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A Risk-Based Method of Deriving Design Fires for Evacuation Safety in Buildings

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Abstract

This article presents a risk-based method for building fire safety design. Because the design fire is the most critical aspect of a building fire safety design, this article uses reliability theory to derive design fires from the fire risk acceptance criteria. The fire scenarios are modeled by an event tree, where different fire protection systems are presented as pivotal events. The number of casualties is estimated by the occupant number and the probability that an untenable condition is reached before occupants evacuate to a safe location. Using the probability and consequence of each fire scenario, the expected risk to life is used to integrate the fire risk acceptance criteria into the determination of the target reliability index. A global optimization method is then applied to the reliability index to obtain the design fires for each scenario. A case study was conducted to demonstrate an application of this proposed method.

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Abbreviations

α :

The fire growth rate (kW/s2)

A :

The floor area of the building (m2)

β :

The reliability index

C :

The coefficient of the fitted expression

C α :

The power of α

C A :

The power of A

C H :

The power of H

C i :

The consequence of scenario i

ERL i :

The expected risk to life of scenario i

ERL i,a :

The acceptable ERL for scenario i

f :

The occupant flow rate per unit of exit width (person/(m s))

f A (t):

The probability density function of ASET

f ig :

The fire ignition frequency per unit floor area (year m2)

f R (t):

The probability density function of RSET

F R (t):

The cumulative probability function

G :

The safety margin

g(m’):

The function of transforming the severity m’ into a measure of fire risk analysis interest

H :

The height of compartment (m)

m’ :

The severity measure

M :

The vector of design parameters

N B :

The number of the geometry group

N p :

Number of occupants in the room (person)

N s :

The number of fire scenarios

P f :

Failure probability

P i :

The occurrence probability of scenario i

P i,f :

The failure probability for scenario i

P i,f,t :

The target failure probability of scenario i

q :

The occupant density (person/m2)

R i :

The risk of fire scenario i

S i :

The scenario of i

t A :

Available safe egress time (s)

t move :

The movement time (s)

t R :

Required safe egress time (s)

μ G :

The mean value of safety margin G (s)

σ G :

The standard deviation of safety margin G

W :

The effective width of the exit (m)

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Acknowledgments

The authors acknowledge the financial support of National Natural Science Foundation of China (Grant No. 51504282), China Postdoctoral Science Foundation funded project (Grant No. 2014M560592), the Opening Fund of Key Laboratory of Fire Suppression and Rescue Technology (Grant No. KF201401), and the Fundamental Research Funds for the Central Universities (Grant No. 16CX02045A). Dr. Ping is supported by the Opening Fund of State Key Laboratory of Fire Science (Grant No. HZ2014-KF14), the Shandong Provincial Natural Science Foundation (No. ZR2014EEQ 036) and the Fundamental Research Funds for the Central Universities (Grant No. 15CX02018A). The authors appreciate the comments from the reviewers.

Author information

Authors and Affiliations

  1. Center for Offshore Engineering and Safety Technology, China University of Petroleum (East China), Qingdao, Shandong, China

    Depeng Kong

  2. State Key Laboratory of Fire Science, University of Science and Technology of China, Hefei, China

    Depeng Kong & Shouxiang Lu

  3. College of Chemical Engineering, China University of Petroleum (East China), Qingdao, Shandong, China

    Ping Ping

Authors
  1. Depeng Kong
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  2. Shouxiang Lu
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Corresponding authors

Correspondence to Depeng Kong or Shouxiang Lu.

Appendix: The Generation of the Analytical Expression for the Limit State Function

Appendix: The Generation of the Analytical Expression for the Limit State Function

In order to generate the analytical expression of ASET and smoke detection time, multiple runs of a two-zone model, CFAST, were performed with variations of the input parameters to generate a number of output values. A multiple linear regression method was then employed to fit an expression of the calculated ASET values. There are three input parameters for the calculation of ASET: fire growth rate, the height and area of the compartment. The variation ranges of these three parameters are as shown in Table 9.

Table 9 The selected values of the input parameters for CFAST multiple runs
Full size table

Scenario 1 is taken as an example here to demonstrate the generation process. In this scenario, in order to obtain the expression of ASET with fire growth rate and compartment geometry, 392 runs of CFAST simulation were conducted, using the values in Table 9. From this regression, the final expression of ASET was obtained as follows:

$$ ASET = 0.13\alpha^{ - 0.262} H^{ - 0.01} A^{0.977} $$
(26)

The error between the analytical expression results and CFAST simulation results is shown in Fig. 5(a). The adjusted R 2 is 0.907.

Figure 5
figure 5

Regression results versus the original CFAST results for Scenario 1

Full size image

In this scenario, the smoke detector works well, and detection time can be assumed to occur when the smoke layer descends to 5% of the compartment height. Similarly, the analytical expression of detection time may also be determined.

$$ t_{\det } = 0.077\alpha^{ - 0.257} H^{ - 0.669} A^{0.876} $$
(27)

The corresponding adjusted R 2 is 0.990. The regression results and original CFAST results are shown in Fig. 5(b).

The analytical expressions of ASET and smoke detection time for Scenario 2 and 3 can be similarly determined by above process.

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Kong, D., Lu, S. & Ping, P. A Risk-Based Method of Deriving Design Fires for Evacuation Safety in Buildings. Fire Technol 53, 771–791 (2017). https://doi.org/10.1007/s10694-016-0600-8

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