Optimal Intensity Measures for the Repair Rate Estimation of Buried Cast Iron Pipelines with Lead-Caulked Joints Subjected to Pulse-like Ground Motions

Abstract

Pulse-like ground motions can cause severe damage to buried cast iron (CI) pipelines, which necessitates the selection of optimal seismic intensity measures (IMs) to estimate pipeline repair rates. Such a selection is essential for mitigating uncertainty in the seismic risk assessment of buried CI pipelines. For the first time, this study systematically screens the optimal scalar and vector IMs for buried cast iron pipelines with lead-caulked joints under pulse-like ground motions by a symmetrical evaluation based on the criteria of efficiency, sufficiency, and proficiency, providing a new method for reducing uncertainty in pipeline seismic risk assessment. We initiate the study by selecting 124 pulse-like ground motions from the NGA-West2 database and identifying 19 scalar and 171 vector IMs as potential candidates. A two-dimensional soil–pipe model is introduced, incorporating variability in the sealing capacity of lead-caulked joints along the axial direction. CI pipeline repair rates are calculated across various scaling factors and apparent wave velocities, yielding 1116 datasets pertinent to CI pipeline damage. The repair rate is adopted as the engineering demand parameter (EDP) to evaluate the efficiency, sufficiency, and proficiency of candidate IMs. Through comprehensive analysis, peak ground velocity (PGV) and the combination of PGV and the time interval between 5% and 75% of normalized Arias intensity ([PGV, Ds_5–75]) are determined as the optimal scalar- and vector-IMs, respectively, for assessing the repair rate of buried CI pipelines under pulse-like ground motions.

1. Introduction

Buried cast iron (CI) pipelines have witnessed prevalent applications for the transmission of natural gas and water [1,2], constituting a crucial component of lifeline engineering. Due to the relatively low stiffness of lead-caulked joints, buried CI pipelines are susceptible to pullout at joints under seismic loading, potentially triggering severe secondary disasters that endanger the lives and property of citizens [3,4,5]. Instances of joint failure in buried CI pipelines came to prominence during the 1971 San Fernando [6], the 1994 Northridge [7,8], and the 2011 Christchurch earthquakes [9]. For instance, during the 2017 Mexico earthquake [10], the water networks were amongst the most significantly affected infrastructure systems. Following the earthquake event, over six million users in approximately 64 municipalities lost water supply services. In Mexico City, five regions experienced severe water shortages due to more than 2300 leaks and pipe breakages in the distribution network. In contrast to non-pulse-like ground motions, pulse-like ground motions exhibit a prominent velocity pulse in the velocity time history of the ground motion, characterized by a large amount of energy arriving in a short time window [11], triggering more extensive damage to long-period structures such as buried pipelines [12]. Consequently, seismic risk assessment of buried CI pipelines subjected to pulse-like ground motions holds substantial engineering significance.

The quantitative assessment of the seismic risk of buried pipelines proceeds with the following key steps [13]: (i) identifying the characteristics (including pipe material, joint type, pipe diameter, burial depth, and backfill soil properties) and limit states of pipelines within the risk area; (ii) determining the seismic hazard of the risk area through probabilistic seismic hazard analysis (PSHA); (iii) evaluating the likelihood of buried pipelines reaching a specific damage state under anticipated seismic hazards using fragility relations or curves; and (iv) integrating associated uncertainties to estimate the occurrence probability of a particular damage state. In step (iii), fragility relations estimate engineering demand parameters (EDPs) as a function of seismic intensity measures (IMs). Appropriate IMs can delineate the primary characteristics of seismic ground motions (e.g., amplitude, frequency content, and duration) and mitigate uncertainties in predicting EDPs. Researchers typically employ efficiency, sufficiency, proficiency, practicality, predictability, and robustness as criteria to select optimal IMs, aiming to reduce uncertainties in assessing the seismic response of engineering structures [14,15].

A magnitude of the present research has elucidated optimal scalar- or vector-IMs for the seismic risk assessment of various structures, including pile foundations [16], buildings [17], bridges [18], concrete dams [19], buried steel pipes [20], liquefiable sites [21], slopes [22,23], and tunnels [24]. To the authors’ knowledge, existing empirical and analytical fragility relations for buried CI pipelines capitalize on various types of IMs to estimate pipeline repair rate (RR), such as peak ground acceleration (PGA; [6]), peak ground velocity (PGV; [25]), and peak ground strain (PGS; [5,26]). While PGV has been commonly used, its selection is often based on empirical observation or convention rather than a systematic comparison against a comprehensive set of candidate IMs under rigorous evaluation criteria such as efficiency, sufficiency, and proficiency [13,27]. Moreover, despite the potential advantages of vector-IMs, few studies have definitively identified not only the optimal scalar-IMs but also the superior predictive capability of vector-IMs for the repair rate estimation of buried cast iron pipelines with lead-caulked joints under pulse-like ground motions.

This study thus aims at identifying optimal IMs for estimating RR of buried CI pipelines with lead-caulked joints subjected to pulse-like ground motions through a symmetrical multi-criteria framework. A two-dimensional soil–pipe model factoring in uncertainty in the sealing capacity of lead-caulked joints along the pipe axis is established in OpenSees 3.1.0. A total of 124 pulse-like ground motions selected from the NGA-West2 database are imposed on the soil–pipe model, and the RR of buried CI pipelines under different scaling factors and apparent wave velocities (C_a) are calculated by nonlinear dynamic analyses. Subsequently, 19 scalar-IMs and their corresponding 171 sets of vector-IMs are selected, and the optimal scalar- and vector-IMs for estimating RR of buried CI pipelines with lead-caulked joints subjected to pulse-like ground motions are identified through the criteria of efficiency, sufficiency, and proficiency. The selected optimal IMs aid in mitigating uncertainties in the seismic risk assessment of buried CI pipelines.

2. Identification of Optimal Seismic Intensity Measures

2.1. Candidate Seismic Intensity Measures

In this study, we selected 19 scalar-IMs to assess RR pertaining to buried CI pipelines. These IMs encompass various aspects of ground motions, including those reflecting peak-amplitude characteristics of ground motions such as PGA and PGV; duration-related IMs like Ds_5–75 and Ds_5–95 [28]; evolutionary IMs that reflect both amplitude and duration characteristics of ground motions, such as cumulative absolute velocity (CAV; [29]), Arias intensity (I_a; [30]), and root-mean-square of velocity (V_RMS; [31]); frequency-related measures like the mean period (T_m; [32]) and the predominant period (T_p; [31]); and IMs related to the response spectra of ground motions, such as acceleration spectrum intensity (ASI) and velocity spectrum intensity (VSI; [31]). Detailed information about these selected IMs is presented in

Table 1. Intensity measures considered in this study.

IMs	Definition	Equation
PGA	Peak ground acceleration	$PGA=\max \left|a\left(t\right)\right|$
PGV	Peak ground velocity	$PGV=\max \left|v(t)\right|$
PGD	Peak ground displacement	$PGD=\max \left|u(t)\right|$
PGV2/PGA	/	/
Ia	Arias intensity	$I_a={\displaystyle \frac{\pi }{2g}}{\displaystyle \underset{0}{\overset{t_{tot}}{\int }}a{(t)}^2}dt$
CAV	Cumulative absolute velocity	$CAV={\displaystyle \underset{0}{\overset{t_{tot}}{\int }}\left|a(t)\right|}dt$
CAV5	CAV excluded the portion of |a(t)| < 0.05 m/s2	$CA{V}_5={\displaystyle \underset{0}{\overset{t_{tot}}{\int }}\chi \left|a(t)\right|}dt, \chi =\left\{\begin{array}{l}1,\left|a(t)\right|\ge 0.05{ \mathrm{m}/\mathrm{s}}^2\\ 0,\left|a(t)\right|<0.05{ \mathrm{m}/\mathrm{s}}^2\end{array}\right.$
ARMS	Root-mean-square of acceleration	$A_{RMS}=\sqrt{{\displaystyle \frac{1}{t_{tot}}}{\displaystyle \underset{0}{\overset{t_{tot}}{\int }}a{(t)}^2}dt}$
VRMS	Root-mean-square of velocity	$V_{RMS}=\sqrt{{\displaystyle \frac{1}{t_{tot}}}{\displaystyle \underset{0}{\overset{t_{tot}}{\int }}v{(t)}^2}dt}$
DRMS	Root-mean-square of displacement	$D_{RMS}=\sqrt{{\displaystyle \frac{1}{t_{tot}}}{\displaystyle \underset{0}{\overset{t_{tot}}{\int }}u{(t)}^2}dt}$
Ds5–75	Time interval between 5% and 75% of the normalized Arias intensity	$D{s}_{5–75}=t(0.75I_a)-t(0.05I_a)$
Ds5–95	Time interval between 5% and 95% of the normalized Arias intensity	$D{s}_{5–95}=t(0.95I_a)-t(0.05I_a)$
Tm	Mean period of a ground motion	$T_m=\frac{{\displaystyle \sum (C_i^2/f_i)}}{{\displaystyle \sum C_i^2}}$
Tp	Predominant period	$T_p=T(\max (S_a))$
ASI	Acceleration spectrum intensity	$ASI={\displaystyle \underset{0.1}{\overset{0.5}{\int }}{S}_a(\xi =5\%,T)}dT$
VSI	Velocity spectrum intensity	$VSI={\displaystyle \underset{0.1}{\overset{2.5}{\int }}{S}_v(\xi =5\%,T)}dT$
Sa (0.3 s)	Spectral acceleration at 0.3 s	/
Sa (0.5 s)	Spectral acceleration at 0.5 s	/
Sa (1.0 s)	Spectral acceleration at 1.0 s	/

. The IMs considered represent various characteristics (e.g., amplitude, frequency content, and duration) of ground motions. Notably, PGS was excluded for the following reasons: (i) the evaluation of PGS becomes even more complex in cases of irregular topography (e.g., variable bedrock depth, hills, canyons, slopes), as well as in the presence of significant lateral soil heterogeneities [33]; (ii) PGS can be deemed equivalent to PGA when C_a is known, since the theoretical value of PGS can be derived from PGV and C_a [5,33,34].

In comparison to scalar-IMs, vector-IMs can generally improve the predictive efficiency in regressing EDPs. Based on the 19 selected scalar-IMs, a total of 171 pairwise combinations of vector-IMs were configured in this study, examples of which include [PGA, I_a], [PGV, Ds_5–75], and [PGV, S_a (0.3 s)]. Note that the values of the candidate IMs were calculated using the (unscaled and scaled) ground motions.

2.2. Criteria for Identifying Optimal IMs

Existing literature predominantly utilizes criteria such as efficiency, sufficiency, proficiency, practicality, predictability, and robustness to identify optimal IMs for predicting the EDPs of interest [14,15,35]. Specifically, the first three metrics, namely efficiency, sufficiency, and proficiency, are the most prevalent criteria [18,36,37]. In this study, we conducted a symmetrical comparison of efficiency, sufficiency, and proficiency across 19 scalar-IMs and 171 vector-IMs, as presented in Section 2.1, to identify the optimal scalar- and vector-IMs for the RR estimation of buried CI pipelines.

Efficiency quantifies the prediction precision of an EDP given an IM and is measured by the standard deviation of residuals during regression analysis. An IM with higher efficiency can reduce the dispersion of the predicted EDP, commonly associated with a lower standard deviation of residuals. To model the relationship between RR and IMs, this study employed a linear regression model in log–log scale [21]:

$$\ln (RR)=a+b\ln (\mathrm{IM})+{\epsilon }_{\ln (RR)},$$

(1)

$$\ln (RR)=a+b\ln ({\mathrm{IM}}_i)+c\ln ({\mathrm{IM}}_j)+{\epsilon }_{\ln (RR)},$$

(2)

where a, b, and c represent regression coefficients; IM_i and IM_j denote the two IMs comprising the vector-IM; ε_ln(RR) signifies the regression residual. The standard deviation of residuals (termed as σ) is used to measure the efficiency of different IMs.

Sufficiency assesses whether the selected IM is independent of earthquake source characteristics, such as moment magnitude (M_w) and rupture distance (R_rup). It can be determined by examining the slopes of linear regressions between ε_ln(RR) and M_w, as well as between ε_ln(RR) and R_rup. An IM with better sufficiency results in higher independence of residuals of EDP on M_w and R_rup, leading to smaller slopes in the linear regressions. The relationship between ε_ln(RR) and M_w, as well as ε_ln(RR) and R_rup, can be formulated as follows [21]:

$${\epsilon }_{\ln (RR)}=c_1+c_2{M}_w+{\epsilon }_{M_w},$$

(3)

$${\epsilon }_{\ln (RR)}=c_3+c_4\ln (R_{rup})+{\epsilon }_{R_{rup}},$$

(4)

where ε_Mw and ε_Rrup stand for the regression residuals relative to M_w and R_rup, respectively; c₁ to c₄ represent regression coefficients. Smaller absolute values of c₂ and c₄ suggest stronger sufficiency of the corresponding IM. With equal weight assigned to M_w and R_rup, the average absolute value of c₂ and c₄ (termed as c_avg) is employed to evaluate the sufficiency of different IMs [21]:

$$c_{avg}={\displaystyle \frac{\left|c_2\right|+\left|c_4\right|}{2}},$$

(5)

Proficiency serves as a composite evaluation index that reflects both the efficiency and practicality of an IM. An IM with higher proficiency implies a more favorable ratio of efficiency to practicality. The proficiency of scalar- and vector-IMs can be computed using the following equations, respectively [18]:

$$\zeta ={\displaystyle \frac{{\sigma }_{\ln (RR)\left|\ln (\mathrm{IM})\right.}}{b}},$$

(6)

$$\zeta ={\displaystyle \frac{{\sigma }_{\ln (RR)|\ln ({\mathrm{IM}}_i), \ln ({\mathrm{IM}}_j)}}{(|b|+|c|)}},$$

(7)

where σ_{ln(RR)|ln(IM)} and σ_{ln(RR)|ln(IMi),ln(IMj)} are the standard deviation of regression residuals for scalar- and vector-IMs, respectively; |b| and |c| are the absolute values of the regression coefficients from Equation (2). Proficiency serves as a composite metric that encapsulates the trade-off between predictive efficiency and practicality. The optimal IM is identified by the minimization of ζ, which provides a direct criterion for selection.

3. Ground Motion Dataset

Extensive research activities have proposed widely applicable methods for identifying pulse-like ground motions [38,39]. Shahi [40] introduced a Continuous Wavelet Transform-based method for this purpose and employed it to identify a series of pulse-like ground motions from the Pacific Earthquake Engineering Research Center’s NGA-West2 database [41]. In this study, 124 ground motions were selected from the pulse-like ground motions identified by Shahi [40]. The spectral acceleration of the selected ground motions is presented in Figure 1, while detailed information about these ground motions is provided in Appendix A,

Table A1. The detailed information on the selected ground motions.

RSN	Earthquake	Station	Year	Mw	Rrup (km)	Vs30 (m/s)
20	Northern Calif-03	Ferndale City Hall	1954	6.50	27.02	219.31
148	Coyote Lake	Gilroy Array #3	1979	5.74	7.42	349.85
159	Imperial Valley-06	Agrarias	1979	6.53	0.65	242.05
161	Imperial Valley-06	Brawley Airport	1979	6.53	10.42	208.71
170	Imperial Valley-06	EC County Center FF	1979	6.53	7.31	192.05
171	Imperial Valley-06	El Centro-Meloland Geot Array	1979	6.53	0.07	264.57
173	Imperial Valley-06	El Centro Array #10	1979	6.53	8.60	202.85
178	Imperial Valley-06	El Centro Array #3	1979	6.53	12.85	162.94
179	Imperial Valley-06	El Centro Array #4	1979	6.53	7.05	208.91
180	Imperial Valley-06	El Centro Array #5	1979	6.53	3.95	205.63
181	Imperial Valley-06	El Centro Array #6	1979	6.53	1.35	203.22
182	Imperial Valley-06	El Centro Array #7	1979	6.53	0.56	210.51
184	Imperial Valley-06	El Centro Differential Array	1979	6.53	5.09	202.26
185	Imperial Valley-06	Holtville Post Office	1979	6.53	7.50	202.89
250	Mammoth Lakes-06	Long Valley Dam (Upr L Abut)	1980	5.94	16.03	537.16
316	Westmorland	Parachute Test Site	1981	5.90	16.66	348.69
319	Westmorland	Westmorland Fire Sta	1981	5.90	6.50	193.67
415	Coalinga-05	Transmitter Hill	1983	5.77	9.51	477.25
451	Morgan Hill	Coyote Lake Dam-Southwest Abutment	1984	6.19	0.53	561.43
503	Taiwan SMART1(40)	SMART1 C00	1986	6.32	59.92	309.41
504	Taiwan SMART1(40)	SMART1 E01	1986	6.32	57.25	308.39
505	Taiwan SMART1(40)	SMART1 I01	1986	6.32	60.11	275.82
506	Taiwan SMART1(40)	SMART1 I07	1986	6.32	59.72	309.41
507	Taiwan SMART1(40)	SMART1 M01	1986	6.32	60.86	268.37
508	Taiwan SMART1(40)	SMART1 M07	1986	6.32	58.92	327.61
510	Taiwan SMART1(40)	SMART1 O07	1986	6.32	57.99	314.33
568	San Salvador	Geotech Investig Center	1986	5.80	6.30	489.34
569	San Salvador	National Geografic Inst	1986	5.80	6.99	455.93
595	Whittier Narrows-01	Bell Gardens-Jaboneria	1987	5.99	17.79	267.13
611	Whittier Narrows-01	Compton-Castlegate St	1987	5.99	23.37	266.90
614	Whittier Narrows-01	Downey-Birchdale	1987	5.99	20.79	245.06
615	Whittier Narrows-01	Downey-Co Maint Bldg	1987	5.99	20.82	271.90
645	Whittier Narrows-01	LB-Orange Ave	1987	5.99	24.54	344.72
668	Whittier Narrows-01	Norwalk-Imp Hwy, S Grnd	1987	5.99	20.42	279.46
692	Whittier Narrows-01	Santa Fe Springs-E. Joslin	1987	5.99	18.49	339.06
722	Superstition Hills-02	Kornbloom Road (temp)	1987	6.54	18.48	266.01
723	Superstition Hills-02	Parachute Test Site	1987	6.54	0.95	348.69
725	Superstition Hills-02	Poe Road (temp)	1987	6.54	11.16	316.64
738	Loma Prieta	Alameda Naval Air Stn Hanger	1989	6.93	71.00	190.00
758	Loma Prieta	Emeryville, Pacific Park #2, Free Field	1989	6.93	76.97	198.74
764	Loma Prieta	Gilroy-Historic Bldg	1989	6.93	10.97	308.55
766	Loma Prieta	Gilroy Array #2	1989	6.93	11.07	270.84
767	Loma Prieta	Gilroy Array #3	1989	6.93	12.82	349.85
783	Loma Prieta	Oakland-Outer Harbor Wharf	1989	6.93	74.26	248.62
784	Loma Prieta	Oakland-Title and Trust	1989	6.93	72.20	306.30
796	Loma Prieta	SF-Presidio	1989	6.93	77.43	594.47
802	Loma Prieta	Saratoga-Aloha Ave	1989	6.93	8.50	380.89
803	Loma Prieta	Saratoga-W Valley Coll	1989	6.93	9.31	347.90
808	Loma Prieta	Treasure Island	1989	6.93	77.42	155.11
828	Cape Mendocino	Petrolia	1992	7.01	8.18	422.17
838	Landers	Barstow	1992	7.28	34.86	370.08
900	Landers	Yermo Fire Station	1992	7.28	23.62	353.63
982	Northridge-01	Jensen Filter Plant	1994	6.69	5.43	373.07
983	Northridge-01	Jensen Filter Plant Generator	1994	6.69	5.43	525.79
1003	Northridge-01	LA-Saturn St	1994	6.69	27.01	308.71
1004	Northridge-01	LA-Sepulveda VA Hospital	1994	6.69	8.44	380.06
1044	Northridge-01	Newhall-Fire Sta	1994	6.69	5.92	269.14
1045	Northridge-01	Newhall-W Pico Canyon Rd	1994	6.69	5.48	285.93
1052	Northridge-01	Pacoima Kagel Canyon	1994	6.69	7.26	508.08
1054	Northridge-01	Pardee-SCE	1994	6.69	7.46	325.67
1063	Northridge-01	Rinaldi Receiving Sta	1994	6.69	6.50	282.25
1084	Northridge-01	Sylmar-Converter Sta	1994	6.69	5.35	251.24
1085	Northridge-01	Sylmar-Converter Sta East	1994	6.69	5.19	370.52
1086	Northridge-01	Sylmar-Olive View Med FF	1994	6.69	5.30	440.54
1106	Kobe, Japan	KJMA	1995	6.90	0.96	312.00
1114	Kobe, Japan	Port Island (0 m)	1995	6.90	3.31	198.00
1119	Kobe, Japan	Takarazuka	1995	6.90	0.27	312.00
1120	Kobe, Japan	Takatori	1995	6.90	1.47	256.00
1148	Kocaeli, Turkey	Arcelik	1999	7.51	13.49	523.00
1176	Kocaeli, Turkey	Yarimca	1999	7.51	4.83	297.00
1244	Chi-Chi, Taiwan	CHY101	1999	7.62	9.94	258.89
1402	Chi-Chi, Taiwan	NST	1999	7.62	38.42	491.08
1492	Chi-Chi, Taiwan	TCU052	1999	7.62	0.66	579.10
1510	Chi-Chi, Taiwan	TCU075	1999	7.62	0.89	573.02
1528	Chi-Chi, Taiwan	TCU101	1999	7.62	2.11	389.41
1602	Duzce, Turkey	Bolu	1999	7.14	12.04	293.57
1605	Duzce, Turkey	Duzce	1999	7.14	6.58	281.86
1752	Northwest China-03	Jiashi	1997	6.10	17.73	240.09
2495	Chi-Chi, Taiwan-03	CHY080	1999	6.20	22.37	496.21
3473	Chi-Chi, Taiwan-06	TCU078	1999	6.30	11.52	443.04
3636	Taiwan SMART1(40)	SMART1 I04	1986	6.32	59.93	314.88
3641	Taiwan SMART1(40)	SMART1 I11	1986	6.32	60.00	309.41
3642	Taiwan SMART1(40)	SMART1 I12	1986	6.32	60.09	275.82
3643	Taiwan SMART1(40)	SMART1 M02	1986	6.32	60.89	306.78
3644	Taiwan SMART1(40)	SMART1 M03	1986	6.32	60.45	306.78
3645	Taiwan SMART1(40)	SMART1 M04	1986	6.32	59.93	306.38
3646	Taiwan SMART1(40)	SMART1 M05	1986	6.32	59.50	306.38
3647	Taiwan SMART1(40)	SMART1 M06	1986	6.32	59.07	308.39
3649	Taiwan SMART1(40)	SMART1 M09	1986	6.32	59.35	321.63
3650	Taiwan SMART1(40)	SMART1 M10	1986	6.32	59.86	321.63
3652	Taiwan SMART1(40)	SMART1 M12	1986	6.32	60.78	275.82
3656	Taiwan SMART1(40)	SMART1 O05	1986	6.32	59.02	286.03
3660	Taiwan SMART1(40)	SMART1 O11	1986	6.32	60.90	295.17
3744	Cape Mendocino	Bunker Hill FAA	1992	7.01	12.24	566.42
4040	Bam, Iran	Bam	2003	6.60	1.70	487.40
4098	Parkfield-02, CA	Parkfield-Cholame 1E	2004	6.00	3.00	326.64
4100	Parkfield-02, CA	Parkfield-Cholame 2WA	2004	6.00	3.01	173.02
4101	Parkfield-02, CA	Parkfield-Cholame 3E	2004	6.00	5.55	397.36
4102	Parkfield-02, CA	Parkfield-Cholame 3W	2004	6.00	3.63	230.57
4103	Parkfield-02, CA	Parkfield-Cholame 4W	2004	6.00	4.23	410.40
4107	Parkfield-02, CA	Parkfield-Fault Zone 1	2004	6.00	2.51	178.27
4113	Parkfield-02, CA	Parkfield-Fault Zone 9	2004	6.00	2.85	372.26
4115	Parkfield-02, CA	Parkfield-Fault Zone 12	2004	6.00	2.65	265.21
4126	Parkfield-02, CA	Parkfield-Stone Corral 1E	2004	6.00	3.79	260.63
4458	Montenegro, Yugo.	Ulcinj-Hotel Olimpic	1979	7.10	5.76	318.74
4480	L’Aquila, Italy	L’Aquila-V. Aterno-Centro Valle	2009	6.30	6.27	475.00
4482	L’Aquila, Italy	L’Aquila-V. Aterno -F. Aterno	2009	6.30	6.55	552.00
4847	Chuetsu-oki	Joetsu Kakizakiku Kakizaki	2007	6.80	11.94	383.43
4850	Chuetsu-oki	Yoshikawaku Joetsu City	2007	6.80	16.86	561.59
4856	Chuetsu-oki	Kashiwazaki City Center	2007	6.80	11.09	294.38
4879	Chuetsu-oki	Yan Sakuramachi City watershed	2007	6.80	18.97	265.82
4896	Chuetsu-oki	Kashiwazaki NPP, Service Hall Array 2.4 m depth	2007	6.80	10.97	201.00
6911	Darfield, New Zealand	HORC	2010	7.00	7.29	326.01
6927	Darfield, New Zealand	LINC	2010	7.00	7.11	263.20
6962	Darfield, New Zealand	ROLC	2010	7.00	1.54	295.74
6969	Darfield, New Zealand	Styx Mill Transfer Station	2010	7.00	20.86	247.50
6975	Darfield, New Zealand	TPLC	2010	7.00	6.11	249.28
8064	Christchurch, New Zealand	Christchurch Cathedral College	2011	6.20	3.26	198.00
8066	Christchurch, New Zealand	Christchurch Hospital	2011	6.20	4.85	194.00
8067	Christchurch, New Zealand	Christchurch Cashmere High School	2011	6.20	4.46	204.00
8090	Christchurch, New Zealand	Hulverstone Drive Pumping Station	2011	6.20	4.35	206.00
8119	Christchurch, New Zealand	Pages Road Pumping Station	2011	6.20	1.98	206.00
8123	Christchurch, New Zealand	Christchurch Resthaven	2011	6.20	5.13	141.00
8130	Christchurch, New Zealand	Shirley Library	2011	6.20	5.60	207.00

. The opted ground motions have M_w ranging from 5.5 to 8, with a mean value of 6.54; R_rup not exceeding 80 km, with a mean value of 20.56 km; and PGV between 15 cm/s and 170 cm/s, with a mean value of 51.76 cm/s.

To ensure sufficient data on the RR of buried CI pipelines for subsequent optimal IM analysis, the PGA of the selected ground motions was scaled by factors of 1.5 and 2.0. Although scaling the PGA increases the absolute values of the IMs, their distribution patterns remain largely unchanged. Consequently, a total of 124 × 3 = 372 ground motions were used for the dynamic response analysis of buried CI pipelines.

4. Numerical Modeling

This study established a two-dimensional soil–pipe model based on the finite element method [42,43,44,45] to calculate the RR of buried CI pipelines with a nominal diameter (DN) of 150 mm, as witnessed in Figure 2, and its validity and accuracy have been verified in a previous study [5]. To comprehensively consider the influence of the C_a, each seismic wave was assigned three different values of C_a (1000 m/s, 2000 m/s, and 3000 m/s), racking up a total of 372 × 3 = 1116 calculation scenarios. The selected values of C_a encompass a representative range of apparent wave propagation velocities observed in real seismic events [33] and are consistent with values commonly adopted in seismic response analysis for buried pipelines [46]. The parameter values involved in the model are listed in

Table 2. Parameters assigned in the two-dimensional soil–pipe model.

Components	Properties	Units	Values
Seismic waves	Wave propagation velocity along axial direction, Ca	m/s	1000; 2000; 3000
Pipe–soil interaction	Soil density, ρs	kg/m3	1900
	Cohesion, c	kPa	0
	Friction angle, φ	°	35
	Burial depth, d	m	1
	Relative soil–pipe yielding displacement, ua	mm	3
Pipe barrel	Elastic modulus, E	GPa	96
	Density, ρp	kg/m3	7000
	Segment length, L	m	6
	Outer diameter, Dos	mm	169
	Wall thickness, e	mm	11
	Joint embedment distance, dj	mm	90

.

4.1. Sealing Capacity of the Lead-Caulked Joints

The lead-caulked joints generally consist of packing (hemp or jute yarn) and caulking (lead or cement) materials. Packing serves to evenly fill the cavity between the bell and spigot, preventing the caulking material from entering the pipeline, while the caulking material ensures the sealing of the joint.

According to post-earthquake investigations [3,4] and numerical studies [47], buried pipelines under seismic wave propagation predominantly exhibit axial failure modes, while bending stresses, torsion, and rotational effects are negligible. Therefore, this study focused solely on analyzing the axial response of the pipeline. The axial sealing capacity of lead-caulked joints primarily involves the relationship between axial force and joint opening, as well as the corresponding joint opening (denoted as λ_l) at which leakage occurs.

Wham et al. [48] compiled axial tensile test results for 17 sets of lead-caulked joints with nominal diameters ranging from 150 mm to 1500 mm, proposing an empirical relationship between axial force (F) and joint opening (λ) for lead-caulked joints, as depicted in Figure 3a. The joint exhibits high initial tensile stiffness, which declines in the wake of the first slip. The axial tensile force reaches its peak, approximately 2.5 F_j, when the joint opening attains 17.78 mm. The axial force at first slip, F_j, can be calculated as follows [48]:

$$F_j=\pi D_{os}{d}_L{a}_C,$$

(8)

where D_os stands for the outer diameter of the pipe; d_L represents the lead caulking depth (which can be assigned as 57 mm for all pipe diameters); a_C signifies the CI–lead adhesion. Wham et al. [48] suggested that a_C abides by a normal distribution with a mean value of 1.63 MPa and a standard deviation of 0.49 MPa.

The joint opening associated with the leakage of lead-caulked joints demonstrates remarkable uncertainty. El Hmadi and O’Rourke [49] established a cumulative probability distribution for axial leakage versus the normalized joint opening (λ_l/d_j), as evidenced by Figure 3b. Herein, λ_l represents the joint opening corresponding to leakage, and d_j denotes the joint embedment depth (90 mm for DN 150 mm CI pipeline). El Hmadi and O’Rourke [49] suggest that λ_l/d_j follows a normal distribution with a mean value of 0.45 and a standard deviation of 0.13.

4.2. Pipeline Simulation

The pipe barrel was modeled by elastic beam-column elements assigned with corresponding elastic modulus, mass per unit length, and cross-sectional area. The model comprised 267 pipe segments (the length of each pipe segment was assigned as 6 m) and 266 joints, totaling approximately 1600 m in length. To mitigate the influence of boundary effects, only the middle 1000 m of the pipeline (encompassing 167 joints) was used to calculate the repair rate. The remaining pipe segments at both ends served as buffer zones to absorb reflected waves, thereby ensuring that the dynamic response in the central region of interest was unaffected by boundary interference. Additionally, the water within the pipeline was assumed to oscillate concurrently with the pipeline, and only the mass of the water was considered in the finite element model [3,50].

4.3. Joint Simulation

The sealing capacity of lead-caulked joints is predominantly contingent upon the CI–lead adhesion (a_C) and the joint opening corresponding to leakage (λ_l). A physical correlation between a_C and λ_l/d_j is anticipated, as both parameters stem from the quality of the lead–cast iron bond. However, the precise correlation coefficient between a_C and λ_l/d_j remains unquantified. In accordance with the established simplification prevalent in seismic fragility analyses of cast iron pipelines, a perfect correlation is therefore assumed herein. Additionally, both parameters are represented by truncated normal distributions to preclude non-physical values [26,34]. The mean values and standard deviations of these parameters are provided in Section 4.1. For each finite element model, a set of 266 samples for a_C and λ_l/d_j was generated using Latin Hypercube Sampling, corresponding to the 266 joints, thereby enabling the determination of the axial force–joint opening relationship for each joint and the joint opening (λ_l) corresponding to leakage. The joints were modeled using zero-length elements that incorporate the axial force–joint opening relationship of lead-caulked joints shown in Figure 3a.

4.4. Soil–Pipe Interaction Simulation

The CI pipeline is assumed to be backfilled with sandy soil. The soil–pipe interaction was simulated using zero-length elements, which were assigned the axial force-relative displacement relationship depicted in Figure 4 [25]. Following the recommendations of ALA [25], the soil–pipe yield displacement (u_a) was set as 3 mm. The peak pipe–soil interaction force per unit length (F_a) is given by the following equation:

$$F_a=\pi D_{os}\left(d+{\displaystyle \frac{D_{os}}{2}}\right){\rho }_{s}g{\displaystyle \frac{1+K_0}{2}}\tan (f_m\varphi ),$$

(9)

where ρ_s and ϕ represent the density and internal friction angle of the backfill soil, respectively; d denotes the burial depth (distance from the ground surface to the top of the pipeline); g is the gravitational acceleration; K₀ refers to the at-rest earth pressure coefficient, assigned as 1.0 in this study; and f_m is friction factor, set as 0.9 in this study.

4.5. Dynamic Analysis

Buried pipelines are primarily affected by seismic-wave propagation in the axial direction, so the ground motion was applied in the axial direction while the degrees of freedom in other directions were fixed. Existing research indicated that the traveling wave effect should be considered during the dynamic analysis of buried pipelines [46,51,52]. For seismic waves propagating along the axial direction of the pipeline, the shape and amplitude of ground motion at various points can be considered consistent, with only a time lag between the two points. This time lag can be calculated using the following equation [50]:

$$\Delta t={\displaystyle \frac{\tau }{C_a}},$$

(10)

where τ represents the distance between two points; C_a denotes the apparent wave propagation velocity along the axial direction of the pipeline. For each scenario, the ground displacements incorporating the traveling wave effect were input into each ground node for dynamic analysis.

The dynamic time-history analysis was performed using the unconditionally stable Newmark-β method (γ = 0.5, β = 0.25). A Rayleigh damping model with a damping ratio of 5% was assigned to the system, with the mass- and stiffness-proportionality coefficients calculated by matching this ratio at frequencies of 0.2 Hz and 20 Hz. The nonlinear equations were solved using the Newton–Raphson algorithm, with convergence determined by an energy increment tolerance of 1.0 × 10⁻⁴ and a maximum of 200 iterations per step.

4.6. Acquisition of Repair Rate

During the dynamic response analysis, the opening time histories of 167 joints within the middle 1000 m of the pipeline were recorded. For instance, Figure 5 depicts the opening time history of a specific joint subjected to the seismic wave RSN723. When the peak joint opening (PJO) exceeds λ_l, the joint is considered as failed. The PJOs for each joint were extracted. Consequently, the number of failed joints, Num_f, in each model can be calculated using the following equation:

$${Num}_f={\displaystyle \sum _{167}I\left(PJO\ge {\lambda }_l\right)},$$

(11)

where I (PJO ≥ λ_l) is a discriminant function that takes a value of 1 when PJO is greater than or equal to λ_l and 0 otherwise.

For each seismic scenario, the average value of Num_f from finite element models was taken as RR for that specific scenario, expressed in repairs per kilometer. A single finite element model is insufficient to fully represent the uncertainties inherent in the parameters a_C and λ_l/d_j. Figure 6 illustrates the variation in the calculated RR with respect to the number of finite element models. The results indicate that the RR stabilizes within an acceptable tolerance once the ensemble size reaches 1000 finite element models, satisfying the precision requirements of the analysis. Consequently, an ensemble of 1000 finite element models was constructed for each seismic scenario to ensure a robust and reliable probabilistic assessment. It should be noted that, to ensure the statistical reliability of the simulation results, an automated procedure was implemented to identify and discard any samples that failed due to numerical non-convergence, followed by supplementing new samples to complete the analysis.

Figure 7 presents the distribution of RR, obtained through numerical modeling, as a function of PGV for three different values of C_a. It can be observed that RR elevates with the increase in PGV and the decrease in C_a. The relationship between RR and PGV is approximately linear in logarithmic scale. The optimal IM for RR assessment under different C_a can be identified based on the data presented in Figure 7.

4.7. Validation of the Numerical Model

The validity of the two-dimensional finite element model developed in this study was assessed through a systematic comparison with a widely recognized empirical fragility relation. This relation synthesizes actual seismic damage observations of buried cast iron pipelines from multiple historical earthquakes [8]. It should be noted that the intensity measure, PGS, in the empirical fragility relation is equal to the ratio of PGV to C_a [46]. The goodness-of-fit between the numerical results and predictive results was quantified using three statistical metrics, with the results summarized in

Table 3. Comparison of model validation metrics for different C_a and the overall dataset.

Ca (m/s)	R2	MSE	MAE
1000	0.75	0.52	0.45
2000	0.73	0.07	0.18
3000	0.90	0.02	0.10
All	0.76	0.20	0.24

.

The finite element model demonstrates strong performance in predicting pipeline repair rates, as evidenced by an overall coefficient of determination (R²) of 0.76 and acceptably low Mean Squared Error (MSE) and Mean Absolute Error (MAE) values against the empirical fragility relation. It is noteworthy that the agreement diminishes under lower C_a. This is primarily because a lower C_a amplifies PGS, driving the pipeline system into a high-damage, strongly nonlinear response regime. Empirical data within this high-PGS range are inherently sparse, which complicates precise validation. Nonetheless, the model’s robust performance across the primary parameter range validates its effectiveness for assessing pipeline repair rates under seismic wave propagation.

5. Results

5.1. Optimal Scalar-IMs

This study elaborated on the efficiency of various scalar-IMs in predicting RR using Equation (1). Utilizing the analysis results with a C_a of 2000 m/s as an illustrative case, Figure 8a,b display the predictive efficiency of PGA and PGV, respectively. The standard deviations of the regression residuals (σ) derived when employing PGA and PGV as IMs are 0.7315 and 0.3698, respectively. When compared to using PGA as the IM, the standard deviation of the residuals is reduced when using PGV, suggesting that PGV outperforms PGA in terms of predictive efficiency.

The sufficiency of various scalar-IMs in predicting RR was investigated based on Equations (3)–(5). Figure 9a,b illustrate the dependence of the regression residuals ε_ln(RR) on M_w and R_rup, respectively. When PGV is utilized as the IM, the slope of the regression line between ε_ln(RR) and M_w is 0.1684, indicating a relatively stronger dependence of the regression residuals of ln(RR) on M_w. Conversely, the slope of the regression line between ε_ln(RR) and ln(R_rup) is −0.0760, suggesting a relatively weaker dependence of the regression residuals of ln(RR) on R_rup.

This study also explored the proficiency of various scalar-IMs in predicting RR using Equation (6). Figure 10a,b present the predictive proficiency of CAV₅ and I_a, respectively. The standard deviations of the regression residuals (σ) obtained when using CAV₅ and I_a as IMs are comparable, at 0.5225 and 0.5204, respectively. However, CAV₅ demonstrates superior predictive practicality compared to I_a, as evidenced by a smaller b value when CAV₅ is used as the IM. Thus, CAV₅ exhibits better predictive proficiency.

Figure 11 depicts the efficiency, sufficiency, and proficiency of various scalar-IMs in predicting RR of buried CI pipelines subjected to pulse-like ground motions. The distribution patterns of predictive efficiency, sufficiency, and proficiency for each IM remain consistent across different values of C_a. PGV exhibits the highest predictive efficiency (σ = 0.39) and proficiency (ζ = 0.24), followed by VSI (σ = 0.50, ζ = 0.33). In terms of sufficiency, CAV, CAV₅, and V_RMS perform best with c_avg values approximately 0.08; PGV ranks closely behind with c_avg values about 0.12. In contrast, VSI shows relatively poorer sufficiency relative to the other IMs (c_avg = 0.25). Considering the predictive efficiency, sufficiency, and proficiency of various scalar-IMs comprehensively, PGV is deemed the optimal scalar-IM for predicting RR of buried CI pipelines subjected to pulse-like ground motions.

5.2. Optimal Vector-IMs

The elucidation of the efficiency of various vector-IMs in predicting RR proceeded with Equation (2). Taking the analysis results with a C_a of 2000 m/s as an illustrative case, Figure 12a,b depict the efficiency analysis outcomes for [PGV, Ds_5–75] and [PGA, T_p], respectively. The standard deviations of regression residuals (σ) obtained when utilizing [PGV, Ds_5–75] and [PGA, T_p] as IMs are 0.3506 and 0.7063, respectively, revealing superior predictive efficiency for [PGV, Ds_5–75].

We then investigated the sufficiency of various vector-IMs in predicting RR using Equations (3)–(5). Figure 13a,b demonstrate the dependence of the regression residuals ε_ln(RR) on M_w and R_rup when [PGV, Ds_5–75] is employed as the IM. The slope of the regression line between ε_ln(RR) and M_w is 0.0069, markedly smaller than that obtained when using PGV as the IM, effectively mitigating the dependence on M_w. Additionally, the slope of the regression line between ε_ln(RR) and ln(R_rup) is −0.0667, suggesting a relatively lower dependence of ε_ln(RR) on R_rup when [PGV, Ds_5–75] is used as the IM.

The proficiency of various vector-IMs in predicting RR was explored using Equation (7). Figure 14a,b present the proficiency of [CAV, VSI] and [PGD, I_a], respectively. The standard deviations of the regression residuals (σ) are comparable, at 0.3964 and 0.3922, respectively. However, [CAV, VSI] exhibits superior predictive practicality (b = 0.7559) compared to [PGD, I_a] (b = 0.4502), indicating a greater predictive proficiency for [CAV, VSI].

Given the extensive number of vector-IMs, presenting the predictive efficiency, sufficiency, and proficiency analysis results for all vector-IMs is impractical. Therefore, Figure 15 displays the analysis results for the top 10 vector-IMs. Akin to scalar-IMs, the distribution patterns of predictive efficiency, sufficiency, and proficiency for various vector-IMs at different C_a values are consistent. As demonstrated by Figure 15a, the efficiency results for the top 10 vector-IMs are closely grouped, with [PGV, CAV] demonstrating the highest predictive efficiency (σ = 0.36). Figure 15b indicates that [PGA, PGD] (c_avg = 0.02) shows the best sufficiency, followed by [D_RMS, ASI] (c_avg = 0.03), while other vector-IMs also revealed good predictive sufficiency (c_avg = 0.05 for [PGD, I_a]). Figure 15c suggests that the predictive proficiency of [CAV, CAV₅] (ζ = 0.12) is significantly superior to that of other vector-IMs, with comparable predictive proficiency observed for the remaining IMs.

As evident from Figure 15, [PGV, Ds_5–75] exhibits good predictive efficiency (σ = 0.37), sufficiency (c_avg = 0.04), and proficiency simultaneously (ζ = 0.21). Therefore, [PGV, Ds_5–75] is identified as the optimal vector-IM for estimating RR of buried CI pipelines subjected to pulse-like ground motions. When comparing the predictive efficiency, sufficiency, and proficiency analysis results using [PGV, Ds_5–75] and PGV as IMs, it is evident that across three values of C_a, the average reductions in σ, c_avg, and ζ are 0.02, 0.09, and 0.03, respectively, underscoring the advantages of using vector-IMs for evaluating RR.

6. Discussion

The regression coefficients for fragility relations of buried CI pipelines using the scalar-IM (PGV) and the vector-IM ([PGV, Ds_5–75]) under varying C_a are summarized in

Table 4. The regression coefficients for the fragility relations of buried CI pipelines under different C_a.

Ca (m/s)	ln(RR) = a + b × ln(PGV)			ln(RR) = a + b × ln(PGV) + c × ln(Ds5–75)
	a	b	RMSE	a	b	c	RMSE
1000	−8.0590	1.7337	0.755	−8.1027	1.6891	0.1884	0.130
2000	−8.4333	1.5625	0.120	−8.4748	1.5201	0.1793	0.036
3000	−8.6550	1.4779	0.055	−8.6951	1.4370	0.1730	0.018

. The common error index, namely the root mean square error (RMSE), is employed to evaluate the overall performance of the fragility relations (presented in Table 4). As a result, the fragility relations using [PGV, Ds_5–75] as IM have relatively low RMSE scores under different C_a, indicating the advantage of vector-IM in reducing the error in RR prediction.

Figure 16 illustrates the predicted RR data versus PGV based on the fragility relations developed, as compared to the empirical data reported by O’Rourke et al. [8]. It clearly shows that the predicted results match reasonably well with the empirical data. The statistical metric, namely the mean absolute error (MAE), is employed to evaluate the agreement between the predicted and empirical RR. The MAE is approximately 0.13 repairs/km when PGV is used as the IM. This value is smaller than the inherent scatter within the empirical dataset (e.g., ranging from 0.16 to 0.51 repairs/km at PGV = 15 cm/s), indicating that the fragility relation appropriately captures the tendency of RR to vary with PGV under pulse-like ground motions. It is noteworthy that when Ds_5–75 varies, there is a discrepancy between the RR predicted by the scalar-IM (PGV) and the vector-IM ([PGV, Ds_5–75]). Specifically, the RR predicted by PGV is 0.28 repairs/km when PGV equals 50 cm/s. Under the same PGV condition, the RR predicted by [PGV, Ds_5–75] are 0.22 and 0.37 repairs/km for Ds_5–75 values of 1 s and 15 s, respectively, corresponding to deviations of 21% and 32%. These findings further highlight the advantage of employing vector-IM in reducing the uncertainty of RR predictions. It should be noted that the empirical data is limited in sample size, which necessitates future collection of well-documented damage cases for further validation and refinement of the proposed models.

This study confirms the advantage of vector-IMs in reducing prediction uncertainty of RR for buried CI pipelines subjected to pulse-like ground motions, yet their practicality should be weighed in seismic risk assessment for actual pipeline networks. Compared to scalar-IMs, vector-IMs are less accessible and involve higher computational complexity, making them difficult to integrate into the PSHA framework. Therefore, in practical applications, the more predictive vector-IMs (e.g., [PGV, Ds_5–75]) are recommended for the seismic risk assessment of critical pipelines with high safety requirements. For preliminary risk analysis of large-scale pipeline networks, easily accessible scalar-IMs (e.g., PGV) remain the pragmatic choice.

The numerical analysis in this study accounts for the variability in both ground motions and joint properties. However, there are still several limitations in this study: (i) the assumption of perfect correlation between a_C and λ_l/d_j does not align with actual conditions; (ii) the findings are primarily applicable to cast iron pipelines with lead-caulked joints subjected to transient ground deformation; and (iii) the inability of the two-dimensional model to accurately account for spatially non-uniform seismic excitation and complex slippage and separation at the soil–pipe interface. Thus, further research is warranted to address these aspects.

7. Conclusions

In this study, a two-dimensional soil–pipe model incorporating the uncertainty in the sealing capacity of lead-caulked joints along the pipeline axis was introduced. A suite of 124 pulse-like ground motions was selected from the NGA-West2 database to conduct nearly 1.116 million nonlinear dynamic analyses for the soil–pipe model, and 19 scalar-IMs and 171 vector-IMs were regarded as potential candidates for identifying the optimal IMs for RR prediction. The RR of CI pipelines was calculated for various scaling factors and apparent wave velocities, resulting in a total of 1116 datasets pertinent to CI pipeline damage. Utilizing RR as the EDP, the predictive efficiency, sufficiency, and proficiency of different IMs were evaluated through regression analysis, ultimately leading to the identification of the optimal scalar- and vector-IMs for estimating RR of buried CI pipelines subjected to pulse-like ground motions. The following conclusions are drawn:

(1)

The distribution patterns of efficiency, sufficiency, and proficiency in predicting RR using various candidate IMs are alike under varying values of C_a. Among the scalar-IMs, PGV exhibits the best predictive efficiency (σ = 0.39) and proficiency (ζ = 0.24), followed by VSI (σ = 0.50, ζ = 0.33). The IMs CAV, CAV₅, and V_RMS demonstrate superior predictive sufficiency, each with a c_avg value of approximately 0.08, and PGV also shows good predictive sufficiency (c_avg = 0.12). However, VSI presents inferior sufficiency compared to the other IMs (c_avg = 0.25). After comprehensively comparing the predictive efficiency, sufficiency, and proficiency of candidate scalar-IMs, PGV is chosen as the optimal scalar-IM for estimating RR of buried CI pipelines subjected to pulse-like ground motions.

(2)

Among the vector-IMs, [PGV, CAV] demonstrates the best efficiency (σ = 0.36). [PGV, PGD] shows the best sufficiency (c_avg = 0.02), followed by [D_RMS, ASI] (c_avg = 0.03). The proficiency of [CAV, CAV₅] is remarkably better than that of other vector-IMs (ζ = 0.12). Considering all three criteria together, [PGV, Ds_5–75] exhibits good predictive efficiency (σ = 0.37), sufficiency (c_avg = 0.04), and proficiency (ζ = 0.21), and is ultimately identified as the optimal vector-IM for estimating RR of buried CI pipelines subjected to pulse-like ground motions. Compared to PGV, the vector-IM [PGV, Ds_5–75] yields improvements across efficiency, sufficiency, and proficiency, with average reductions of approximately 5% in σ, 69% in c_avg, and 12% in ζ. This confirms that adopting vector-IMs offers advantages in estimating the RR of buried CI pipelines with lead-caulked joints.

(3)

The symmetrical multi-criteria framework developed in this study successfully identified optimal IMs through a balanced consideration of efficiency, sufficiency, and proficiency. These findings hold practical implications for pipeline seismic risk prevention and management. The scalar-IM (PGV) can serve as a practical parameter for prioritizing maintenance and retrofit planning in large-scale pipeline networks owing to its data availability and computational simplicity. The vector-IM ([PGV, Ds_5–75]) can be adopted to reduce uncertainty in site-specific probabilistic risk assessments for high-risk critical pipelines. These findings provide a quantitative basis for seismic design guidelines of buried cast iron pipelines.

The obtained results are considered applicable to DN150 cast iron pipelines with lead-caulked joints subjected to pulse-like ground motions. The applicability of these findings to other pipe diameters, pipe materials, or joint types requires further validation. Moreover, the inclusion of other seismic scenarios, including non-pulse-like, long-duration, and short-duration ground motions, as well as permanent ground deformation induced by liquefaction or fault displacement, represents a critical direction for future work. Extending the analysis to three-dimensional modeling would enable a more realistic simulation of seismic input and soil–pipe interaction. Future research should also validate the proposed intensity measures through field case studies and extend the present methodology to complex terrains such as slopes and canyons.