Development of Mapping Function to Estimate Bond–Slip and Bond Strength of RC Beams Using Genetic Programming

Jeong, Hoseong; Ji, Seongwoo; Kim, Jae Hyun; Choi, Seung-Ho; Heo, Inwook; Kim, Kang Su

doi:10.1186/s40069-022-00536-6

International Journal of Concrete Structures and Materials

Table 3 Summary of data.

From: Development of Mapping Function to Estimate Bond–Slip and Bond Strength of RC Beams Using Genetic Programming

\({\varvec{\tau}} - {\varvec{s}}\) data (Pull-out specimens)
Researchers	S	\(N_{{\text{s}}}\) (EA)	N (EA)	\(f^{\prime}_{{\text{c}}}\)(MPa)	c (mm)	\(d_{{\text{b}}}\) (mm)	\(c/d_{{\text{b}}}\)	\(A_{{{\text{st1}}}} /S_{{{\text{st}}}}\)	s (mm)	\({\varvec{\tau}}\) (MPa)
Baena et al., (2009)	P	2	14	27	92–94	12–16	5.8–7.8	0	0–25	0–13
Campione et al., (2004)	P	4	28	34	36	12	3	0–0.9	0–12.1	0–16
Eligehausen et al., (1982)	P	8	56	29–32	57–96	19–32	3	0–3.6	0–12.1	0–16
Engstrom et al., (1998)	P	3	21	28–29	16	16	1	0–0.4	0–15	0–8
Harajli et al., (1995)	P	2	14	22	60–80	20–25	3–3.2	0.9–1.1	0–18.1	0–13
Kim et al., (2015)	P	2	14	29–33	75	16	4.7	0	0–4.6	0–25
Lee et al., (2012)	P	5	35	26–42	45	13	3.4	0	0–10	0–18
Liu et al., (2020)	P	5	35	38–82	90–94	12–20	4.5–7.8	0	0–12	0–32
Ma et al., (2017)	P	3	21	25	30–66	18–22	1.4–3.7	0	0–1.5	0–8
Melo et al., (2015)	P	1	7	16	94	12	7.8	0	0–10	0–13
Mo and Chan (1996)	P	1	7	27	66–69	13	5.1–5.3	0	0–1.1	0–9
John Robert Prince and Singh (2013)	P	6	42	20–37	38–94	12–25	1.5–7.8	0	0–15.3	0–18
Solyom and Balázs (2020)	P	6	42	35	47–72	6–8	7.8–12	0	0–10	0–15
Song et al., (2015)	P	48	336	8–53	15–67	14–16	1.1–4.2	0–0.3	0–16.1	0–25
Soroushian and Choi (1989)	P	5	35	30–32	48–96	16–32	3	0.8–1.5	0–12.1	0–17
Soroushian et al., (1991)	P	8	56	24–54	75–96	25–32	3	0–1	0–12.7	0–20
Sturm and Visintin (2019)	P	3	21	150	20–75	16	1.3–4.7	0	0–2	0–48
Wu et al., (2021)	P	132	924	5–48	64–69	12–22	2.9–5.8	0	0–14.2	0–22
Yalciner et al., (2012)	P	6	42	23–51	15–45	14	1.1–3.2	0	0–11.9	0–27
Zhou et al., (2015)	P	1	7	18	91	18	5.1	1.3	0–10	0–5
de Almeida Filho et al., (2008)	P	4	28	32–50	45–72	10–16	4.5	0	0–6.3	0–22
Total (or min–max)		255	1,785	5–150	15–96	6–32	1–5.8	0–3.6	0–25	0–48
\({\varvec{\tau}} - {\varvec{s}}\) data (Beam specimens)
Desnerck et al., (2010)	B	5	35	64	38–59	12–40	1.4–3.7	0.6–1.6	0–2	0–28
Hou et al., (2020)	B	3	21	39	30	16	2	0–0.4	0–2.2	0–13
Robert and David (1961)	B	10	70	24–31	38–44	13–25	1.5–3.4	1	0–0.8	0–11
Petean et al., (2013)	B	4	28	50–51	41–42	16–18	2.3–2.6	1.7–2	0–4	0–25
Seis and Beycioğlu (2017)	B	3	21	38	44–46	8–12	3.7–5.8	1	0–0.7	0–8
Yerlici and Ozturan (2000)	BE	4	28	71–93	15	12–16	0.9–1.3	0	0–0.3	0–14
de Almeida Filho et al., (2008)	B	2	14	30	42–45	10–16	2.6–4.5	0.6–1.6	0–4.2	0–12
Total (or min–max)		31	217	24–93	15–59	8–40	0.9–5.8	0–2	0–4.2	0–28
\(\tau_{\max }\) data only (Beam specimens)
Lin and Zhao (2016)	B	6	6	30	40	20	2.0	0.8–1.6	–	8–9
Kemp and Wilhelm (1979)	BE	6	6	29–30	25–76	16	1.6–4.8	0–0.8	–	4–7
Yerlici and Ozturan (2000)	BE	32	32	64–93	15–30	12–26	0.6–1.9	0–0.9	–	9–18
Total (or min–max)		44	44	29–93	15–76	12–26	0.6–4.8	0–1.6	–	4–18

\(A_{{{\text{st1}}}}\): cross-sectional area of transverse reinforcement (one leg, mm²), \(L_{{\text{e}}}\): embedded length (mm), \(N\): number of data points (EA), \(N_{{\text{s}}}\): number of specimens (EA), \(S\): type of specimens (P: Pull-out, B: Beam, BE: Beam end), \(S_{{{\text{st}}}}\): spacing of transverse reinforcement (mm), \(c\): minimum value among bottom cover, side cover, and spacing (mm), \(d_{{\text{b}}}\): diameter of rebar (mm), \(f_{c}^{^{\prime}}\): compressive strength of concrete (MPa), \(s\): slip (mm), \(\tau\): bond stress (MPa).
Specimens that \(\tau_{{{\text{max}}}} \pi d_{{\text{b}}} L_{{\text{e}}} \ge A_{{\text{s}}} f_{{\text{y}}}\) were excluded from data sets.

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