## 1 Introduction  
Corrosion of steel in concrete has been recognized as a major reason for damage and deterioration of reinforced concrete structures worldwide, mainly due to the presence of chlorides [1, 2, 3, 4]. Tidal and splash zones of marine concrete structures are particularly vulnerable to corrosion due to not only the relatively abundant oxygen, water, and chloride but also to wet-dry cycles [5, 6, 7]. Treating corrosion is costly, about 3-4% of each country's gross domestic product (GDP) [8]. In 2013, USD 2.5 trillion, or 3.4% of the global GDP, was estimated to be used to address the global corrosion problem [9]. Cathodic protection (CP) has been recognized as an effective and reliable method for corrosion protection of reinforced concrete structures damaged by chloride penetration [10, 11]. It is primarily categorized into impressed current CP (ICCP) and sacrificial anode one (SACP), depending on the way of delivering electric current to the structure. In ICCP, a rectifier provides electric current from an insoluble anode to a cathode; SACP utilizes the potential difference between an anode and a cathode, i.e., an anode such as aluminum, zinc, and magnesium has a lower potential than a cathode, which results in current flow [12, 13]. One representative advantage of ICCP is that it is easier to apply to materials with high resistivity because the current intensity can be controlled, whereas ICCP can induce hydrogen embrittlement in rebar because of the significantly negative CP potential [14]. On the one hand, SACP can provide easier and cheaper corrosion protection; however, its application to the high-resistance environment is not straightforward since the current intensity is low, which leads to a substantial reduction in the effectiveness of CP and resultant throwing power [15, 16]. This leads to limitations of SACP system application for tidal and splash zones, considering that throwing power is reported to be only a few centimeters, depending on the surrounding environments (e.g., concrete resistivity) [17, 18, 19]. To overcome these critical limitations of SACP, for example, a hybrid CPsystem that combines SACP and ICCP was proposed [20; 21]; however, this method increases the system complexity. If there exists a way to efficiently protect the tidal or splash zone by only the SACP system, it will greatly benefit the corrosion protection market. A conductive mortar has been developed and supported by many researchers for improvements of electrical, mechanical, and other properties (e.g., volume and contact resistivity, wear resistance, and oxidation resistance) and for various purposes (e.g., deicing, self-monitoring material, and extension of fatigue life) [22; 23]. In particular, the carbon fiber conductive mortar was widely considered and experimentally tested for CP systems [23; 24; 25; 26; 27]. For example, [PERSON] and [PERSON] [23] evaluated the volume and contact resistivity of the conductive mortar as a primary step for the anode design of the CP system. [PERSON] and [PERSON] [24] considered the conductive mortar as the primary anode for the ICCP system and verified its effectiveness through experiments in the dry condition. [PERSON], [PERSON], [PERSON] and [PERSON] [25] proposed an anode system in which the primary anode is combined with the conductive mortar anode made of nickel-coated carbon fiber. They tested the ICCP system using this anode system for the concrete specimens with and without chloride contamination under both dry and wet conditions. [PERSON] and [PERSON] [26] took into account a similar ICCP system using conductive mortar combined with the primary anode. They focused on the current distribution by the conductive mortar anode as a function of the initial corrosion state, concrete resistivity, and current density magnitude. [PERSON] and [PERSON] [27] continued to investigate the mechanical, electrical, and electrochemical properties of conductive mortar. In addition, [PERSON] et al.