https://doi.org/10.14311/APP.2022.33.0391 Acta Polytechnica CTU Proceedings 33:391–397, 2022 © 2022 The Author(s). Licensed under a CC-BY 4.0 licence Published by the Czech Technical University in Prague ANALYTICAL SIMULATION ON EXPERIMENTAL SEISMIC RESPONSE OF HEADED ANCHORS EMBEDDED IN REINFORCED CONCRETE Seiji Nagataa,∗, Toyofumi Matsuoa, Hironori Morozumib, Keizo Ohtomoa a Central Research Institute of Electric Power Industry, Abiko, Abiko-shi, Chiba-ken, Japan b Kansai Electric Power, Co., Inc., Nakanoshima, Kita-ku, Osaka-shi, Osaka-fu, Japan ∗ corresponding author: n-seiji@criepi.denken.or.jp Abstract. This paper deal with a series of dynamic response analyses, carried out to give numerical correlation of hysteretic behavior of cast-in-place anchorages obtained by the static loading and shake table tests. Specimens for the analyses are reinforced concrete rectangular blocks with embedded headed anchors. Failure modes expected are the steel bolt failure and the concrete cone failure, associated with the respective embedment depth. Initial flexural cracks presumed seismic damage on the concrete block is developed with bending loading. In the analytical model, nonlinear hysteretic behavior of the anchorage is idealized by translational and rotational springs in which properties estimated from the hysteretic loops of the static loading tests. It was shown that the overall force and displacement performance under dynamic loads are well simulated based on the analytical models presented herein. Keywords: Dynamic response analyses, headed anchor bolt, nonlinear hysteretic behavior. 1. Introduction Design and construction of seismically resilient rein- forced concrete (hereinafter, RC) structures will con- tribute toward the sustainable society in an earth- quake prone country like Japan. Structural resiliency for a RC structure supporting industrial equipment can be attributed to its global as well as local behav- ior. For instance, in RC structures of the cooling sys- tem facilities at the thermal or nuclear power plants, the equipment and piping are generally installed on the RC members using anchors [1], [2]. In the mean- time, the current seismic design allows RC structures to sustain partial damage such as cracks of concrete and yielding of reinforcements, unless they exceed the ultimate state [3]. However, if such seismic damage develops around the anchors, it is necessary to eval- uate the seismic safety of the RC structure as well as the effect of the crack on the anchorage strength. From such background, the authors have carried out a series of the experiments related to the strength and the hysteretic behavior of the cast-in-place headed anchor bolts during an earthquake event considering the effects of the flexural cracks [4, 5]. In the present paper, the dynamic response anal- yses are performed to give numerical correlation of the nonlinear hysteretic behavior of the anchorages obtained by the past experiments (the static loading and the shake table tests). In the analyses, the hys- teretic behavior of the anchorage is idealized as trans- lational and rotational springs. The properties of the springs such as stiffness and damping ratio are iden- tified based on the static loading tests results. Then the dynamic response analyses are conducted to sim- ulate the force and displacement hysteresis obtained by the shake table tests. 2. Experimental conditions and results 2.1. Experimental conditions The test specimens and test cases for this analyti- cal study are presented in Figure 1 and Table 1, re- spectively. The specimens are RC rectangular brocks with four headed anchors welded to a baseplate. The material properties of the anchors and reinforcing bars are listed in Table 2. The experimental meth- ods for assessing the strength and the hysteretic be- havior are the static loading tests and shake table tests. The main parameters of these tests are the failure modes of the anchorages and the initial flex- ural cracking around the anchors in the RC blocks. The failure modes expected in the anchorages are the steel bolt yielding and the concrete cone failure (here- inafter, bolt yield type and concrete failure type, re- spectively), associated with the bolt length (250 mm and 100 mm respectively). The initial flexural cracks presumed seismic damage on the concrete block is developed by bending test preliminary conducted as illustrated in Figure 2. The bending moment is ap- plied until the main reinforcing bars yield and the maximum residual crack width exceeds 2.0 mm. Figure 3 presents the experimental condition and the loading pattern in the static loading test. In these tests, a steel support and a weight (20 kN) are at- tached on the RC specimen, and a horizontal load 391 https://doi.org/10.14311/APP.2022.33.0391 https://creativecommons.org/licenses/by/4.0/ https://www.cvut.cz/en S. Nagata, T. Matsuo, H. Morozumi, K. Ohtomo Acta Polytechnica CTU Proceedings � �D��%ROW�\LHOG�W\SH��� �E��&RQFUHWH�IDLOXUH�W\SH� Figure 1. Test specimens (Unit: mm). Specimen Failure mode Bolt length Initial cracks Test method Strength of concrete [mm] ! N/mm2" S-B0 Bolt yield 250 Without Static loading test 39.1 S-C0 Concrete failure 100 Without Static loading test 39.2 S-B1 Bolt yield 250 With Static loading test 39.6 D-B0 Bolt yield 250 Without Shake table test 42.5 D-C0 Concrete failure 100 Without Shake table test 42.6 D-B1 Bolt yield 250 With Shake table test 43.1 Table 1. Test cases. Diameter Young’s modulus Yield strength Tensile strength [mm] ! kN/mm2" ! N/mm2" Anchor bolt 22 208.5 330.2 464.1 Reinforcing bar 19 190.7 401.9 582.9 Table 2. Development of initial flexural cracks. �D��/RDGLQJ�FRQGLWLRQ� � �E��0RPHQW�DQG�FXUYDWXUH�UHODWLRQ� �F��)OH[XUDO�FUDFNV��6�%��� 㻜 㻠㻜㻜 㻜 㻜㻚㻜㻝 㻯㼍㼘㼏㼡㼘㼍㼠㼕㼛㼚 㻿㻙㻮㻝 㻰㻙㻮㻝 㻮 㼑㼚 㼐㼕 㼚㼓 㻌㻹 㼛 㼙 㼑㼚 㼠㻌 㻔㼗 㻺 䞉㼙 㻕 㻯㼡㼞㼢㼍㼠㼡㼞㼑㻌㻔㻝㻛㼙㻕 㼅㼕㼑㼘㼐 㻯㼞㼍㼏㼗 Figure 2. Development of initial flexural cracks. � �D��([SHULPHQWDO�FRQGLWLRQ� �E��/RDGLQJ�SDWWHUQ� Figure 3. Loading conditions in the static loading test. 392 vol. 33/2022 Seismic Response of Headed Anchors (a) Experimental Condition (b) Input wave -800 0 800 0 10 20 30 A cc el er at io n (G al ) Time (s) Maximum: 709.5 Gal Time History of Input Motion 101 102 103 104 10-1 100 101 102 A cc el er at io n (G al ) Frequency (Hz) Natural Frequency Band of Specimen Acceleration Response Spectrum (Damping Ratio: 2%) Figure 4. Loading conditions in the shake table test. Specimen Magnification of input Motions [%] D−A0 20 40 60 80 100 120 140 160 180 200 D−C0 20 40 60 80 100 120 140 160 180 − D−A1 20 40 60 80 100 120 140 160 180 200 Table 3. Magnification of input wave in the shake table tests. � �D��6�%��DQG�'�%�� � �E��6�&��DQG�'�&�� � �F��6�%��DQG�'�%�� ��� � �� ��� � �� /D WH UD O�) RU FH ��N 1 � /DWHUDO�'LVSODFHPHQW��PP� 6�%� '�%������ '�%������ '�%������ ��� � �� ��� � �� /D WH UD O�) RU FH ��N 1 � /DWHUDO�'LVSODFHPHQW��PP� 6�&� '�&������ '�&������ '�&������ ��� � �� ��� � �� /D WH UD O�) RU FH ��N 1 � /DWHUDO�'LVSODFHPHQW��PP� 6�%� '�%������ '�%������ '�%������ Figure 5. Lateral force and lateral displacement relationships based on the static and dynamic tests. is applied to the gravity center of the weight. The lateral displacement is stepwisely increased until the specimen will suffer from significant damage. In the shake table test, the RC specimen is set on the hor- izontal uniaxial shake table, and then the steel sup- ports and weights are attached on the specimen (see Figure 4). The floor response acceleration is used as an input wave, obtained through the seismic response analysis on the RC head race (duct) equipped with seawater pipes [2]. As shown in Table 3, the input magnification is initiated with 20 % and then it is increased by 20 % increment until the shaking table capacity (200 %). 2.2. Experimental results Figure 5 compares the hysteresis curves associated with the lateral force and displacement derived from the static loading as well as the shake table tests. The lateral force in the shaking table test was calculated by multiplying the measured lateral acceleration with the mass of the superstructure. In the case of the bolt yield type without the initial crack (S−B0 and D−B0), the restoring force in the post peak region keeps stable forces compared to the concrete failure types (S−C0 and D−C0). The effect of the initial flexural cracks on the anchorage strength appears in- significant in both bolt yield type specimens (S−B1 and D−B1). These results clearly show that the non- linear hysteretic loops under the shake table tests well cover the ones under the static loading test. 3. Analytical conditions and results 3.1. Analytical conditions In this study, numerical analyses are performed with respect to an equivalent linear analysis and a step-by- step nonlinear analysis. The analytical model for the 393 S. Nagata, T. Matsuo, H. Morozumi, K. Ohtomo Acta Polytechnica CTU Proceedings Figure 6. Analytical idealization for the specimen. Figure 7. Components in lateral displacement. test specimen is shown in Figure 6. The steel weight, the steel support and the anchorage part of the RC specimen are idealized as the lumped mass, the beam element and the spring element (translation and ro- tation), respectively. To evaluate the stiffness and the damping ratio required in the spring elements, the lateral displacement of the static test is decom- posed into the translation and the rotation compo- nents as shown in Figure 7. The equivalent stiffness and the equivalent damping ratio, defined in Figure 8, are identified for the equivalent linear analysis, while the nonlinear slip model (see Figure 9) is used for the nonlinear analysis. Figure 10 shows the equivalent stiffness of the translational and rotational components based on the static loading tests. The equivalent stiffness de- creased as the lateral displacement increase and the equivalent stiffness decreased in accordance with the degree of initial damage. In all the specimens, the equivalent stiffness of the translation component is some ten times higher than that of the rotation com- ponent. This indicates that the lateral displacement during the experiments is mainly caused by the rota- tion component at the anchoring. The nonlinear hys- teresis model is introduced to the rotational spring because of relatively larger deformation appeared in the rotation component. The equivalent damping ratios based on the lat- eral force and displacement loops of the static load- ing tests are presented in Figure 11. These damping ratios of the concrete failure type tend to be slightly lower than that of the bolt yield type. The initial Figure 8. Equivalent stiffness and damping ratio. Figure 9. Nonlinear model for rotational spring [6]. damage may bring slightly lower equivalent damp- ing ratio. In the both equivalent linear and nonlin- ear analysis, the stiffness-proportional damping is ap- plied and the damping ratio is assigned to the natural frequency obtained based on the eigenvalue analysis for each model. 3.2. Analytical results Figure 12 shows the analytical results of the shake table test based on the linear model, comparing with the experimental results. In the specimen D-B0 (the bolt yield type without the initial damage), The numerical analyses well simulate the dynamic be- haviours associated with restoring forces as well as displacement response under considerably large non- linearity states brought by input magnification. On the other hand, a good numerical correlation is observed on the specimen D-C0 (concrete failure type without initial damage) up to the 160 % input. How- ever, this correlation deteriorates under the 180 % in- put where the significant nonlinearity appears due to significant concrete damage. The equivalent analy- sis, which employs equivalent stiffness and damping ratio based on the static loading hysteresis, demon- strates a well numerical correlation on the overall dy- namic hysteresis behaviour on the bolt yielding type (the specimen D-B1) that involves the effect of initial flexural cracks nonlinearity. 394 vol. 33/2022 Seismic Response of Headed Anchors � �D��6�%�� � �E��6�&�� �F��6�%�� � ��� � �� 7UDQVODWLRQ 5RWDWLRQ 6W LII QH VV ��N 1 �P P � /DWHUDO�'LVSODFHPHQW��PP� � ��� � �� 7UDQVODWLRQ 5RWDWLRQ 6W LII QH VV ��N 1 �P P � /DWHUDO�'LVSODFHPHQW��PP� � ��� � �� 7UDQVODWLRQ 5RWDWLRQ 6W LII QH VV ��N 1 �P P � /DWHUDO�'LVSODFHPHQW��PP� Figure 10. Equivalent stiffness based on the static loading tests. � �D��6�%�� � �E��6�&�� � �F��6�%�� � ��� � �� ' DP SL QJ �5 DW LR ��� � /DWHUDO�'LVSODFHPHQW��PP� � ��� � �� ' DP SL QJ �5 DW LR ��� � /DWHUDO�'LVSODFHPHQW��PP� � ��� � �� ' DP SL QJ �5 DW LR ��� � /DWHUDO�'LVSODFHPHQW��PP� Figure 11. Equivalent damping ratios based on the static loading tests. As discussed previously, the nonlinear hysteresis model (Figure 9) is introduced to the rotational spring because of relatively larger deformation ap- peared in the rotation component. Then, the nu- merical analysis for the shake table test using this model is performed, resulting in hysteresis curves as plotted in Figure 13. These analysis and experiment curves demonstrated that use of the nonlinear hys- teretic model improves the degree of numerical corre- lations, especially in strong nonlinearity observed in the specimen D-C0 and D-B1. 4. Conclusions In this paper, the dynamic response analyses on the cast-in-place headed anchor bolts are conducted to simulate the lateral force and displacement perfor- mance under the shake table tests. The main param- eters are the failure modes of the anchorage and the initial flexural cracks in the RC brock. In the ana- lytical model, the hysteretic behavior of the anchor- age is idealized as translational and rotational springs whose mechanical properties are identified based on the static loading tests. Based on these analytical simulations conducted herein, the hysteretic behavior under dynamic loads simulate well to those under the static loads. Insignificant nonlinear response of the anchors allows to employ the equivalent linear stiff- ness and damping ratio in the simulations. On the other hand, significant nonlinearity on the anchorage under relatively excessive seismic loads will require the nonlinear hysteretic model for the anchorage to provide more narrow numerical correlations. Acknowledgements This research is a part of the project research ’Advanced Study on the Verification Method of Seismic Performance of Underground Reinforced Concrete Structures in Nu- clear Power Plants’ which was jointly carried out by Kan- sai Electric Power Co. Inc., Hokkaido Electric Power Co. Inc., Tohoku Electric Power Co. Inc., Tokyo Electric Power Company Holdings, Inc., Chubu Electric Power Co. Inc., Hokuriku Electric Power Co. Inc., Chugoku Electric Power Co. Inc., Shikoku Electric Power Co. Inc., Kyusyu Electric Power Co. Inc., The Japan Atomic Power Com- pany, Electric Power Development Co., Ltd. and Japan Nuclear Fuel Limited. The authors are grateful for the in- terest and advice by the above power companies, as well as to the members of the evaluation committee, which was organized by the Japan Society of Civil Engineers and chaired by Professor K. Maekawa of Yokohama National University. 395 S. Nagata, T. Matsuo, H. Morozumi, K. Ohtomo Acta Polytechnica CTU Proceedings � �D��'�%�� � �E��'�&�� � �F��'�%�� )LJXUH�����$QDO\WLFDO�UHVXOWV�EDVHG�RQ�WKH�OLQHDU�PRGHO� ��� � �� ��� � �� ([S� $QDO�/D WH UD O�) RU FH ��N 1 � /DWHUDO�'LVSODFHPHQW��PP� $PSOLWXGH����� ��� � �� ��� � �� ([S� $QDO�/D WH UD O�) RU FH ��N 1 � /DWHUDO�'LVSODFHPHQW��PP� $PSOLWXGH����� ��� � �� ��� � �� ([S� $QDO�/D WH UD O�) RU FH ��N 1 � /DWHUDO�'LVSODFHPHQW��PP� $PSOLWXGH����� ��� � �� ��� � �� ([S� $QDO�/D WH UD O�) RU FH ��N 1 � /DWHUDO�'LVSODFHPHQW��PP� $PSOLWXGH����� ��� � �� ��� � �� ([S� $QDO�/D WH UD O�) RU FH ��N 1 � /DWHUDO�'LVSODFHPHQW��PP� $PSOLWXGH����� ��� � �� ��� � �� ([S� $QDO�/D WH UD O�) RU FH ��N 1 � /DWHUDO�'LVSODFHPHQW��PP� $PSOLWXGH����� ��� � �� ��� � �� ([S� $QDO�/D WH UD O�) RU FH ��N 1 � /DWHUDO�'LVSODFHPHQW��PP� $PSOLWXGH����� ��� � �� ��� � �� ([S� $QDO�/D WH UD O�) RU FH ��N 1 � /DWHUDO�'LVSODFHPHQW��PP� $PSOLWXGH����� ��� � �� ��� � �� ([S� $QDO�/D WH UD O�) RU FH ��N 1 � /DWHUDO�'LVSODFHPHQW��PP� $PSOLWXGH����� Figure 12. Analytical results based on the linear model. � �D��'�%�� � �E��'�&�� � �F��'�%�� )LJXUH�����$QDO\WLFDO�UHVXOWV�EDVHG�RQ�WKH�QRQOLQHDU�PRGHO�� ��� � �� ��� � �� ([S� $QDO�/D WH UD O�) RU FH ��N 1 � /DWHUDO�'LVSODFHPHQW��PP� $PSOLWXGH����� ��� � �� ��� � �� ([S� $QDO�/D WH UD O�) RU FH ��N 1 � /DWHUDO�'LVSODFHPHQW��PP� $PSOLWXGH����� ��� � �� ��� � �� ([S� $QDO�/D WH UD O�) RU FH ��N 1 � /DWHUDO�'LVSODFHPHQW��PP� $PSOLWXGH����� Figure 13. Analytical results based on the nonlinear model. 396 vol. 33/2022 Seismic Response of Headed Anchors References [1] The Japan Electric Association. The technical code for seismic design of nuclear power plants JEAC4601-2015, 2015. [2] The Nuclear Civil Engineering Committee. Guideline and Recommendation for Seismic Performance Verification of Underground Reinforced Concrete Structures in Nuclear Power Stations, Japan Society of Civil Engineers, 2018. [3] [4] S. Nagata, T. Matsuo, H. Akira, et al. Study on structural performance of anchors embedded at the base of equipment and piping Proc. Japan Society of Civil Engineering - Annual Meeting, 2017. [5] S. Nagata, T. Matsuo, H. Morozumi, et al. Study on structural performance of anchors embedded at the base of equipment and piping considering seismic damage of RC structure, Proc. Japan Society of Civil Engineering - Annual Meeting, 2018. [6] ARK INFORMATION SYSTEMS, INC. TDAP III user’s guide, ver.3.11. https://www.ark-info-sys.co. jp/jp/product/tdap/english/. 397 https://www.ark-info-sys.co.jp/jp/product/tdap/english/