index
1 INTRODUCTION
In the design of fire safety provisions for common building situations, the appropriate structural fire
resistance for elements is selected from guidance based upon building height and occupancy
characteristics (HM Government, 2020; BSI, 2017, 2015). This has been expanded upon in recent
British Standards (BS 9991 and BS 9999), informed by work carried out by Kirby et al. (Kirby et al.,
2004), to include consideration of ventilation conditions and risk. Whilst novel, the ventilation
dependant fire resistance tables developed by Kirby, et al., have several limitations, as discussed in
Hopkin (Hopkin, 2017). Recent advances in design approaches, including the introduction and
widespread adoption of travelling fires (Stern-Gottfried & Rein, 2012) and the use of failure
probability as a performance measure to assess the acceptability of fire resistance levels, provide an
opportunity to revisit the work of Kirby, et al. to establish current relevance. In England, general
structural performance expectations and those in the event of accidents excluding fire are covered by
Part A of the Building Regulations. For the purpose of informing robustness provisions, the
consequences of structural failure are differentiated through Consequence Classes (CC). Structural
performance in the event of fire is covered by Part B of the Building Regulations, with the
consequences of fire induced structural failure differentiated through trigger heights. For the purpose
of harmonisation and consistency of performance, there are benefits in using a single means of
differentiating failure consequences, irrespective of the cause / accident. It is proposed that this should
be through Consequence Classes and the associated failure probabilities, as discussed in Hopkin, et
al. (Hopkin et al., 2017). To this end, probabilistically informed fire resistance recommendations (in
function of Consequence Class) are developed herein, utilising current knowledge in respect of
reliability indices (to define adequate performance) and fire models (capturing travelling fires for
large enclosure fire dynamics).
The tool used, SFEPRAPY (Fu & Hopkin, 2020), is an open-source package that has been presented
previously (Fu et al., 2019). It is designed to streamflow Monte Carlo Simulations (MCS),
particularly for the purpose of probabilistic applications of the time equivalence method. It has been
adapted for the analysis presented herein to consider stochastic parameters associated with
compartment geometry. This allows a generalised assessment to be carried out, like that by Kirby et
al., but utilising contemporary input parameters and design fire models. Through safety targets
(failure probabilities) linked to a given building Consequence Class, SFEPRAPY is applied to conduc
t a scoping review and propose alternative fire resistance periods for residential, retail and office type
buildings in England, as a function of their size (number of storeys, total floor area, etc).
2 DEFINING APPROPRIATE PERFORMANCE IN FIRE
The Building Regulations in England set out the minimum expectations under a life safety purview
for structural performance in events of fire, with Regulation B3(1) stating: “The building shall be
designed and constructed so that, in the event of fire, its stability will be maintained for a reasonable
period”. Regulation B3(1) does not explicitly define the duration of structural stability required in the
event of fire, with the structural fire safety performance objectives for a building varying in function
of the consequences of fire-induced collapse (Hopkin et al., 2020). This is elaborated through a
bifurcation of objectives for different scales of building: a) provision of adequate time for means of
escape, cognisant of building size; and b) adequate likelihood of surviving burnout. The former is
most relevant to buildings that are small and do not have sleeping hazards. In such instances,
structural fire performance is predominately dictated by the time required to facilitate typically quick
escape and fire & rescue service intervention. This study addresses the latter, i.e., structural
performance to provide an adequate likelihood of surviving burnout, where evacuation and fire &
rescue service intervention is potentially protracted.
Following the above, adequate structural fire performance can be demonstrated through the balancing
of the uncertain future costs and benefits of safety investments. Works by others (Joint Committee
on Structural Safety, 2001; ISO, 2014; BSI, 2005; Van Coile et al., 2017; Hopkin, Fu & Van Coile,
2020) quantify acceptable structural failure probabilities for buildings by optimising the cost/benefit
ratio. For the purposes of this analysis, the cost-optimised failure probabilities (alternatively defined
as reliability index
β
) from the JCSS probabilistic model code (Joint Committee on Structural Safety,
2001) and ISO 2394:2014 are adopted. A tentative connection between Consequence Class (HM
Government, 2013) and reliability index is proposed, as summarised in Table 1, considering a one-
year reference period.
Table 1. Consequence Class, building height (no. of storeys) and allowable failure probability
considering residential, retail and office type buildings*
Consequence Class (or Building Class)
CC2A
CC2B
CC3
No. of storeys
≤4
>4, ≤15
>15
Reliability index,
𝜷
[-]
3.7
4.2
4.4
Allowable failure probability (
𝑷
𝒇,𝒂
) [
𝒚𝒆𝒂
𝒓
―
𝟏
]
≈1×10⁻⁴
≈1×10⁻⁵
≈5×10⁻⁶
*Note the Consequence Class (or Building Class) also depends on building usage/characteristics. Specific to residential,
retail and office building types, the only relevant parameter is the number of storeys.
3 DERIVATION OF STRUCTURAL FAILURE PROBABILITY FOR A GIVEN
BUILDING
Once the maximum allowable failure probability has been defined, the probability of fire induced
structural failure must be evaluated. A simplistic failure criterion has been adopted (Equation 1),
whereby an element exposed to a fire of severity (defined through thermal time-equivalence) in
exceedance of the element’s structural fire resistance is deemed to result in global structural failure.
The (conditional) probability of fire-induced structural failure,
𝑃
𝑓,𝑓𝑖
, combined with the probability
of a structurally significant fire occurring,
𝑝
𝑓𝑖
, should remain lower than, or equal to the target
probability of failure,
𝑃
𝑓,𝑎
(Equation 1).
The probability of a structurally significant fire occurring can be evaluated based on a combination
of the probability of ignition and subsequent interventions prior to the fire becoming fully developed
(Equation 2). Through this approach, sprinklers are included in the evaluation of the probability of a
structurally significant fire occurring (as a preventative measure mitigating structurally significant
fires). This is the approach of the natural fire safety concept valorisation project (NFSC) (Schleich &
Cajot, 2001) underpinning EN 1991-1-2.
𝑝
𝑓𝑖
⋅
𝑃
𝑓,𝑓𝑖
≤
𝑃
𝑓,𝑎
(1)
𝑝
𝑓𝑖
=
𝑝
1
⋅
𝐴
⋅
𝑝
2
⋅
𝑝
3
⋅
𝑝
4
(2)
Where:
𝑝
1
is the probability of a severe fire occurring including the influence of occupants and standard
fire service (per m2 per year).
A
is the area of compartment/occupancy (m2).
𝑝
2
is the probability of unsuccessful fire suppression by FRS intervention (considering improved
professionalism/performance).
𝑝
3
is the probability of unsuccessful fire suppression associated with fire alarm and detection
systems.
𝑝
4
is the probability of unsuccessful fire suppression by active fire protection systems (sprinkler).
Table 2 shows the adopted probability parameter values for the purposes of this study. The sprinkler
system reliability (i.e.,
1
―
𝑝
4
) adopted was based on PD 7974-7:2019 (BSI, 2019) and sprinkler
statistics as garnered by the NFPA in 2017 (Ahrens, 2017). Sprinkler reliabilities of 91% and 93%
were adopted for residential and office/retail areas, respectively.
Figure 1. Simplified SFEPARPY streamflow
The conditional failure probability due to a structurally significant fire,
𝑃
𝑓,𝑓𝑖
, is effectively the
survival function (or complementary CDF) of a collection of time equivalence values,
𝑡
𝑒𝑞,𝑖
, and can
be evaluated as
1
―
𝑃
(
𝑡
𝑒𝑞,𝑖
≤
x
)
. Figure 2 shows the solved cumulative density function (CDF) of
time equivalence from a MCS study comprised of 100k iterations per occupancy based upon the
parameters in Table 2, using SFEPRAPY (Figure 1).
Figure 2. CDF of time equivalence
solved from an MCS study using
SFEPRAPY
Table 2. Probability parameters adopted in accordance with
NFSC
Occupancy
𝒑
𝟏
*
[
𝒎
―
𝟐
𝒚𝒆𝒂
𝒓
―
𝟏
]
𝒑
𝟐
†
𝒑
𝟑
‡
𝒑
𝟒
§
Residential
6.5×10⁻⁷
0.2
0.0625
1 (0.09)
Office
3.0×10⁻⁷
0.2
0.25
1 (0.07)
Retail
4.0×10⁻⁷
0.2
0.25
1 (0.07)
*6.5×10⁻⁷, 3.0×10⁻⁷ and 4.0×10⁻⁷ are adopted based upon the NFSC report
for residential, office and retail occupancy types, respectively.
†0.2 is adopted based upon the NFSC report assuming a professional fire
service is provided to intervene, should a fire occur, in 20 to 30 minutes
after the alarm activation.
‡0.0625 and 0.2 are adopted for residential and office/retail areas,
respectively, based upon the NFSC report. This assumes that smoke and
heat detectors are provided in the residential and office/retail areas,
accordingly.
§Values in brackets consider situations where an appropriate sprinkler
system is provided.
4 MODELS AND INPUTS
Enclosure fire dynamics are complex, and the development of fire is dependent upon compartment
geometry, lining materials, ventilation, etc. These parameters will ultimately govern whether a fire is
able to develop to an extent where all combustible material is near-simultaneously involved (i.e.,
flashover, parametric fire (BSI, 2002)) or whether the fire moves in search of both available un-burnt
fuel and/or oxygen (i.e., a travelling fire (Stern-Gottfried & Rein, 2012)). This study is premised on
both forms of fire development being credible scenarios. The choice of when to transition from one
fire model to another is based upon the various parameters including fuel load density and
compartment opening factors, etc. is specified within SFEPRAPY (Fu et al., 2019), as originally
adopted by Hopkin et al. (Hopkin et al., 2017).
Table 3 summarises the key input parameters used in this study. The data for the fuel load and heat
release rate, HRR, per unit area is obtained from PD 7974-1:2019 (BSI, 2019) and EN 1991-1-2 (BSI,
2002) and the data for the fuel load for retail areas is from EN 1991-1-2 (BSI, 2002). It is recognised
that not all available fuel will generally be consumed in event of fire, therefore, a uniform distribution
has been adopted between the combustion efficiency specified in BS EN 1991-1-2 (80%) and that of
PD 6688-1-2 (100%) (BSI, 2007). Glazing failure in fire has been considered following the principle
set out in the JCSS probabilistic model code (JCSS, 2001). The room and window geometry
parameters used are as per the work carried out by Kirby (Kirby et al., 2004).
Table 3. Key parameters adopted for the time equivalence MCS
Parameter
Distribution
Residential
Office
Retail
Fire load density [MJ/m²]
Gumbel
Mean: 780
SD: 234
Mean: 420
SD: 126
Mean: 600
SD: 180
HRR per unit area‡ [MW/m²]
Uniform
(0.32, 0.57)
(0.15, 0.65)
(0.27, 1.00)
Room height [m]
Uniform
2.4*
(2.8, 4.5)
(4.5, 7.0)
Floor area [m²]
Uniform
(9, 30)
(50, 1000)
(50, 1000)
Window height to room height ratio [-]
Uniform
(0.3, 0.9)
(0.3, 0.9)
(0.5, 1.0)
Window area to floor area ratio [-]
Uniform
(0.05, 0.2)
(0.05, 0.4)
(0.05, 0.4)
Fuel combustion efficiency‡ [-]
Uniform
(0.8, 1.0)
(0.8, 1.0)
(0.8, 1.0)
Glazing breakage percentage‡ [-]
Complementary
Lognormal†
Mean: 0.2
SD: 0.2
Mean: 0.2
SD: 0.2
Mean: 0.2
SD: 0.2
Model uncertainty factor§ [-]
Lognormal
Mean: 1
SD: 0.25
Mean: 1
SD: 0.25
Mean: 1
SD: 0.25
*Constant is used in lieu of random values based upon a distribution. †Truncated between 0 and 1. ‡Parameters not
considered in Kirby et al. §Truncated between 0 and 3.
5 THE REQUIRED STRUCTURAL FIRE PERFORMANCE
Based upon the established safety format defined previously (Equation 1). The minimum required
fire resistance period,
𝐹𝑅
, can be evaluated as per Equation 3. Where
𝑄
is the quantile function of the
solved time equivalence CDF, as shown in Figure 2.
𝐹𝑅
=
𝑄
(
1
―
𝑃
𝑓,𝑎
𝑝
1
⋅
𝐴
⋅
𝑝
2
⋅
𝑝
3
⋅
𝑝
4
)
(3)
The solved fire resistance periods are presented in Figure 3 considering buildings that are not provided
and provided with sprinklers, respectively. These figures may be used to interpret the fire resistance
periods for a given building height (in terms of no. of storeys) and floor area.
Without sprinklers
With sprinklers
Figure 3. Contour plots of the solved structural fire-resistance rating at various building heights and
total floor area (without and with sprinklers);
𝑨
𝒊
denotes floor area per storey
6 COMPARISON WITH GUIDANCE
For a fixed building footprint with floor area increasing with height, Table 4 shows the minimum fire
resistance periods recommended in the contemporary guidance of BS 9999:2017 (as proposed in
Kirby, et al.) and derived from the analysis presented in this study (“SFEPRAPY”). This study
considers a building comprised of single occupancy based upon generalised compartment properties.
Table 4. Minimum required fire resistance periods, a comparison between the derived and
recommendation in contemporary guidance
Fire resistance periods based upon no. of storeys
𝑺
or building height
𝑯
◊ (values in bracket include sprinklers) [min]
Occupancy
Method
Floor
area
per
storey
CC2A
𝐒
≤
𝟒
𝟓
<
𝑯
≤
𝟏𝟖
m
CC2B
𝟒
<
𝑺
≤
𝟏𝟓
𝟏𝟖
<
𝑯
≤
𝟑𝟎
m
CC3
𝑺
>
𝟏𝟓
𝑯
≥
𝟑𝟎
m
BS 9999†
-
60 (60)
90 (60)
120 (120)
800 m²
60 (60)
165 (60)
>180 (90)
Residential
SFEPRAPY
1600 m²
60 (60)
>180 (75)
>180 (120)
BS 9999‡
-
60 (30)
90 (60)
120 (120)
1000 m²
45 (45)
90 (45)
105 (60)
Office
SFEPRAPY
2000 m²
45 (45)
105 (60)
120 (75)
BS 9999§
-
60 (60)
90 (60)
120 (120)
1000 m²
45 (45)
105 (60)
120 (75)
Retail
SFEPRAPY
2000 m²
60 (45)
120 (75)
135 (90)
*Assuming appropriate sprinkler system specification is provided. †Corresponds to risk profile C1/C2/C3 as defined in BS 9999:2017.
‡Corresponds to risk profile A1/A2, reduction to fire resistance when sprinkler is provided only applies to A1. §Corresponds to risk
profile B1/B2, reduction to fire resistance with sprinklers only applies to B1. ◊ For comparison purposes, the recommendations in BS
9999 are included, however, the building heights defined in BS 9999 do not perfectly align with no. of storeys. For the purposes of this
study, the building height bands in BS 9999 (>5, ≤18 m), (>18, ≤30 m) and (≥30 m) are crudely mapped to ≤4, ≤15 and >15
storeys, respectively.
7 CONCLUSIONS
This paper presents a reliability-based approach to specifying fire resistance periods, using building
area and Consequence Class to differentiate fire-induced failure consequences. Utilising the proposed
reliability-based failure criteria for different building types, the potential importance of considering
both floor area and the number of storeys in the specification of appropriate fire resistance ratings has
been demonstrated. For a generalised storey area, the fire resistance ratings have been compared
against the contemporary guidance in the UK and are broadly in agreement, with the proposed
approach and methodology typically yielding a lower fire resistance when sprinklers are included.
For a residential building, of the floorplate investigated, the study shows significantly higher fire
resistance periods without sprinklers when compared to the guidance recommendations. In all cases,
it is shown that the inclusion of sprinklers has a significant influence on the required passive fire
protection to structural elements.
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