Load‐deformation behavior of locally corroded reinforced concrete retaining wall segments: Experimental results

Local reinforcement corrosion damage reduces the load‐bearing capacity of reinforced concrete structures and, even more severely, their deformation capacity. This problem is of particular concern for cantilever retaining walls, whose loading is dominated by earth pressure and hence, depends on the wall deformations. With a limited deformation capacity at the ultimate limit state due to the locally corroded reinforcement, the earth pressure may not drop to its reduced value typically assumed in design, and simultaneously, the structural resistance may be severely impaired by the cross‐section loss. Load redistributions are impeded since retaining walls are statically determined vertically and typically segmented longitudinally. This increases the risk that affected structures collapse, exhibiting a brittle failure. The situation is aggravated by the fact that the wall deformations prior to failure are too small to be detected by conventional monitoring, as indicated by a previous study.

vertically and typically segmented longitudinally. This increases the risk that affected structures collapse, exhibiting a brittle failure. The situation is aggravated by the fact that the wall deformations prior to failure are too small to be detected by conventional monitoring, as indicated by a previous study. To improve the basis for quantifying the related risks and the magnitude of prefailure deflections, this study investigates the load-deformation behavior of cantilever retaining walls affected by local pitting corrosion, focusing on (i) the influence of the corrosion pit distribution among different reinforcing bars on the load-bearing and deformation capacity and (ii) the interdependence of corrosion, reduced deformation capacity and deformation-dependent loading. To this end, eight large-scale experiments on retaining wall segments were conducted in the Large Universal Shell Element Tester (LUSET), simulating the lower part of a 4.65-m-tall cantilever retaining wall. Five specimens contained initial damage (pitting corrosion simulated by a spherical mill). In the remaining three specimens, artificial corrosion damage was induced during the experiments. For two of the latter specimens, the loading was adapted in real-time control depending on their deformation to simulate the decreasing earth pressure. These are the first large-scale hybrid tests in the field of corrosion research to our knowledge.
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The experiments confirmed that the ultimate load and the corresponding deformation strongly differ depending on the corrosion pit distribution, even among specimens with equal mean cross-section loss. Furthermore, it was found that the deformation increase due to corrosion damage depends on the loading and, hence, on the compaction of the backfill. The observed deformation increase ranged between 0.8 and 1.4 mm per meter height at 40% crosssection loss, with loose soil causing a larger deformation increase. The load transfer between the damaged and undamaged reinforcing bars was found to take place in the first two crack elements above the construction joint. Local bending moments occurred in the reinforcing bars in the vicinity of the corrosion pits due to the shift of the center of gravity of the bar at the pit. Fiber optic strain sensing allowed visualizing the bending moment decrease in the embedded part of the damaged bars as a consequence of a lateral bearing pressure.

K E Y W O R D S
corrosion, deformation capacity, hybrid tests, large-scale experiments, load-deformation behaviour, pit geometry, pitting, retaining walls

| INTRODUCTION
Many cantilever retaining walls built in the 1960s and 1970s along Swiss motorways and railroads are affected by severe local pitting corrosion, as revealed, for example, by a pilot study of the Swiss Federal Roads Office 1 on 36 retaining walls carried out in 2013. According to this study, the corrosion pits are located exclusively at the construction joint between footing and wall and primarily affect the main tensile reinforcement on the rear side, see Figure 1a,b. The corrosion is most likely caused by honeycombs resulting from poor concrete compaction in this region, which impeded the passivation of the reinforcement and enabled local ingress of water and oxygen. The electric connection between the relatively small part of unprotected reinforcement (acting as anode) with the large amount of passivated reinforcement in the remaining part of the retaining wall (acting as cathode) led to the formation of a strong macro element and rapidly progressing pitting corrosion 2 (see Figure 1c), affecting approximately 25% of the main tensile reinforcement with a mean cross-section loss of 37% (total cross-section loss: 9.5%). 1 The wall thickness above the footing (for many objects between 0.5 and 1.2 m) impedes detecting the corroding reinforcement at the wall's rear side with conventional methods applied at the front side, such as potential mapping or georadar measurements. 1 Therefore, even severe corrosion damage is likely to remain undetected until failure.
Retaining walls are mainly loaded by earth pressure, whose magnitude depends on the deformation of the loaded structure. Code provisions in the 1960s and 1970s (in Switzerland, SIA 162 3 ) recommended designing F I G U R E 1 Retaining walls with locally corroded reinforcement: (a) affected wall along motorway (picture from Reference 1); (b) detail of construction joint with corroded reinforcement (picture from Reference 1); (c) example of reinforcing bar with local corrosion damage, extracted during the pilot study. cantilever retaining walls for reduced earth pressure, often assuming merely active earth pressure at the ultimate limit state (ULS). Hence, it was implicitly assumed that the deformation capacity is sufficient for the earth pressure to drop from pressure at rest to active pressure. However, the occurrence of pitting corrosion not only reduces the load-bearing capacity of a structure, but also-and much more pronouncedly-impairs its deformation capacity [3][4][5][6][7] : recent studies 8,9 show that limited cross-section losses of only 17% might reduce deformation capacity by as much as 82% due to strain localization in the vicinity of the corrosion pit. Hence, considerable uncertainty arises whether the residual deformation capacity of corroding retaining walls is sufficient to reach active earth pressure at ULS. Otherwise, affected structures are at risk of failing in a brittle manner since (i) the reduced load-bearing capacity will hardly be sufficient to resist an earth pressure substantially exceeding the value assumed in design (active pressure), and (ii) most retaining walls are segmented by closely spaced dilatation joints. Although sometimes provided with (rather weak) shear dowels, this segmentation impedes the activation of plate bending and a corresponding load redistribution in the longitudinal direction. Moreover, the potentially small deformation increase due to corrosion until failure challenges a successful application of the observation method, 10 that is, a permanent monitoring of a structure's deformation to detect the exceeding of a predefined limit at an early stage.
The assessment of the residual deformation capacity of corroding structures is demanding, as it depends on various aspects on different structural levels. 8 On the level of the reinforcing bar, the microstructural composition of the bar and the pit morphology are most relevant. Quenched and self-tempered (QST) reinforcing bars, making up for most modern reinforcement, reveal a distinct microstructure over their cross-section, and hence, change their mechanical properties continuously for an increasing cross-section loss. [11][12][13][14] The pit morphology strongly influences the behavior of reinforcing bars in the pit region by two distinct mechanisms. Depending on the pit length, a triaxial stress state can influence the apparent mechanical steel characteristics and potentially lead to (i) a higher strength of the bar than nominally expected 15,16 and (ii) an altered tensile stiffness (higher or lower) in the pit vicinity. Furthermore, for unilateral corrosion damage, local bending moments occur in the vicinity of the pit due to the shift of the centroidal bar axis, which can disproportionally impair the load-bearing capacity. [17][18][19][20] On the level of a reinforced concrete cross-section, the distribution of the corrosion damage among the reinforcing bars strongly influences the deformation capacity. When comparing two identical structures with the same mean cross-section loss but different corrosion pit distribution, a recent study 8 concluded that the deformation capacity for the structure with few severely corroded bars is much higher than that of the structure with many slightly corroded bars. This is due to a varying influence of strain localization and implies that knowledge of the mean cross-section loss of a corroded structure is insufficient to draw reliable conclusions on its load-deformation behavior, particularly regarding deformation capacity.
The pit morphology and pit distribution significantly influence the load (re-)distribution in a reinforced concrete cross-section between reinforcing bars with and without cross-section loss, and govern a structure's loaddeformation behavior in case of pure pitting corrosion (where in contrast to uniform or mixed corrosion, no appreciable deterioration of bond due to corrosion is expected). Experimental studies on damaged bare reinforcing bars with different pit geometries and structural elements with systematically varied pit distributions are needed to develop and validate models for the corresponding structural effects. Whereas individual experimental results and first modelling approaches exist for bare reinforcing bars, [15][16][17][18][19][20]46 experimental data reflecting these effects are scarce for structural elements.
The hazard potential of locally corroding retaining walls is substantial due to a large number of potentially affected structures, the difficulty of corrosion detection, and the various critical aspects, particularly the interdependence of corrosion, altered load-deformation behavior and deformation-dependent loading. Since this interdependence and the underlying load-transfer mechanisms have barely been investigated on a structural level, a comprehensive experimental campaign on retaining walls with locally damaged reinforcement was set up at ETH Zurich. It aimed at investigating (i) the general load-deformation behavior of uncorroded retaining walls as a reference (behavior of construction joint, footing and lap splice), (ii) the influence of the corrosion pit distribution on the load-deformation behavior, and (iii) the interaction between the deformation increase due to corrosion damage and the deformation-dependent loading. For this purpose, eight large-scale experiments on retaining wall segments of 2 m in width and height were conducted in the Large Universal Shell Element Tester (LUSET), 21 simulating the lower part of 4.65-m-tall retaining walls. Five specimens with varying initial corrosion damage were loaded until failure. The three remaining specimens were loaded to characteristic load, and corrosion damage was subsequently increased. Two of the latter were tested in a hybrid mode, with the load being adapted depending on the actual wall deflection, to simulate the decrease of the earth pressure loading with increasing deformation due to corrosion. To the authors' knowledge, these are the first large-scale hybrid tests conducted in corrosion research.
This paper presents the design of the specimens (Section 2) and the experimental setup (Section 3), including details on the instrumentation and the hybrid testing. The experimental results are comprehensively discussed in Section 4, focusing on the influence of the corrosion pit distribution on the load-deformation behavior, the loadtransfer mechanism in the pit region, and the occurrence of local bending effects. A comprehensive discussion of the load-deformation behavior of the footing and lap splice region, and the theoretical assessment of the experimental data based on the Corroded Tension Chord Model, 8,22 is envisaged for a future separate publication. The geotechnical aspects of the problem, particularly the relation between earth pressure and a structure's deformation, are part of a separate research project; comprehensive information can be found in the corresponding publication. 23

| DESIGN OF EXISTING RETAINING WALLS
Accurate knowledge of typical design parameters of existing cantilever retaining walls is indispensable for producing representative specimens for experimental purposes. Therefore, prior to the experimental campaign, a parametric study was carried out based on 158 sections of 30 cantilever retaining walls located in different regions of Switzerland and built in different years, mainly between 1968 and 1985 ( Table 1). The data were collected mainly from the original construction plans of retaining walls, including those assessed in the pilot study. 1 Figure 2 shows the relations between the different geometric parameters of the assessed walls, with Figure 2a defining the parameters (h eff = wall height above footing, t inf = wall thickness above footing, t foot = thickness of footing, and w foot = width of footing). All sections of one retaining wall are indicated with a marker of identical shape and color. As seen from Figure 2b, retaining walls with heights (above footing) up to 3 m typically exhibit a slenderness between 1:4 and 1:7, whereas the slenderness of higher walls varies roughly between 1:5 and 1:12. This is presumably owed to a minimum wall thickness due to the detailing rules (e.g., minimum bar spacing), causing lower walls to be less slender. The wide range of slenderness is potentially also caused by the various boundary conditions of the respective projects. According to Figure 2c, the slenderness of footings tends to be smaller and less correlated to the wall height, with most values between 1:3 and 1:10. Figure 2d indicates that the footing thicknesses range from 0.5 to 1 times the wall thickness at its base. This is reasonable, as the wall base moment is carried by one side or shared between two sides of the footing depending on its position (L-shaped or reversed-T-shaped wall).
Most of the analyzed retaining walls are segmented longitudinally at distances of roughly 0.7 to 2 times the wall height. The segments are sometimes connected with shear dowels (e.g., ;20@500) to avoid differential deformations of two neighboring segments in service. However, these dowels are neither designed for nor sufficient to compensate for a reduction in structural resistance of a segment. Hence, cantilever retaining walls are statically determined vertically and cannot redistribute substantial loads in the longitudinal direction by plate action. Figure 3 shows the reinforcement properties of the analyzed retaining walls. The design values of the bending moment due to active earth pressure (assuming a triangular distribution) acting on a retaining wall m Ed and the bending resistance m Rd can be approximated by with γ soil = specific weight of soil, γ q = partial safety factor, z ≈ 0:8 Á t inf = lever arm of internal forces, a s = reinforcement cross-sectional area per unit length, ρ ¼ a s =t inf = reinforcement ratio at wall base, f yd = design value of reinforcing steel yield stress, and K ah = Coulomb's horizontal earth pressure coefficient 24 where φ ¼ internal angle of friction and δ ¼ wall friction angle. Setting m Ed ¼ m Rd , one gets the reinforcement ratio required to ensure structural safety: which is proportional to the geometrical parameter h 3 eff =t 2 inf . Note that the actual yield stress of the reinforcement (depending on the time it was produced) needs to be used in Equation (3). Figure 3a illustrates the correlation of the reinforcement ratios in the assessed walls with Equation (3), along with a black line indicating a degree of compliance doc ¼ 1:0 when assuming typical values of K ah ¼ 0:28 (gravel sand with φ ¼ 30 and δ ¼ 2=3φ), γ soil ¼ 20 kN=m 3 , f yd ¼ 240 MPa, and γ q ¼ 1:0 according to the Swiss Design Code SIA 162 of 1968 25 (in vigor until 1989). The reinforcement ratio of almost all analyzed wall sections lies above the minimum, with tall and slender walls exhibiting higher safety margins than low and compact walls. Figure 3b,c illustrates the reinforcing bar diameters ; and spacings s used depending on the crosssectional area of reinforcement.

| EXPERIMENTAL DESIGN
Eight cantilever retaining wall segments were prepared and subsequently tested in the LUSET 21 at the structures laboratory of ETH Zurich. Representative dimensions and reinforcement layouts were chosen based on the parametric study described in Section 2. The test specimens represented the lower part of a 4.65-m-tall retaining wall segment, which was achieved by applying the corresponding bending moment and shear force, caused by earth pressure on the upper (not physically represented) part of the wall, along the top edge of the specimens with the LUSET. All specimens were identical except for the corrosion damage and the loading, which were the only parameters that varied throughout the experimental campaign.

| Geometry and reinforcement layout
As shown in Figure 4a, the specimens consisted of a 1.7 m tall and 2.0 m wide wall with a thickness of 0.38 m, built on a footing measuring 1.4 Á 2.1 Á 0.4 m 3 . The specimens are rather slender (h eff =t inf ¼ 4:65=0:38 ≈ 12 : 1) compared to the assessed walls, as illustrated in Figure 2b. This slenderness was deliberately chosen to explore the behavior of a typical bending element, minimizing the influence of shear deformations and avoiding the formation of a direct compression strut. The height of the footing was defined with the ratio h foot =t inf ¼ 1 using Figure 2d, and its length was bounded by the yoke dimensions of the testing machine. Figure 4b illustrates the schematic reinforcement layout; the photos in Figure 5a,b show the footing and the wall before casting, and Figure 5c shows the reference specimen prior to testing. The reinforcement ratio of the main tensile reinforcement was chosen such that the degree of compliance according to the design code SIA 162 of 1968 25 with the parameters defined in Section 2 equaled doc ¼ 1:0 ( Figure 3a). This led to a ratio ρ ¼ 0:33%, which was achieved with reinforcing bars of diameter ; ¼ 18 mm and a typical bar spacing of s ¼ 200 mm (see Figure 3b,c). The specimens were cast in two steps, as common for retaining walls, starting with the footing and continuing with the wall. Therefore, the vertical reinforcement was anchored in the footing and spliced just above the construction joint over a length of 50;, representing the typical detailing of existing retaining walls (no seismic design), see Figure 5b.
Additional transverse reinforcement ;14, longitudinal reinforcement ;12, and stirrups ;12 were placed in the footing to account for shrinkage and ensure a proper transfer of the moment and shear force from the construction joint to the supports. In the wall, shrinkage reinforcement ;12@150 was placed longitudinally, and the load introduction zone at the wall head was confined with stirrups ;8. No shear reinforcement was placed in the wall. All reinforcing bars had a minimum concrete cover of 30 mm.

| Experimental program
The experimental campaign consisted of two test series, with five and three specimens, respectively. Series CD ("Corrosion Distribution") aimed at investigating the influence of different corrosion pit distributions on the load-deformation behavior of cantilever retaining walls since theoretical studies indicated a pronounced influence. 8 Series EP ("Earth Pressure") addressed the influence of a decreasing earth pressure loading with increasing wall deformation due to corrosion damage. The experimental program is summarized in Table 2  where the individual cross-section loss per reinforcing bar ζ i and the mean cross-section loss ζ m per specimen are defined as with A s,lost = lost cross-sectional area of the reinforcing bar, A s = original cross-sectional area of the bar, n c = number of damaged (corroded) bars, and n tot = total number of reinforcing bars (damaged and undamaged, all with the same nominal diameter).
In the specimens of Series CD, the cross-sections of a number of reinforcing bars were reduced before casting, and the load was increased during the experiments until failure (without further reduction of the bar T A B L E 2 Experimental program. The cross-section loss per bar and the mean cross-section loss are defined according to Equation (4). cross-sections). After the reference test CD-0 without any damaged reinforcing bars, Specimen CD-3-10 (ζ m ¼ 0:03, ζ i ¼ 0:1) provided insight into the behavior of a segment with few slightly damaged reinforcing bars. In the following three specimens (CD-9-15/30/var), the mean crosssection loss was held constant at ζ m ¼ 0:09, similar to that found in the pilot study, 1 by providing (i) a few severely damaged reinforcing bars (CD-9-30, ζ i ¼ 0:3), (ii) many slightly damaged bars (CD-9-15, ζ i ¼ 0:15), and (iii) many bars with different cross-section losses (CD-9-var).
In the specimens of Series EP, the cross-section of four reinforcing bars was reduced with drilling machines after applying the characteristic load (see Sections 3.5 and 3.7 for more details). In Specimen EP-CL, the load was held constant during drilling and increased to failure after the bars had been completely drilled through. In the Tests EP-LD ("Low Density," loose soil) and EP-HD ("High Density," compacted soil), a different characteristic load was applied and subsequently decreased during drilling, depending on the increasing wall deformation (see Section 3.7). Again, the load was increased to failure after the four bars had been completely drilled through.

| Material properties
The main tensile reinforcement ;18 originated from the same production batch for all specimens. It consisted of B500B cold-worked bars with the product name "BSW-Superring TWR" (producer: Badische Stahlwerke GmbH). For this type of reinforcing bar, the microstructure is homogeneous over the entire cross-section, other than in QST bars that exhibit a distinct microstructure over the cross-section. Conventional tension tests were carried out at a strain rate of 0.01%/s to determine the steel stress-strain characteristics. The results are shown in Figure 6 along with the typical values of the dynamic yield stress f y,dyn , dynamic tensile strength f u,dyn , and strain at peak stress A gt ¼ ε f u,dyn , as well as the static values f y,stat and f u,stat determined by stopping the deformation-controlled loading for 2 min after reaching the yield stress and close to the tensile strength, respectively.
A conventional concrete C25/30 with a maximum aggregate size of 16 mm was used. On the day of each experiment, two cube and three cylinder compression tests and two double punch tests 26 were carried out to determine the concrete compressive (f cc and f c ) and tensile strength f ct . This was done separately for the footing and the wall since the wall was cast approximately 30 days after the footing (see Section 3.1) and thus exhibited different concrete properties. Table 3 summarizses the mean values of the concrete material tests, along with the maximum absolute deviation in parentheses.

| Artificial corrosion damage
The cross-section of the n c ¼ 0…6 reinforcing bars per specimen affected by corrosion, as indicated in Table 2, which were anchored in the footing and passing into the wall, was reduced mechanically just above the construction joint using a spherical mill to simulate corrosion damage. This procedure had already been successfully applied by Cairns et al. 27 It has the advantage that the diameter of the mill and the penetration depth define the cross-section loss and the pit geometry. Preceding pilot tests on bare reinforcing bars and tension chords comparing this degradation method to others, for example, electrochemically induced corrosion damage, showed only minor differences regarding the load-deformation behavior. 28 No accumulation of corrosion products and resulting cracks or spalling of the concrete cover are to be expected in case of honeycombs, since (i) no pressure can build up in the highly porous concrete and (ii) most products are washed away with the entering water. 2 The mill diameter was chosen to be 20 mm, closely matching the average pit length found in the pilot study. 1 The bars were provided with a single pit (in contrast to several pits in series) since several bars extracted from existing walls during the pilot study 1 exhibited this pit configuration. Moreover, a study on the influence of the pit geometry on the bar load-deformation behavior indicated that a single pit is the worst possible configuration regarding the loss of deformation capacity. 18 In Series CD, the cross-section of the n c ¼ 0…6 bars per specimen was reduced before casting, and the region around the pit was scanned using the 3D-scanning system ATOS Core ® by GOM to have a reference measurement of the calculated cross-section loss (see Figure 7a). In Series EP, the cross-section of n c ¼ 4 reinforcing bars per specimen was reduced simultaneously in steps of Δζ i ¼ 0:05 during each experiment. To this end, four industrial drilling machines fitted with an automatic feed and a high-precision laser distance sensing system were fixed to the footing by means of four concrete anchors per machine (see Figure 7b). By combining the measured penetration depth with the radii of the reinforcing bar and the spherical mill, the removed and remaining cross-sectional areas were precisely known throughout the entire experiment.
In order to provide access to the reinforcing bars to be drilled during the experiment, a recess of 100 mm height, 60 mm depth, and 40 mm width was provided around the future corrosion pit during casting by means of a styrofoam formwork inlay (see Figure 4b, Detail A, and Figure 7c,d). Identical recesses were also provided in the Series CD for reinforcing bars containing initial damage to have comparable experimental conditions. While the recesses facilitate access for precisely controlled drilling, they have the apparent disadvantage of a locally missing bond. However, this is no major concern here since the bond strength in the affected region is also reduced in the real retaining walls due to the honeycombs triggering the corrosion damage (see Section 1). Figure 8a shows one of the specimens of Series EP installed in the LUSET; the identical setup, but without drilling machines at the base, was used in Series CD. The specimen footing was placed onto two steel strips positioned on the bottom yokes of the LUSET, which ensured a properly T A B L E 3 Results of concrete material tests for footing and wall of each specimen in (MPa): mean values and maximum absolute deviation (in parentheses).  defined load introduction, and clamped with preloaded M36 bolts (see Figure 4a). At the top edge of the specimen, five load introduction plates were placed onto a mortar layer, connecting the tensile reinforcement at the specimen head to the plates by means of reinforcing bar couplers (BARTEC ® Type X18-24) fixed with M24 bolts (Figure 4b).

| Test setup and instrumentation
This ensured a direct contact of the plates to the specimen and a slip-free moment and shear force introduction. Each of the five load introduction plates was subsequently connected to the corresponding top yoke of thLUSET using preloaded M36 bolts. All reinforcing bars of the main tensile reinforcement were instrumented with a fiber optic strain sensing system (Odisi 6104 from Luna Inc. 29 ), which enabled a quasicontinuous strain sensing along the entire length of the bars using a virtual gauge length of 1.3 mm. [30][31][32] To this end, optical glass fibers were placed into small grooves of 1 Â 1 mm cross-section carved along the inner side of the reinforcing bars (opposite the present or future artificial corrosion pit) and glued with epoxy resin 30-32 (see Figure 8b,c). Note that a transition zone of approximately 10 cm length exists at both ends of each bar where the glass fiber leaves the groove and continues in a protecting tube and, therefore, is not bonded to the bar ( Figure 8b). Hence, the fiber optic measurements do not extend over the full reinforcing bar length. Measurements were carefully post-processed using the consolidating methods and filters described in Section B.1 in the appendix.
A three-dimensional digital image correlation (DIC) system (VIC-3D of Correlated Solutions, 33 FLIR Grasshopper 3 cameras with a resolution of 4096 Â 3000 px) was used to measure the surface deformations of the specimens. To this end, the footing and wall's surface (at the side in tension) were primed white and speckled black. Besides recording the overall deformations, the kinematics of the cracks occurring during the tests were automatically determined from the deformation field using the Automated Crack Detection and Measurement tool ACDM. 30,34,35 Different correlation parameters were used depending on the purpose, resulting in a measurement precision of approximately 20…40 μm for the outof-plane displacement and 10 μm for the crack kinematics (see Section B.2 in appendix).
The applied loads were measured using the load pins installed at the 50 actuators of LUSET (out of 100) used in this configuration, and the resultants were calculated with the actuator's position measurements. Lagrangian optimization was used to reduce possible noise (see Section B.3 in appendix).

| Boundary conditions and loading
As a boundary condition, it was assumed that the simulated retaining wall is built on rock or stiff, compacted ground such that wall deflections resulting from a rotation of the footing can be neglected. Consequently, the bottom yokes of the LUSET were controlled to zero rotation and displacement throughout all experiments. The top yokes applied a combination of normal force, out-ofplane shear force and bending moment at the specimen head. Figure 9a shows the triangular loading of the simulated 4.65-m-tall retaining wall (blue and light gray) and that of the specimen (red and dark gray), along with the F I G U R E 8 Test setup and detail of instrumentation: (a) specimen in the Large Universal Shell Element Tester (LUSET) with installed drilling machines for hybrid test; (b) glass fiber glued in groove, with adjacent transition zone where the fiber continues in protecting tube; (c) location of fiber in the reinforcing bar with respect to drilling direction, with global coordinate system shown for reference. corresponding shear force and moment lines, bending stiffness, and deflection. The loading of the specimens was chosen such that the moment at the construction joint M j and the displacement at the specimen head v exp z ¼ h ð Þ were equal to that of a retaining wall with h eff ¼ 4:65 m subjected to a triangular earth pressure distribution q eff z ð Þ. The bending moment M top and shear force V top to be applied at the specimen head can thus be determined by solving the following two equations for M top and V top (see Figure 9a): The solution of Equation (5) is plotted in red in Figure 9b as a function of the distributed load q (earth pressure) acting at the location of the construction joint. The analytical solution can be found in Appendix A. A simplified, bilinear load path was implemented in the control system of the LUSET, yielding a good approximation (see Figure A1 and black lines in Figure 9b). A quasi-static loading rate of dM j =dt ¼ 5 kNm= min was chosen.
The specimens were first loaded with a normal force of N top ¼ h eff À h À Á t inf bγ conc ¼ À56 kN, simulating the self-weight of the fictitious upper part of the retaining wall (geometry of wall with h eff ¼ 4:65 m, h ¼ 1:7 m, t inf ¼ 0:38 m, b ¼ 2:0 m, and γ conc ¼ 25 kN=m 3 ) but neglecting wall friction. As an exception, Specimen CD-0 was tested without normal force. Subsequently, the shear force at the specimen head was increased continuously at a rate of dV top =dt ¼ 2:95 kN= min (corresponding to dM j =dt ¼ 5 kNm= min ) until a shear force V top ¼ 132 kN was reached. Subsequently, the shear force was increased at dV top =dt ¼ 1:96 kN= min (corresponding to dM j =dt ¼ 3:33 kNm= min ), and an additional bending moment was applied at the specimen head at a rate of dM top =dt ¼ 1:66 kNm= min; the total bending moment rate at the construction joint thus remained constant at dM j =dt ¼ 5 kNm= min .
In Series CD, the load was monotonically increased until failure. The specimens of Series EP were first loaded to the characteristic load following the load path of Figure 9b, and subsequently, four reinforcing bars were damaged by drilling while the load was either kept constant (EP-CL) or reduced as a function of the deformations (EP-LD and EP-HD, see Table 2). For Specimens EP-CL and EP-LD, the characteristic moment at the construction joint M j,k was determined assuming loose soil with K 0 ¼ 1 À sinφ, K ah = horizontal earth pressure coefficient (see Equation (2)), and K ¼ K ah þ K 0 ð Þ =2 = mean earth pressure coefficient, as often used in serviceability limit state (SLS) design. This resulted in a bending moment at the construction joint of M j,k ¼ 288 kNm q ¼ 39:9 kN=m 2 ð Þ . For Specimen EP-HD, the same soil parameters were assumed, but the earth pressure was determined assuming compaction in five layers using a model provided by Perozzi and Puzrin, 23 resulting in M j,k ¼ 394 kNm q ¼ 54:7 kN=m 2 ð Þ . If the V top = 132 kN Applied loads: (a) loading, deflection, bending stiffness, moment, and shear force distribution over height for the simulated retaining wall (blue) and the specimen (red), illustrated for a moment at the joint M j ¼ 460 kNm (q ¼ 128 kN=m); (b) load path for moment and shear force at the top, M top and V top , respectively, resulting from Equation (5). Red curves show the theoretically exact path, black lines represent the simplified path implemented in the control system of the Large Universal Shell Element Tester (LUSET). specimen did not fail after drilling through the reinforcing bars, the load was subsequently increased again, following the load path illustrated in Figure 9b.

| Hybrid tests
Series EP, including the two hybrid tests, aimed at investigating (i) the deflection increase in the SLS due to corrosion and, hence, an expected decrease in stiffness, and (ii) the interaction between corrosion, increasing deflection and decreasing earth pressure, that is, the soilstructure interaction with increasing corrosion damage. Figure 10 shows the control loops for the hybrid tests. The feed of the drilling machines was controlled using the penetration depth measurement resulting from the corresponding distance laser (orange loop in Figure 10). Together with the bar diameter and the mill radius, the current cross-section loss was obtained from the penetration depth by integration, which was compared to the current set point. Subsequently, the controller regulated the corresponding machine feed to meet the set point.
To simulate the decreasing earth pressure with increasing deformation, the load applied during the drilling phase in the Tests EP-LD and EP-HD was controlled in function of the specimen head displacement (blue loop in Figure 10). The displacement was measured using an additional high-precision distance laser, which was installed on a stiff rod connected to the specimen footing (to avoid any errors due to potential unwanted movements of the specimen base in the LUSET). The model describing the earth pressure behaviour was developed within a companion project at the Chair of Geomechanics at ETH Zurich 23 and customized to fit the input-output structure of the hybrid tests. It relates the displacement at z ¼ h ¼ 1:7 m of the simulated wall with h eff ¼ 4:65 m to an earth pressure distribution and the resulting bending moment acting at the construction joint M j , see Figure 10. As outlined in Section 3.6, two different earth pressure distributions were adopted, simulating loose soil (EP-LD) and compacted soil (EP-HD). The base moment M j was converted to an equivalent shear force and bending moment at the specimen head, M top and V top , respectively, which were forwarded to the LUSET control system as new set points.

| General load-deformation behavior
This section elaborates on the general load-deformation behavior of the specimens and, hence, cantilever retaining walls with a similar reinforcement layout, independent of a potential corrosion damage. The particularities in the case of pitting corrosion damage are described in Section 4.2. Figure 11a shows a front view of specimen CD-0 with the crack pattern at the end of the test. The gray shaded area illustrates the area of interest (AOI) evaluated in the DIC post-processing; a dash-dotted line marks the construction joint, and a dashed line indicates the top end of the lap splice (LS) region. Bending cracks occurring in the LS region are shown in yellow and red, those at the upper LS boundary in green, and bending cracks above the LS in blue, whereas all other cracks are plotted in black. The thickness of the crack lines is proportional to the (scaled-up, 36:1) crack opening. Figure 11b,c shows the measured opening of the construction joint (black) and the bending cracks (colored according to Figure 11a) versus the moment at the construction joint M j at different scales of the abscissa. The bending crack opening was extracted from the DIC data using the ACDM techniques described in Section 3.5. The latter was not possible to determine the crack opening of the construction joint since it is located at the border of the AOI. Therefore, it was determined as displacement of the lower part of the AOI with reference to two plates fixed at the side of the footing. This results in a slightly higher noise level compared to the ACDM data. Figure 11b,c shows that the opening of the construction joint is one order of magnitude larger than that of the remaining bending cracks. This is due to the crack-width contribution of (i) the footing, where the reinforcement is anchored with its deformation accumulating towards the crack at the joint, and (ii) the lower LS boundary, which concentrates the deformation of the adjacent 1-2 crack elements in the crack at the LS boundary, as outlined in a recent study 36 : the boundary elements of a LS contribute most to its total deformation, whereas the inner elements behave approximately as conventional crack elements with twice as much reinforcement. This is also reflected by the opening of the cracks at the upper end of the LS (z ¼ 900 mm), which are more than twice as large as the crack openings inside the LS (compare green and red lines in Figure 11c), despite the much lower bending moment at this location. The latter underlines the much stiffer behavior of the LS compared to an element with continuous reinforcement. In addition, the crack spacing inside the LS is significantly smaller than above the LS, confirming the theoretical approach of Haefliger et al. 36 regarding the double reinforcement ratio. Figure 11d shows the deflections of Specimen CD-0 for different load steps. The curves are almost linear for all load steps, with the wall essentially rotating as a rigid body around the construction joint. This behavior is due to a combination of the disproportionally decreasing bending moment in z and the significantly increased stiffness in the LS region. At the upper end of the LS (z ¼ 900 mm), an additional kink occurs in the deflection curve (clearly visible for M j ¼ 500 kNm, where a gray straight line representing the extrapolation of the deformation of the lower part was added as reference). These observations are in accordance with the comparably large crack opening at this location, seen in Figure 11a,c (green lines). Overall, the deformation of a cantilever retaining wall containing a LS right above the construction joint (which is the typical case in practice) can be well approximated by a rigid body rotating around the joint. This observation is independent of a potential corrosion damage, which merely affects the (maximum) rotation angle but does not influence the general shape of the deflection curve. Consequently, the LS placed at the construction joint significantly stiffens the lowest part of the retaining wall and strongly reduces its deformation capacity. Figure 12a shows the load-deformation behavior in terms of the moment at the construction joint M j versus displacement of the specimen head v top in the five experiments of Series CD with increasing load at constant cross-section loss. The behavior of the reference test CD-0 without any cross-section loss is shown in black, and that of Specimen CD-3-10 with a slight mean crosssection loss (ζ m ¼ 0:03) in blue. The tests CD-9-30, CD-9-15, and CD-9-var, with a varying number of corroded bars of different residual cross-sectional areas but equal mean cross-section loss of ζ m ¼ 0:09, are shown in green, orange and purple, respectively. Triangles indicate the maximum moment at the construction joint M j,u and the corresponding displacement of the specimen head v top,u ; the corresponding numerical values are compiled in Table 4. Compared to the reference test CD-0, the displacement at maximum load of Specimen CD-3-10 was reduced by 11% (À4.7 mm), whereas the maximum load itself slightly increased by 2.9% (+15 kNm). The latter effect is presumably due to a triaxial stress state at the corrosion pit, leading to an increase of the exhibited tensile strength for slight cross-section losses; the related effects are currently being investigated by the authors. In the specimens CD-9-30, CD-9-var, and CD-9-15, the displacement at maximum load was reduced by 40.8%, 29.1%, and 23.2% (À12.6, À10.0, and À7.6 mm), respectively, and the maximum load decreased by 13.0%, 7.1%, and 2.1% (À68, À37, and À11 kNm), respectively. Figure 12b summarizes the results by comparing the Tests CD-3-10 and CD-9-15/30/var with the reference test CD-0 in terms of the variation of the deformation capacity (ratio v top,u ζ ð Þ=v top,u ζ ¼ 0 ð Þ, circles) and the moment capacity (ratio M j,u ζ ð Þ=M j,u ζ ¼ 0 ð Þ, squares) with the mean cross-section loss ζ m . The results confirm that (i) the reduction of moment capacity is approximately proportional to the mean cross-section loss, (ii) the deformation capacity is disproportionally reduced, and (iii) neither of the two capacity losses can be explained merely by the mean cross-section loss, as evidenced by the different results obtained in the Tests CD-9-15/30/ var, all with equal mean cross-section loss of ζ m ¼ 0:09. Accordingly, among two corroding structures exhibiting an identical mean cross-section loss, the one containing few corroded reinforcing bars with a severe cross-section loss tends to exhibit lower capacities than the structure containing a larger number of corroding reinforcing bars with a smaller cross-section loss. This effect is due to a more severe strain localization for larger cross-section losses and depends on the individual pit distribution among the reinforcing bars. It was theoretically explained by Haefliger and Kaufmann 8 for tension chords,  Table 2; maximum load and corresponding displacement indicated with a triangle); (b) variation of moment capacity ratios (squares) and deformation capacity ratios (circles) with mean cross-section loss.

| Implications of corrosion on loaddeformation behavior
including the tension stiffening effect, and by Chen et al. 9 for bare reinforcing bars, and is validated for members subject to bending by the experiments presented in this paper. Note, however, that theoretical calculations 8 predict a trend reversal for structures containing an even smaller amount of damaged bars with larger cross-section loss (exemplified in the mentioned study 8 for 20% of bars at ζ i ¼ 0:45 or 10% of bars at ζ i ¼ 0:9). The specimens of the CD series were provided with a varying number of recesses, that is, an unbonded length of 100 mm (three for CD-3-10 and CD-9-30, five for CD-9-var, and six for CD-9-15). Since the deformation capacity is closely related to the bond conditions, a part of the observed deformations of these specimens may have been due to the unbonded length. Hence, the already reduced deformation capacity observed in the experiments even overestimates that of the real retaining walls. On the other hand, the honeycombs cause a substantial reduction of the bond stresses (though not to zero as in the case of a recess), partly counteracting the overestimation. Figure 13a,b shows the load-deformation behavior of the three experiments of Series EP with increasing crosssection loss during the entire experiments and in detail during the drilling phase, respectively; note that the part of the experiments where the four reinforcing bars were drilled is shown in color. Before the cross-section reduction, Specimens EP-CL and EP-HD were subjected to one unloading-reloading cycle in the elastic load range. For these tests, a downwards pointing triangle indicates the maximum load and the corresponding displacement reached upon increasing the load after all four artificially corroded bars had been drilled through, that is, at failure of the remaining uncorroded reinforcing bars.
As described in Section 3.7, after loading the specimens to a specified moment at the construction joint in load control mode, the control system was switched to the hybrid mode for the drilling phase. The load was either kept constant for EP-CL (blue line) or decreased for EP-LD and EP-HD (orange and green lines) in function of the displacement of the specimen head. The black dotted curves indicate the targeted load paths according to the model, 23 which the control system followed very well. A circle marks the beginning of the drilling phase, and a square indicates its end, that is, the point where the bars were completely drilled through.
When switching from load control mode to hybrid mode, the system was set to hold the current actuator positions for a short time (approximately 6 min). A slight T A B L E 4 Peak moment at construction joint M j,u and corresponding displacement of the specimen head v top,u . drop in the load was observed for EP-HD (compare the locations of load peak and the circle in Figure 13b), as frequently observed in structural testing and investigated, for example, by Haefliger et al. 14 This relaxation is caused by the change in the strain rate (in this case, by the machine stop and the subsequent constant position holding) and occurs pronouncedly for reinforcing steel loaded in its inelastic range. For a moment of M j ¼ 400 kNm, the 10 reinforcing bars exhibited a steel stress at the wall base of σ s ≈ 477 MPa and a corresponding total strain of ε s ¼ 0:26% (according to Figure 6), that is, they were just at the beginning of the inelastic load range with a plastic steel strain ε s,pl ¼ ε s À σ s =E s ¼ 0:03%. After the four reinforcing bars had been drilled through, the system was switched back to load control, keeping the last applied load constant. Subsequently, the load was increased until the undamaged bars failed. Upward pointing triangles in Figure 13b indicate the start of the load increase. For the specimens EP-CL and EP-LD, the time between switching to load control and the start of the load increase was approximately 23 and 19 min, respectively. A significant deformation increase was observed during this time in both specimens, which can be attributed to creep of (mainly) the reinforcing bars under constant load: while the stresses in the concrete were relatively low, the remaining six reinforcing bars exhibited steel stresses of σ s ≈ 547 MPa (EP-CL) and σ s ≈ 511 MPa (EP-LD; total strain ε s ¼ 0:44% and ε s ¼ 0:31%, using Figure 6), and hence, a plastic steel strain of ε s,pl ¼ 0:17% and ε s,pl ¼ 0:06%, respectively. In line with the shorter duration under constant load and lower stress, 14 the creep deformation was lower for Specimen EP-LD compared to EP-CL. In Specimen EP-HD, the time between switching the control mode and the subsequent start of the load increase was only 2 min, and accordingly, no significant creep deformation was observed. Figure 13c shows the displacement increase of the specimen head versus the mean cross-section loss; note that the displacement is considered between the start of drilling and the complete cross-section loss of the damaged bars, without the subsequent creep deformation (that is, the displacement measured between the circle and the corresponding square in Figure 13a,b). The shape of the curves reflects the reduction of the cross-section in steps of Δζ i ¼ 0:05. The displacement increase was highest under constant load (EP-CL), whereas it was significantly lower under deformation-dependent, decreasing load (À16% and À46% for EP-LD and EP-HD, respectively). This lower increase is likely due to the global unloading of specimens: although the six reinforcing bars without cross-section loss could compensate for the strength loss of the four drilled bars and, therefore, exhibited higher stresses near the construction joint, the loading of the entire structure decreased, resulting in significantly reduced deformations. In addition to the load decrease, smaller deformations were presumably also caused by the stiffer unloading behavior, as observed in the unloading branches prior to the drilling phase for EP-CL and EP-HD (see Figure 13a). This stiffer behavior is due to partial slip reversal and a corresponding reversal of bond stresses 37,38 and appears to clearly outweigh the loss of stiffness caused by the cross-section loss of the damaged bars, as outlined in the following section. Figure 14 shows the stress distribution obtained from the fiber optic strain sensing data in reinforcing bars of the hybrid tests (a) EP-CL, (b) EP-LD, and (c) EP-HD for various individual cross-section losses ζ i . For each specimen, one undamaged and one damaged pair of reinforcing bars is shown, with a pair consisting of the reinforcing bar crossing the construction joint (L) and its corresponding splicing bar (S; note the different scale of the abscissa for L-and S-bars). The black curve corresponds to the state without any cross-section loss prior to drilling (ζ i ¼ 0), and the orange curve corresponds to a cross-section loss of the damaged bars of ζ i ¼ 0:9 for Specimen EP-CL and ζ i ¼ 0:8 for EP-LD and EP-HD. The gray curves correspond to cross-section losses between these values, shown at intervals of Δζ i ¼ 0:1. The blue vertical lines represent the reinforcing bars; a red area indicates the section penetrated by the mill. A square indicates the recess around the corrosion pit and marks the unbonded length of the damaged reinforcing bar. A solid horizontal line at z ¼ 0 specifies the construction joint, and the dashed horizontal lines visualize the mean crack locations extracted from the ACDM data. The fiber optic measurements are missing for the lowest part of the spliced reinforcing bars (S) since the bars were not instrumented there (see Figure 8b).

| Load-transfer mechanism and load distribution among bars
The measurements of the damaged L-bars in the pit region À50 mm ≤ z ≤ 180 mm reveal a superposition of tensile and bending stresses and cannot directly be compared to other results of the graph. For this reason, the pit region is excluded from the following interpretations and analyed in detail in Section 4.4.
For all three experiments, a stress increase (difference between the orange and the black curve) for the undamaged L-bar and a stress decrease for the damaged L-bar (for z > 180 mm) is visible with increasing cross-section loss ζ i : the cross-section loss was accompanied by a loss of tensile stiffness of the affected L-bars in the pit region, which triggered a load transfer towards the stiffer undamaged bars. This load transfer is facilitated by a difference in bond shear stresses acting along the individual bars over a certain transfer length, whose extent is mainly governed by the in-plane wall stiffness and the bond strength. It approximately corresponded to the first two crack elements in the experiments: The stress increase in the undamaged L-and S-bars started within the second crack element (z ¼ 370, 300, and 240 mm for EP-CL, EP-LD, and EP-HD) and extended in negative z-direction towards the construction joint. At the joint, the stress increase was highest in the L-bar, whereas the S-bar must exhibit zero stress at its end by equilibrium. The damaged L-bars exhibited a stress decrease over the same length (for z > 180 mm, see Section 4.4 for the part below). The corresponding S-bars were unloaded in the upper part of the transfer length and loaded closer to the construction joint. The latter occurred due to the stiffness loss of the neighboring damaged L-bars, which the S-bars partly compensated.
In the footing, at depths À50 mm ≥ z ≥ À 150 mm, the reinforcing bars essentially exhibited a pull-out behavior without a pronounced load transfer between the bars along the short embedment length between the construction joint (z ¼ 0 mm) and the beginning of the bent part at z ¼ À217 mm.
The load transfer mechanism between corroded and uncorroded reinforcing bars has to be superimposed with the load transfer due to the lap splice 36 and with the global loading of the specimens. In the Specimens EP-LD and EP-HD, the load-transfer length was shorter than in Specimen EP-CL due to the pronounced unloading of the former specimens. Accordingly, the stress increase of the undamaged L-bar at the joint in Specimen EP-HD was approximately half of that in EP-CL. All other bars of Specimen EP-HD exhibited a stress decrease, that is, they were unloaded. Considering the generally stiffer unloading behavior commented in Section 4.2, the findings of Figure 14c are in line with the lower displacement increase in Specimen EP-HD illustrated in Figure 13c. Figure 15a shows the variation of the mean stresses of the undamaged L-bars at the construction joint σ s,uc in the specimens of Series CD versus the bending moment at the joint M j . A cross marks the rupture of the glass fibers (not to be confused with failure of the specimens). Figure 15b shows the difference in the mean stresses at the construction joint of the specimens of Series CD compared to Specimen CD-3-10. The latter is used as a reference in this plot since some of the fiber optical strain data of specimen CD-0, which would be the natural choice of reference, contained excessive noise due to technical issues during the test. Again, the fiber failure is marked with a cross, and the failure of a specimen is indicated with three triangles indicating possible failure stress levels (whose actual value is unknown since the glass fibers had ruptured at this point).
Deviations of the steel stresses in the uncorroded bars (Figure 15a) from the reference test, and a persisting stress difference in Figure 15b, indicate a load transfer from the damaged to the undamaged reinforcing bars. Note that assessing this load transfer by directly comparing the stresses in the damaged bars in the vicinity of the construction joint is not possible due to the superimposed bending effects in the pit region mentioned before. As shown in Figure 15b, the mean steel stresses in the specimens CD-9-15 (red line) and CD-3-10 (reference) were virtually identical. This is remarkable since the total steel cross-sectional area of CD-9-15 is 6% lower than that of CD-3-10, and hence, a more pronounced load transfer to the undamaged bars would have been expected. As the load transfer between damaged and undamaged reinforcing bars is related to a difference in tensile stiffness, this observation implies an almost equal stiffness of the damaged bars in Specimens CD-3-10 and CD-9-15 despite the obviously different steel cross-sectional areas. This apparent contradiction can be resolved by considering that the stress trajectories in the vicinity of the corrosion pit are strongly deviated due to the local change in cross-section (corrosion pit), causing triaxial stress states, which affect the local tensile stiffness and yield behavior (considering, e.g., von Mises plasticity). Furthermore, it can be observed from Figure 15b that the steel stress differences of the specimens CD-9-15/30/var vary despite their identical total steel cross-sectional area, with CD-9-30 (green line) containing few bars with high cross-section loss exhibiting a stronger load transfer than CD-9-var (magenta) or CD-9-15 (red), which contain more bars with smaller cross-section losses. These findings confirm the conclusions drawn from Figure 12, that is, the loaddeformation behavior cannot be explained based on the mean cross-section loss alone. The results can be attributed to the superposition of the influence of the mentioned triaxial stress state and the local bending moments in the pit region, combined with the resulting variation of the localization effect explained by Haefliger and Kaufmann. 8 Figure 15c shows the observed stress increase in the undamaged L-bars at the construction joint for the tests of Series EP as a function of the individual cross-section loss ζ i . The increase was calculated as the difference in the mean steel stress of all undamaged L-bars at a given cross-section loss and at the beginning of the drilling phase (without cross-section loss). The curves in Figure 15c are similar to those of Figure 13c and confirm the findings of Figure 14: (i) The stresses in the undamaged reinforcing bars at the joint increased with the cross-section loss due to the load transfer from the less stiff damaged bars; (ii) the global unloading of the Specimens EP-LD and EP-HD resulted in a significantly lower stress increase compared to Specimen EP-CL tested under constant load.

| Bending effects in the reinforcing bars near the corrosion pit
In reinforcing bars loaded in tension and affected by unilateral corrosion, bending moments in the vicinity of the corrosion pits have been encountered in experimental campaigns 17,19,39 (note that throughout this section, the terms bending moment and shear force, as well as deflections, refer to the individual reinforcing bars, rather than the wall). Several models have been developed that adjust the effective reinforcing steel parameters to account for the altered strength of the affected reinforcing bars. [17][18][19] The bending moments are a second-order effect caused by the shift of the center of gravity of the bar near the unilateral pit, causing the reinforcing bar to act essentially as a bending-resistant tie (see Figure 16a, showing the deflection, moment, and shear force distributions for a bar in tension). The embedment of the reinforcing bar in the surrounding concrete restrains its lateral deformation, causing lateral reactions (bearing pressure) and corresponding variations of the bending moment along the bar axis, as in a beam on an elastic foundation, see Figure 16b. The magnitude of the bearing pressure, corresponding to the second derivative of the bending moments, depends on the tensile force, the maximum pit depth, and the stiffness of the surrounding concrete. Figure 17 illustrates the observed behavior of selected damaged L-reinforcing bars of Series EP (same bars as shown in Figure 14). The left graph in Figure 17a,b shows the stress variation, measured at the backside of the bar, in the vicinity of the pit for a varying cross-section loss ζ i with respect to the state prior to drilling (ζ i ¼ 0), that is, In Specimen EP-CL (Figure 17a), the stress variation depends solely on the cross-section loss since the moment at the joint M j ¼ 288 kNm was held constant during drilling, that is, Δσ s ¼ Δσ s z, ζ i ð Þ. The same holds in good approximation for Specimen EP-LD (Figure 17b) considering the minor moment reduction during drilling. The blue curves indicate the stress distribution for ζ i ¼ 0:1, and the orange curves show the stress distribution for ζ i ¼ 0:9 (EP-CL) and ζ i ¼ 0:8 (EP-LD), respectively. The gray curves show the stress variation for intermediate cross-section losses at intervals of Δζ i ¼ 0:1. Two black horizontal lines indicate the construction joint and the end of the recess, marking the unbonded length of the reinforcing bar. The drilling axis and the diameter of the mill are shown as red stripes, and a green area indicates the region with steel stresses above the yield strength f y ¼ 554 MPa. Its edge is curved since the plots show the difference between the yield strength and the stresses prior to drilling (see Figure 14), which varied along the bar axis primarily due to bond, but also slightly in the recess.
Since the glass fiber is glued on the reinforcing bar side opposite to the mill (see Figure 8c), the measured stresses are caused by the normal force N s and the bending moment M s in the reinforcing bar. For steel stresses below the yield strength, that is, Δσ s ≤ f y À σ s ζ i ¼ 0 ð Þ , the stress variation is thus with ΔN s and ΔM s = variation of normal force and bending moment and I x = second moment of inertia of the reinforcing bar cross-section, all at a specific location along the bar axis. As usual in second-order analyses, the bending moment and its variation depend on the normal force, which in this case is influenced by the cross-section loss, as the latter influences the internal load transfer between the bars. The bending moment also depends on the maximum pit depth (hence, the cross-section loss) and the location z due to the bearing pressure. The normal force varies along the length of the bar due to the bond stresses and, therefore, generally also depends on the location z. Note that Equation (8) only approximates the actual steel stresses in the immediate vicinity of the pit: the effects of the triaxial stress state would have to be considered over a length corresponding to 1-2 bar diameters on either side of the pit edges. Figure 17a,b shows that at the pit, a local steel stress reduction-compared to the steel stresses in the adjoining parts of the reinforcing bars-occurred for cross-section losses below ζ i ¼ 0:4…0:6. This is due to the bending F I G U R E 1 6 Second-order effect for reinforcing bars with unilateral corrosion pit: deflection, moment, and shear force distributions (a) for a reinforcing bar in tension and (b) for one of the damaged reinforcing bars in the specimens. The embedment above and below the recess restrains the bar deformation and causes lateral bearing pressure (green).  (12)) and bearing pressure (based on Equation (14)) along one damaged reinforcing bar in (a) Specimen EP-CL (constant load in drilling phase) and (b) Specimen EP-LD (hybrid test with deformation-dependent decreasing load) for varying cross-section losses, referred to the state prior to drilling (drilled section indicated by red stripes); (c,d) lateral deflection of the reinforcing bar in Specimens EP-CL and EP-LD, respectively, for varying crosssection losses. moment caused by the local shift of the centre of gravity and the acting tensile force (see Figure 16a). For larger cross-section losses, the steel stresses approached the yield stress, and the local steel stress reduction vanished, presumably since a local plastic hinge formed. Away from the drilling axis and in the embedded parts close to the recess, the steel stress variation increased with the cross-section loss but decreased with the distance from the recess. The embedded parts of the reinforcing bars remained elastic for all measurements, that is, Rewriting Equation (8), one gets the bending moment in the reinforcing bar and, using the relationship dN s ¼ π;τ b dx, 40 its derivative corresponds to the shear force with τ b = bond shear stress. However, the shear force cannot be directly determined from the measured data (i.e., the steel stresses obtained from fiber optic strain measurements) since the share of steel stress variations caused by (i) bond shear stresses and (ii) bending moment variations due to the shear force is unknown. Nevertheless, a good estimation can be found using the shear force variation which is identical to the shear force since the latter is zero (in good approximation) prior to drilling. Inserting Equation (10) in Equation (11) yields the shear force where Δτ b = variation of bond stresses due to cross-section loss. As Δτ b tends to be much smaller than τ b , this formulation improves the estimation quality of the shear force. Additionally, many bond models assume a zone of reduced (or even absent) bond in the vicinity of cracks or a surface perpendicular to the bar (for example, Eligehausen et al. 41 suggested reduced bond over a distance of 5; ¼ 90 mm from the crack). This further reduces the influence of bond in Equation (12) since the considered region is located at the construction joint, where a crack is present. The middle plots in Figure 17a,b show the shear forces calculated using Equation (12) with Δτ b ¼ 0, with maxima of 2.7 kN near the recess in both specimens. Considering a strong bond stress variation of Δτ b ¼ À5 or À 10MPa, the maximum shear force would merely change by 0.2 and 0.4 kN to 2.9 and 3.1 kN, respectively, confirming the subordinate influence of bond on the results. Differentiating Equation (10) with respect to z yields the bearing pressure acting on the bar and the surrounding concrete which can be reformulated, again using Equations (11) and (12), as Neglecting the second term in the parentheses in Equation (14) is justified since the variation of the bond stresses along the bar axis is almost constant at a specific section under increasing load in the elastic range. [42][43][44] The right plots in Figure 17a,b show the bearing pressure obtained from Equation (14). Since differentiating experimental data leads to a high variability, a low pass filter with a lower cut-off frequency (compared to the post-processing of the other fiber optic measurements) was used to compensate for additional noise, with the drawback of flattening the maxima (see Section B.1 in the appendix). Hence, the absolute values are subjected to higher uncertainty, whereas the overall distribution (location of roots and maxima) remains unaffected. Positive values of the bearing pressure correspond to forces directed towards the concrete surface, negative values to forces directed to the specimen's inside. The values along the recess are artifacts of measurement inaccuracy in the pit region and the calculation procedures and, therefore, are shown as dotted lines. Relevant bearing pressures occurred over a distance of 100…150 mm on either side of the recess, changing their signs twice for lower crosssection losses and three times for larger cross-section losses, in line with the increase in the acting bending moment. Figure 17c,d shows the estimated deflection of the corresponding reinforcing bars in Specimens EP-CL and EP-LD, obtained by integrating the curvatures corresponding to the steel stress variations twice. Since the negative stresses may partly be overestimated due to the superimposed unloading of the damaged bars, the plotted deflections are merely an approximation. Nevertheless, Figure 17 gives a valuable insight into the processes evolving in the pit region and the neighboring concrete sections despite the uncertainties. Figure 18a shows the absolute bearing pressure and (b) the bending moment and the bending stress in the reinforcing bar at the transitions to the recess, that is, at z ¼ 0 mm (solid lines) and z ¼ 100 mm (dashed lines), for an increasing cross-section loss. Despite the uncertainty regarding the absolute values due to the low-pass filter, these sections of the reinforcing bar exhibit an increasing bending moment (and consequently increasing local lateral forces) up to a cross-section loss of ζ i ¼ 0:55 for EP-CL and ζ i ¼ 0:4 for EP-LD, respectively. Subsequently, the bending moment remains constant, indicating that the normal force in the bar (transferred over the pit) decreased at a similar rate as the eccentricity of the center of gravity, that is, approximately half the maximum pit depth, increased.

| CONCLUSIONS AND RECOMMENDATIONS FOR FUTURE RESEARCH
The structural safety of cantilever retaining walls with locally corroded reinforcement is concerning due to considerable uncertainties: Corrosion at the rear of the wall base is difficult to detect with standard techniques due to the common wall dimensions, but the related localized damage strongly reduces the load-bearing and deformation capacity. On the other hand, the earth pressure (a retaining wall's main loading) is typically deformation dependent, and many walls have been designed for loads at the lower limit of the possible range (active pressure) relying on a sufficient deformation capacity. Thus, if the residual deformation capacity is insufficient, the actual load acting on the walls will be higher than assumed in design. The situation is further aggravated by the fact that many aspects related to the quantification of the residual deformation capacity are scarcely investigated, such as, for example, the influence of the corrosion pit distribution among different reinforcing bars and the influence of the local stress state in the vicinity of corrosion pits. This complicates a comparison of deformation capacity and deformation demand, whereas the latter is still under investigation itself. 23 Moreover, the statically determined system of cantilever walls in the vertical direction, along with the closely spaced segmentation in the longitudinal direction, impede substantial load redistributions. In conclusion, the risk for a brittle failure of affected structures-presumably without prior detectable deformations-is high.
In order to improve the basis for the quantification of the related risks and the deformations prior to failure, this study investigated the load-deformation behavior of retaining walls with localized corrosion of the main tensile reinforcement, focusing on (i) the influence of the corrosion pit distribution among different reinforcing bars and (ii) the interdependence of deformationdependent loading, corrosion, and deformation capacity. To this end, eight large-scale experiments on retaining wall segments with varying corrosion pit distribution were conducted in the LUSET, 21 revealing the following results: • Cantilever retaining walls containing a lap splice right above the construction joint deform almost as a rigid body rotating around the joint. This is caused by the significantly higher bending stiffness in the lap splice region, leading to a large crack opening at the construction joint, amounting to several millimeters in the present experimental series. Hence, lap splices placed directly at the construction joint impair the deformation capacity of the walls. • The load-deformation behavior, specifically the maximum load and corresponding deformation, strongly depends on the corrosion pit distribution: The deformation capacity is lower for a structure containing few bars with a large cross-section loss (here, 30% of bars at ζ i ¼ 0:3) than one containing many bars with lower cross-section loss (here, 60% of bars at ζ i ¼ 0:15). This result confirms previous theoretical studies 8 and can be attributed to a varying localization effect. It demonstrates that merely indicating the mean cross-section loss of a structure (here, in both cases equal, ζ m ¼ 0:09) is insufficient to draw reliable conclusions on its loaddeformation behavior. Note, however, that theoretical calculations 8 predict a trend reversal for structures containing an even smaller amount of damaged bars with larger cross-section loss (exemplified in that study 8 for 20% of bars at ζ i ¼ 0:45 or 10% of bars at ζ i ¼ 0:9). • The relative reduction of the deformation capacity observed in the tests is more pronounced than the relative reduction in load-bearing capacity, as predicted by Haefliger and Kaufmann 8 and Chen et al. 9 However, it is to note that a part of the exhibited deformation of the specimens might be attributed to the unbonded length in the recess, and hence, the reduced deformation capacity of the tests might even be overestimated. • Stresses in the undamaged reinforcing bars backcalculated from the measured strains indicate that the local tensile stiffness in the vicinity of the corrosion pit is higher than could be assumed when merely considering the reduction of cross-sectional area. This effect may be attributed to a triaxial stress state caused by the strongly deviated stress trajectories in the pit region. Together with locally acting bending moments in the pit vicinity, the latter effect presumably also influences the yield behavior of damaged bars in the pit region (considering, e.g., von Mises plasticity). • The displacement increase of the specimen head due to an increasing cross-section loss was found to be nonlinear, laying in the range of 0.8-1.4 mm per meter height for a maximum cross-section loss of 40% (40% of bars drilled through, that is, ζ i ¼ 1:0), depending on the actual earth pressure. This corresponds to a total displacement of 3.7-6.5 mm at the head of a 4.65-m-tall retaining wall, considering that the deformation localizes in the construction joint. This magnitude of displacement is potentially too small for a successful application of the observation method, as it is highly challenging to recognize an increasing displacement trend resulting from an increasing crosssection loss in field data, and distinguish it from displacements caused by many other effects (seasonal and daily temperature variations, temporary water pressure, etc.). • The displacement increase of the specimen head due to an increasing cross-section loss was lower in the hybrid test simulating compacted soil than in that simulating loose soil, although the earth pressure is higher in the first case. This was attributed to a more pronounced decrease of the earth pressure in compacted soil with increasing wall deformation 23 : the load increase of the undamaged reinforcing bars due to the internal force redistribution caused by corrosion damage is balanced or even outweighed by the strong decrease of the total applied load. The latter observation was confirmed by the fiber optic strain measurements of the undamaged reinforcing bars. However, further investigations are needed to confirm these findings. • The load transfer between the damaged and the undamaged reinforcing bars for an increasing cross-section loss was found to occur in the region up to the first or second crack above the construction joint (depending on the total external load). • As stated in previous works, 17,19 unilateral local corrosion damage leads to bending moments in the vicinity of the pit. Additional strains attributed to such bending moments present at the pit and in the adjacent embedded part of the reinforcing bars were measured with fiber optic strain sensing. The results allow conclusions on the bearing pressure distribution acting laterally on the bar and the length over which the bending moment decreases to zero (roughly 120-150 mm in this study, corresponding to 6…8 bar diameters).
This study outlines the importance of further research on reinforcing bars affected by pitting corrosion and describing their load-deformation behavior on a sound mechanical basis. The authors are currently investigating the influence of the triaxial stress state due to deviated stress trajectories (axial tensile stiffness and apparent tensile strength) and the influence of local bending moments due to the shift of the center of gravity in the pit region on the tensile resistance. A publication detailing the modelling approach outlined by Haefliger and Kaufmann 22 for locally corroded structural elements in bending based on the Corroded Tension Chord Model 8 is envisaged.

DATA AVAILABILITY STATEMENT
The data that support the findings of this study are available from the corresponding author upon reasonable request.

ORCID
F I G U R E A 1 Deviation between the expected displacement of the specimen head and of a 4.65 m tall retaining wall at z ¼ h (assuming α cr ¼ 1=3 and α y ¼ 1=9). The loading is given in Figure 9a (triangular) and Figure 9b ( With the cracking moment and h ¼ 1:7 m, h eff ¼ 4:65 m, t inf ¼ 0:38 m, b ¼ 2:0 m, and assuming f ct ¼ 3:5 MPa, Equation (A7) yields the red curves plotted in Figure 9b. As mentioned in Section 3.6, the loading path of Figure 9b, red curves, was further simplified (black curves) for the implementation in the control system of the LUSET. Whereas the first condition of Equation (A6) was exactly met, the second condition was approximated. Figure A1 shows the deviation between the expected displacement of the specimen head and the 4.65 m tall retaining wall at z ¼ h (assuming α cr ¼ 1=3 and α y ¼ 1=9). For the elastic range, the expected absolute deviation is <0.2 mm, and for the plastic range, it increases with a peak value at failure of approximately 1.2 mm. Given the uncertainties of the assumptions (bending stiffness, effective cracking moment, etc.), these values are acceptable.
A P P END I X B: DATA POSTPROCESSING AND DATA ACCURACY B.1 | Fiber optic strain data The strain data of the fiber optic measurement recorded with 1.25 Hz (1 measurement every 0.8 s) was first consolidated to 0.104 Hz (1 measurement every 9.6 s) using the median in the time domain. This procedure reliably rejects outlying data. Afterward, the influence of the ribs of the reinforcing bar surface on the local strains was reduced by applying a moving average filter in the space domain. 31 A window size of 16 for a virtual gauge length of 1.3 mm was chosen to approximately meet the double rib spacing of 10.5 mm (16 Á 1:3 mm ¼ 20:8 mm ≈ 21 mm ¼ 2 Á 10:5 mm). A low-pass filter with a cutoff frequency of 0.05/mm (the sampling frequency is 1/1.3 = 0.77/mm) was applied in the space domain to reduce noise further. The chosen frequency corresponds to keeping a periodic signal with a wavelength larger than 1/0.05 = 20 mm, and attenuating signals with smaller wavelengths. For a bar diameter of 18 mm, this cutoff frequency leads to results at low noise without losing relevant information: for slender instrumented elements with negligible shear deformations, like reinforcing bars, strain data at a spatial resolution smaller than the thickness of the instrumented carrier material do not provide useful additional information. However, note that for the evaluations shown in Section 4.4, a lowpass filter with a cutoff frequency of 0.02/mm was applied to prevent a substantial noise increase for the derivatives. The curve's shape remains valid for this cutoff frequency, but the absolute values have to be interpreted with care.

B.2 | Deformation data of DIC
The sampling frequency of the DIC system during the experiments was 0.1 Hz (1 picture every 10 s). For correlating the pictures, a subset size of 31 pixels and a step size of 8 pixels were chosen for the deformation measurements, and a subset size of 15 pixels and a step size of 2 pixels for evaluating the crack kinematics with ACDM. The different correlation parameters enabled high accuracy for measuring the out-ofplane deformations (where it is essential to determine the absolute movement of the top and the bottom part of the specimen with little noise) and simultaneously a high accuracy for detecting the cracks and determining their kinematics (where it is essential to localize connecting strain peaks with a high spatial resolution). A moving average filter was subsequently applied in the time domain (same virtual subset over several pictures) with a window size of 15 for the deformation measurements and 5 for the crack kinematics. Since the specimens slightly rotated as rigid bodies at the beginning of the experiment (due to slip in the clamping), a rigid body motion removal technique based on Sorkine-Hornung and Rabinovich 45 was applied using the data of the front side of the footing.
Prior to each experiment, a zero-displacement test (ZDT) and a zero-strain test (ZST) were carried out following the recommendations by Mata-Falc on et al. 30 and technical guidelines of VDI. 46 Whereas the ZDT gives information on the noise floor depending on the correlation parameters (subset size and step size), the ZST gives information on the noise floor depending on the displacement of the AOI for one specific set of correlation parameters. For the ZDT, the specimen was held in place, and approximately 80 pictures were taken; for the ZST, the specimen was moved stress-free in the YZ-plane, following a virtual square of 100 mm side length, and approximately 700 pictures were taken.
In the ZDT, where the measured mean virtual displacement u k is almost zero for all subsets, the standard deviation s k of the virtual displacement in z-direction estimates the noise floor for the actual in-plane displacement field during the experiment for a given calibration parameter set; the standard deviation in y-direction estimates the noise floor out-of-plane s k ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi P n i¼1 u i,k À u k ð Þ 2 n À 1 s ≈ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi P n i¼1 u 2 with k ¼ k th subset, i ¼ i th picture, n = total number of pictures of ZDT, u i,k = measured displacement (in yor z-direction) in k th subset and i th picture. Figure B1a shows the in-plane and out-of-plane standard deviation for CD-9-30 as a function of the chosen subset size. The blue line represents the median of the in-plane standard deviation, that is, the standard deviation of the virtually measured displacements in the z-direction, evaluated over all subsets of the AOI; the blue line represents the median of the out-of-plane standard deviation (y-direction). Four histograms characterize the standard deviation distributions for two specific subset sizes, and gray lines indicate the maximum and minimum histogram boundaries. The noise floor decreases logarithmically for larger subset sizes due to the stronger averaging effect for bigger subsets, at a trade-off of an increasing information loss. Therefore, as explained above, two different correlation parameter sets were chosen for different purposes (in-plane crack kinematics and out-of-plane displacement measurements). For the evaluation of the ZST, the rigid body motion was removed from the displacement data (leading to zero mean displacement). Hence, the remaining measured virtual displacement in each subarea corresponds to noise. The AOI was divided into 20 Á 20 ¼ 400 subareas; Figure B1b shows the standard deviation of the virtual displacement of CD-9-30 per subarea, evaluated with the in-plane correlation parameters (subset size 15, step size 2). Here, the standard deviation s k was calculated according to Equation (B1), with k ¼ k th subarea (instead of subset) and n = total number of pictures of ZST. A slightly higher noise is visible at the border of the AOI, which can be attributed to a distortion of the camera lenses. Nevertheless, the average noise of 5 μm for the whole AOI is very low.
In Figure B1c, box plots characterize the distribution of the standard deviation s k for the measured virtual displacements among the 400 subareas at specific absolute displacements of the specimen. Again, it is distinguished between measured in-plane and out-of-plane displacement and correlation parameters (z-direction, subset size 15, step size 2, and y-direction, subset size 31, step size 8, respectively). As expected, the noise for the measured out-of-plane displacements is higher than for the in-plane displacements, and its corresponding distribution (characterized by the interquartile range and the neighboring values) is broader. Nevertheless, the result is not influenced by the absolute displacement of the specimen. Hence, the noise floor can be assumed constant for the experimental results and is approximately 11 μm out-of-plane and 4 μm in-plane on average. Table B1 summarizes the analyzed noise values for all experiments. In conclusion, the out-of-plane displacement can be determined with a measurement precision of approximately 2 e s k ¼ 20…40 μm. The crack opening and In-plane Out-of-plane Test name ZDT ZST ZDT ZST slip (in-plane displacement) can be determined with a measurement precision of approximately 2 e s k ¼ 10 μm.

B.3 | Force data
The Lagrangian optimization method was applied to the 50 independently measured force signals during the experiment to account for possible noise and nonlinearities of the load-pins. The six global equilibrium conditions served as equality constraints. The three force and moment resultants were calculated accounting for the displaced yoke positions, that is, using the actuator stroke and the corresponding direction vector calculated by the LUSET control system.