Rhonciscus (Lutjaniformes: Haemulidae) is described from various specimens collected by small-scale fishers from the insular upper slope of western Puerto Rico. The new species was molecularly recovered as sister to the Eastern Pacific R. branickii, to which it bears many morphological similarities. It is distinguished from other Rhonciscus species by the number of scale rows between the dorsal fin and the lateral line (7), larger and thus fewer scales along the lateral line (48–50), large eyes (9.4–10.4 times in SL), longer caudal peduncle (15.2–20% of SL), larger sized penultimate (14.7–19.1% in SL) and last (7.4–9.5% in SL) dorsal fin spines which translates to a less deeply notched dorsal fin, and its opalescent silver with golden specks live coloration. This grunt, only now recognized by ichthyologists, but well known by local fishers that target snappers and groupers between 200 and 500 m in depth, occurs in far deeper waters than any western Atlantic grunt.A fourth species of the genus  The family Haemulidae  is one of the two clades grouped in the order Lutjaniformes Bleeker , a tropiPomadasys Lacepède, 1802  included several loosely related species from tropical and temperate seas. Species in this polyphyletic assemblage exhibit color and morphological convergence which has resulted in several of them being uncritically assigned to Pomadasys (Rhonciscus (sensu lato)Pomadasys  and Rhonciscus . These two genera were considered junior synonyms of Pomadasys until Rhonciscus comprises rather elongate species found in marine and brackish waters, but also in rivers and freshwater streams. It presently includes three species, R. crocro, distributed from southern Florida (USA) to at least Rio de Janeiro (Brazil), in the western Atlantic (WA), and two Eastern Pacific (EP) species: R. branickii  from southern Baja California (Mexico) to Paita (Perú), and R. bayanus  from Mazatlán (Mexico) to Rio Tumbes, Perú. Both R. crocro and R. bayanus can be found in freshwater rivers or streams flowing into the ocean. A fourth, unrecognized Rhonciscus species is described based on 14 specimens captured by fishers off the west coast of Puerto Rico, WA.As for the New World species, cala con boya, used by the deep-water, small-scale artisanal fleet. The specimens were deposited at the ichthyology collections of the Sam Noble Museum of Natural History of the University of Oklahoma  and the Florida Museum of Natural History of the University of Florida . Institutional abbreviations follow Rhonciscus species is included in In May 2017 two specimens were collected by the same fisherman from the insular upper slope (280–360 m) off the west coast of Puerto Rico . Both grunts were caught incidentally on hooks at the end of buoyed vertical line gear, locally known as Rhonciscus plus Haemulon sciurus (outgroup) were used for molecular comparisons and a preliminary phylogenetic reconstruction. GenBank accession numbers are as follows: R. bayanusMF446583; R. branickiiJQ741307, JQ741308, MF956957, HQ676794; R. crocroJQ741309; and H. sciurusEU697541. COI sequences were cleaned and trimmed with Geneious 9.1.8 . The online version of this work is archived and available from the following digital repositories: PeerJ, PubMed Central SCIE and CLOCKSS.”“The electronic version of this article in Portable Document Format (PDF) will represent a published work according to the International Commission on Zoological Nomenclature (ICZN), and hence the new names contained in the electronic version are effectively published under that Code from the electronic edition alone. This published work and the nomenclatural acts it contains have been registered in ZooBank, the online registration system for the ICZN. The ZooBank LSIDs (Life Science Identifiers) can be resolved and the associated information viewed through any standard web browser by appending the LSID to the prefix “All applicable international, national, and/or institutional guidelines for the care and use of animals were strictly followed. All animal sample collection protocols complied with the current laws of Puerto Rico.” Specimens were collected under the authorization of the Puerto Rico Department of Natural and Environmental Resources research permit # 2017-IC-031 granted to M. Schärer-Umpierre.Rhonciscus pauco sp. nov.urn:lsid:zoobank.org:act:6BF57CB4-60DE-4FCE-BF33-B02DF8E7FE05Opalescent GruntRonco opalescente) dorsal-fin rays; anal-fin rays III, 7; pectoral-fin rays 15–16, 17(1); rather elongate body, maximum depth 32–37.4% SL; convex predorsal profile; eye large, its diameter 9.4% to 10.4% SL; snout subequal to eye, its length 7.6% to 11.5% SL; very coarse serrations on angle of preopercular margin; pectoral fin long (28–32.5% SL) extending beyond the tip of pelvic fin, barely reaching anus; head length 30–37.3% SL; longest dorsal-fin spine (fifth) (12.1–19.1% SL); relatively long and much thicker second anal-fin spine (16.4–21.8% SL), long caudal peduncle (15.2–20% of SL), and a large size of the penultimate (14.7–19.1% in SL) and last dorsal-fin (7.4–9.5% in SL) spines which translate to a less deeply notched dorsal fin, eye diameter 0.5 to 0.6 times length of anal fin spine; maxilla reaching anterior border of pupil; seven scale rows between dorsal fin and lateral line; 48 to 50 lateral–line scales.Description. Measurements are presented as percentage of SL in Color in life. Body opalescent silver with golden specks; some of the spines reflect iridescent blue in direct light. Opaque to translucent dorsal, anal, fins and dusky caudal fin . Mr. Font was the first to report and provided specimens to MS, although it is recognized by various fishers as a component of the deep-water catch in western Puerto Rico.Comparisons. Rhonciscus pauco is morphologically very close to its sister EP species R. branickii with which many measurements and counts overlaps. However, it can be distinguished from the three species of the genus, the WA R. crocro, and both EP species, R. bayanus and R. branickii, by the seven scale rows between the dorsal fin and the lateral line; R. branickii has five according to R. bayanus and R. crocro have eight scale rows above the lateral line. It differs clearly from its WA congener by having 48–50 lateral–line scales (vs 66–72 in R. crocro) and 11 short lower gill rakers (vs 7–9 in R. crocro). Our scale counts for R. crocro differ from those presented by R. bayanus. Rhonciscus pauco has much larger eyes (9.4–10.4% of SL) compared to 7.2–8.1% in R. bayanus, 7.1–8.9% in R. branickii, and 6.7–7.8% in R. crocro. R. branickii ranged between 2.9 and 3.8 times in head length while R. pauco  compared to 11.9–16.3% in R. bayanus, 14.0–15.5% in R. branickii and 11.1–14.9% in R. crocro. The larger size of the penultimate (14.7–19.1% in SL) and last dorsal-fin (7.4–9.5% in SL) spines translate to a less deeply notched dorsal fin in R. pauco. Additionally, similarly sized R. pauco can be distinguished from its EP sister species R. branickii by having longer snouts and longer maxilla (3.24–4.09 and 3–3.77 in HL in R. pauco vs 4.41–5.27 and 3.86–4.69 in R. branickii). A detailed comparison of morphometric proportions is included in R. branickii; R. pauco is light silver to golden in color, with opalescence, while its sister species EP is dull dark brown, without bright colors or opalescence, and with a darker marking along the entire opercular margin.Furthermore, R. pauco is captured incidentally with the snappers Etelis oculatus and Pristipomoides macropthalmus but discarded due to its low market value. It is commonly referred to as burro, ronco or viejo, the latter name also used by some fishers to identify the congener grunt, R. crocro, that is not rare in shallow, brackish waters of large volume rivers throughout Puerto Rico  collected in the eastern Pacific off Panama at 430 to 500 m, only six Caribbean grunt species occur at one hundred meters depth or below, with 120 m as the maximum known depth  as well as in 1 m or less in depth in the Rio Grande de Añasco where it flows into the ocean . The two EP Rhonciscus species are also reported in shallow water, especially R. bayanus, known at depths less than 10 m  yet consistent with values of two other trans-isthmian pairs in the genus Anisotremus (2.0–2.4%) (Anisotremus surinamensis (WA) and A. interruptus (EP) to 18% between Genyatremus cavifrons (WA) and G. pacifici (EP). Interspecific distance values near 2% divergence have been reported in both freshwater and marine fishes (R. pauco and R. branickii are larger than the intraspecific genetic distances (R. pauco: 0% and R. branickii: 0.2–0.8%).Finally, the phylogenetic tree , which i.0–2.4%) . The COIe fishes . In any It is common to find variable intra- and interspecific distances and defining a threshold becomes difficult as the mutation rate varies considerably among species. A small distance may indicate very strong differentiation between sister species that have diverged comparatively recently, while COI will not detect “substantial” differentiation. Perhaps this marker in this group evolves quite slowly despite the irrefutable fact that the new species is reproductively isolated, adapted to different environmental conditions, yet resembling its EP sibling species. The magnitude of variability in the mtDNA divergence between all pairs of trans-isthmic grunts is consistent with an asynchronous divergence, as described for other taxa .Additional material examined:Rhonciscus pauco: 240 mm SL, mouth of the Rio Grande de Añasco, Puerto Rico 2021. 250 mm SL, mouth of the Rio Grande de Añasco, Puerto Rico 2021.195 mm SL, Puerto Rico 2021. 198 mm SL, mouth of the Rio Grande de Añasco, Puerto Rico 2021. 205 mm SL, mouth of the Rio Grande de Añasco. Puerto Rico 2021. 237 mm SL, mouth of the Rio Grande de Añasco, Puerto Rico 2021. 205 mm SL, mouth of the Rio Grande de Añasco, Puerto Rico 2021. 199 mm SL, mouth of the Rio Grande de Añasco, Puerto Rico 2021. 210 mm SL, mouth of the Rio Grande de Añasco, Puerto Rico 2021. 215 mm SL, mouth of the Rio Grande de Añasco, Puerto Rico 2021. 206 mm SL, mouth of the Rio Grande de Añasco, Puerto Rico 2021. 199 mm SL, mouth of the Rio Grande de Añasco, Puerto Rico 2021.Rhonciscus bayanus: CIRUV 186.2 mm SL. Gorgona Island, Colombia, 2018. Photograph 185.6 mm SL. Chiapas, Mexico, 2011. Rhonciscus branickii: CICIMAR 159.2 mm SL. Piura, Peru, 2009. CICIMAR 234.4 mm SL. Baja California, Mexico, 2010. CICIMAR 191.2 mm SL. Baja California, Mexico, 2010. CICIMAR 193.7 mm SL. Baja California, Mexico, 2010. CIRUV 170.4 mm SL. Gorgona Island, Colombia, 2018.Rhonciscus crocro: Holotype MNHN 733 185.7 SL, Martinique Island, West Indies, 1830. CICIMAR 220.4 mm SL. Buritaca, Colombia, 2010. INVEMAR 245.5 mm SL. Ciénaga Grande, Colombia, 2010. INVEMAR 176.7 mm SL. Buritaca, Colombia, 2010. Photograph 332.1 mm SL. Rio Grande de Añasco, Puerto Rico, 2018.Rhonciscus are frequently found in estuaries, rivers and freshwater streams makes this finding quite remarkable.Based on morphology, geographic distribution, and molecular analyses, this study describes as a new species the first known western Atlantic deep-sea-dwelling grunt collected from the upper Puerto Rican slope. This finding is an issue of evolutionary and biogeographic interest for the family, which is composed of shallow water species, commonly found on upper shelf waters up to 100 m in depth with a strong preference for shallow environments of less than 40 m. Moreover, the fact that some species of the genus 10.7717/peerj.13502/supp-1Supplemental Information 1Click here for additional data file.10.7717/peerj.13502/supp-2Supplemental Information 2Click here for additional data file.10.7717/peerj.13502/supp-3Supplemental Information 3Click here for additional data file.


Growing primary breast cancers (PT) can initiate local recurrences (LR), regional lymph nodes (pLN) and distant metastases (MET). Components of these progressions are initiation, frequency, growth duration, and survival. These characteristics describe principles which proposed molecular concepts and hypotheses must align with.In a population-based retrospective modeling approach using data from the Munich Cancer Registry key steps and factors associated with metastasis were identified and quantified. Analysis of 66.800 patient datasets over four time periods since 1978, reliable evidence is obtained even in small subgroups. Together with results of clinical trials on prevention and adjuvant treatment (AT) principles for the MET process and AT are derived.The median growth periods for PT/MET/LR/pLN comes to 12.5/8.8/5/3.5 years, respectively. Even if 30% of METs only appear after 10 years, a pre-diagnosis MET initiation principle not a delayed one should be true. The growth times of PTs and METs vary by a factor of 10 or more but their ratio is robust at about 1.4. Principles of AT are 50% PT eradication, the selective and partial eradication of bone and lung METs. This cannot be improved by extending the duration of the previously known ATs.A paradigm of ten principles for the MET process and ATs is derived from real world data and clinical trials indicates that there is no rationale for the long-term application of endocrine ATs, risk of PTs by hormone replacement therapies, or cascading initiation of METs. The principles show limits and opportunities for innovation also through alternative interpretations of well-known studies. The outlined MET process should be generalizable to all solid tumors.The online version contains supplementary material available at 10.1007/s00432-022-04369-4. Biomedical research regularly increases the complexity of cancer. More and more details are emerging on the association with risk factors, the steps involved in carcinogenesis, and processes such as clonal evolution that ultimately result in genetically heterogeneous primary tumors (PTs)  which are basic conditions, bottlenecks through which molecular hypotheses and scientific terms for prognosis and prediction have to go.MCR has data starting from 1978. It has been population-based for the currently underlying 4.9 million population since 1998, and is included in Cancer Incidence of Five Continents  with faster growth of prevalent PTs and a risk of new PTs or the long-term endocrine AT with a preventive and adjuvant effect are examples. Statistical analyses were performed by using SAS V 9.4 and R V 3.1.3.Growing and evolutionarily developing PTs may have already disseminated DNA (ctDNA) and circulating tumor cells (TC) to form local or distant small foci through alterations in the tumor microenvironment  , 13% pN + and a total of about 36 pLNs are to be expected. If PTs reach a diameter of 15 mm after about 14 months, 42 more LNs are infiltrated, in total 25% pLNs. In today's serial sentinel preparation, small PTs have about 12% macro-METs and almost as many isolated TCs and micro-METs  ATs the survival curves of MET-free time do not separate in the first months  However, the principles also illustrate the limits of ATs and the necessary further development of prognostic and predictive factors. In particular, the gradual progress in median post-MET survival of about 11 months and the increasingly expensive treatment costs over the last 3 decades is an ongoing challenge. Below is the link to the electronic supplementary material.


A bridge bearing anchor transmits various loads of a superstructure to a substructure. Most anchors are generally designed without consideration of characteristics such as concrete pedestal, grout bedding, and anchor socket. This study investigated the shear behavior of anchors in accordance with the edge distance, embedment depth, compressive strength of concrete, and height of the concrete pedestal in order to simulate the practical characteristics of the bridge bearing anchors. The actual shear capacity of the anchor differs from the shear strengths calculated by the ACI 318 and EN 1992-4; especially, the importance of the embedment depth is underestimated in these codes. An increase in the height of the concrete pedestal has a negative effect on the shear capacity because of the stress concentration. The grout is fractured prior to the occurrence of local damages in concrete, resulting in a secondary moment. As a result, the effect of the level arm is observed. An equation, which can predict the relative cracking degree of concrete, is proposed by analyzing the displacement of grout and concrete. High strain occurs in the stirrups close to the anchor, and the behavior of the strain is more influenced by the embedment depth than the edge distance. The comparison of obtained and analytically evaluated failure loads by calculations according to EN 1992-4, Schmid model and Sharma model was conducted to consider the effect of supplementary reinforcement. Finally, the design equation of concrete breakout strength is modified to predict the more precise shear resistance of a bridge bearing anchor. Based on the databases developed by previous studies, anchors were introduced in ACI 349 (Appendix B)4. However, the ACI 349 presents an equation that directly correlates the failure behavior of an anchor system with its elastic and plastic behavior. This results in the overestimation of the fracture behavior of the anchor system rather than the actual behavior. Fuchs et al. proposed a concrete capacity design (CCD) method considering fracture properties of concrete5. Theoretical formula depending on the linear elastic fracture mechanics was reported based on the experimental results. The CCD method provides a theoretical background for the current ACI 318 and EN 1992-4, which contains concrete anchor-related design standards.General anchors under tensile and shear loads, which are eventually reflected in the design code, have been extensively studied7. Besides various studies have been conducted on post-installed anchors that used for reconstruction and rehabilitation, as well as on cast-in-place anchors installed before the concrete is hardened9. The shear behavior of anchor groups having different configurations has also been thoroughly studied by considering various experimental studies14. Recently, many studies on anchors using fiber-reinforced polymer (FRP) reinforcing bars have been performed with the development of FRP technology15. In addition, various studies are also being performed such as the behavior of steel fiber-reinforced concrete (SFRC) anchor systems for improving the tensile strength of concrete and predicting the strength of anchors through machine running18. The shear and tensile behavior of single and anchor groups in SFRC are evaluated by giving appropriate design recommendations19.The behavior of high-strength anchors with large diameters has been extensively studied to further secure stability for their application in mainly nuclear power plants20. The bridge bearing anchor exhibits characteristics such as a concrete pedestal installed on the substructure, grout bedding on the concrete pedestal, and anchor socket embedded in the concrete, as shown in Fig. 121. Grout bedding levels any slope of the surface of abutment. It also protects the section of fixing bolts between the concrete and underside of the base plate22. The concrete pedestal is a small part compared to the abutment; however, it plays a major role as a structural member, which safely transmits the loads through the bearing capacity of the concrete. Although many studies about the concrete pedestal have been conducted, localized failures in bridge pedestal are yet to be clearly addressed23. In bridge bearing anchors, cast-in round steel sockets without spiral are mainly used. An anchor socket has the features of an easy-to-replace component after the anchor bolts have been damaged. Most of the previous studies have focused on anchors, which is directly embedded in concrete without anchor sockets; however, the shear behavior of anchors using anchor sockets has not yet been evaluated.A bridge bearing anchor is an important system to transfer various loads, such as vehicle and wind loads, from a superstructure to a substructure. The bearing must be completely connected so that the tensile stress, shear stress, and bending stress can be transferred to the concrete of the substructure through the bridge bearing anchor system24. Recently, many bridge bearing anchors were actually damaged by the Pohang earthquake in South Korea, which has lower peak ground acceleration (PGA) than design PGA of the bridges25. In many previous incidents, a bridge superstructure has collapsed due to earthquakes, such as the: San Fernado earthquake (1971), the Loma Prieta earthquake (1989), the Northridge Earthquake (1994), and the Kobe earthquake (1995)27. Because of these events, the philosophy of the seismic design of a bridge has changed from the only focus of strength to consideration of ductility, as well as importance of the bearing have begun to be highlighted29. Therefore, seismic isolation systems, such as isolation bearings and dampers, have been introduced resulting in improvement of resistance to seismic force; however, there is no reassessment of the design of bearing anchors.Although bridge bearing anchors exhibit very different characteristics from general cast-in-place anchors, a bridge bearing anchor is designed based on the design code of a general anchor without considering any of the abovementioned characteristics. Thus many structural stability problems are encountered in bridge bearing anchors such as breakout failure of concrete pedestal, damage to grout bedding, and failure of anchor bolts, which are shown in Fig. 2Accordingly, this study aims to investigate the behavior of bridge bearing anchors under shear loading. The bridge bearing anchors considering the described features were tested under a quasi-static load. Following are the specific objectives of this study: (1) compare the experimental and predicted strength of the current code; (2) evaluate the effects of edge distance, embedment depth, compressive strength of concrete, and bearing height on shear capacity; (3) analyze the effects of grout bedding and stirrup reinforcement; and (4) modify the strength equation of the bridge bearing anchor.30. For better stability, it is recommended that grout bedding height should not exceed 50 mm beyond the top of the concrete pedestal; thus, the height of the grout bedding was set to 50 mm31.Height of concrete pedestal and grout bedding: The height of the concrete pedestal plays an important role in determining the load capacity of concrete pedestals. In this study, 70 and 150 mm heights were set as variables for the concrete pedestal, which are generally the pedestal heights depending on the space under the bridge superstructureEdge distance: The minimum edge distance for a cast-in anchor without torsion is stipulated to satisfy the specified cover requirement for reinforcement in the ACI 318. The edge distance of the anchor is an important factor in supporting the bridge bearing system, which resists the horizontal load. To induce concrete breakout failure, the edge distance was set to 6d, 5d, 4.5d, 3.2d, and 2.7d, where d is the diameter of the anchor socket.Embedment depth of anchor socket: It is recommended to ensure that the anchor socket reaches at least the upper surface of the reinforcement in the substructure. However, in many cases, the embedment depth is too short to avoid interference with the dense reinforcement. The embedment variables were established to determine its effect on the shear capacity and to confirm the bearing stress distribution along the anchor socket, which is indicated by the power term in the code. Here, embedment depth variables were set from the depth reaching the upper surface of the reinforcement in the substructure to the surface of the abutment.w/b of 0.16.Compressive strength of concrete pedestal and grout bedding: the substructure of abutment and the concrete pedestal are generally poured together with the same mixture. In bridge abutment, a compressive strength of 30 MPa is mostly used, followed by high-strength concrete of approximately 60 MPa strength. The mixture properties are listed in Table In this test program, a total of twenty-one specimens of bridge bearing anchors with seventeen variables were fabricated and tested under monotonic shear load. Four duplicated variables were set for validating the main variable in the concrete breakout capacity. The designation of the specimens reflects the edge distance, embedment depth of the anchor socket, height of the concrete pedestal, and compressive strength of concrete by the mixture. The details of each test variable are given below and listed in Table –6 mm/mm, respectively.In a general bridge bearing anchor, reinforcement should be embedded in both concrete pedestal and substructure to obtain an additional confinement effect, which secures the bearing capacity of concrete and carries the shear capacity of the anchor steel. In this study, No. 5 bars with a nominal yield strength of Grade 60 steel were used with a horizontal spacing of 100 mm and vertical spacing of 120 mm. The reinforcement was bent 90° from top of the concrete pedestal and embedded in the substructure to satisfy the required development length. According to the tensile test of the bar, the yield strength and strain were 446.13 MPa and 2110 × 1032. For anchor sockets, the nominal yield strength of Grade 55 steel with a diameter (d) of 70 mm was used, which was designed to be engaged with anchor bolts with a screw line of 30 mm diameter and 50 mm length. All specimens had the same geometry, cross-sectional dimensions of 450 mm × 500 mm in the grout bedding section, 780 mm × 1080 mm in the concrete pedestal section, and 1400 mm × 1300 mm in the substructure section, as shown in Fig. In addition, a hex structural anchor bolt with a diameter of 30 mm was used, in accordance with ASTM A490M Grade 10.9  deformed beyond the yield strength and the ductility of the anchor system increased, which agree with the findings of SegleFor all specimens with a concrete pedestal height of 150 mm and embedment depth of 150 mm, the shear capacities were measured to be smaller than the predicted strengths calculated using ACI 318 and close to the predicted strengths using EN 1992-4, as shown in Table 23. This result is also attributed to the load not being well-transferred to the substructure but concentrated on the pedestal, as reported by the Korea Expressway Corporation43. Therefore, to minimize the stress concentration in the pedestal and to transfer the load well to the substructure, the edge distance needs to be increased with the increase of the height for proper bridge bearing anchor systems30.For HN-4.5d-15 and HN-6d-15 specimens in Fig. 44. The load displacement curves of the anchor for the concrete compressive strength were evaluated as shown in Fig. 45. There were only few cracks in the concrete pedestal of LH-4.5d-15 specimen , otherwise ψed,V = 1.Thus, the grout effect of the bridge bearing anchor in shear can be obtained as by subtracting the level arm effect created by grout failure from shear strength of anchor embedded in the grout, as follows:48. As the edge distance increased, the grout effect in shear decreased significantly compared to the small decrease shown with embedment depth increase. This is because the grout having a constant edge distance was destroyed first, forming a level arm ahead of concrete failure. The calculation results were similar to the experimental results. While the LN-5d-15 specimen showed a lower maximum shear load than the strength calculated by equation in ACI 318, the specimens with an edge distance less than 5d exhibited the opposite results because these specimens have a positive grout in shear at 50 mm height of grout, as shown in Table Figure 51. Mohamed et al. considered grout properties on shear strength in column base connections and reported that the formation of grout struts plays a major role in the ultimate strength of the connection even beyond the elastic range zone52. A grout bedding is designed to have a shorter edge distance than that of concrete in bridge bearing anchor. The current design code does not reflect the effects of grout; however, it should be considered to limit the height of grout bedding to minimize this negative effect in terms of overall stability in shear.Furthermore, specimens with a relatively short edge distance of less than 4.5d showed progress on the same inclined failure surface on the grout and concrete pedestal Figs. , A.15. T53. However, it is not easy to identify internal cracks that do not extend to the free surface under certain loading, because the concrete around the anchor is located under the grout bedding. These small internal cracks in the concrete may not yet have a significant effect on structural performance; however, they might be vulnerable to chemical penetration, such as de-icing materials coming down from the bridge girder by affecting the durability of concrete54. ACI 224R-01 recommends a maximum allowable crack width of 0.18 mm for concrete exposed to de-icing chemicals55. Meanwhile, non-destructive testing (NDT) of concrete cracks is normally used for the maintenance of these concrete structures, and numerous methods are changing with the development of detection devices56. However, Titman emphasized the need for care and experience despite the advantages of the NDT methods, and indicated that inaccurate interpretation can be made in the absence of a specialized technique57.Inspection and maintenance of bridge bearing anchor are generally performed on visible destructions, such as failure of the anchor bolt, concrete pedestal, and large cracks both in grout bedding and concrete pedestal2 = 0.97 and 0.91, respectively. Therefore, it can be represented as Fig. As previously described, cracks occur in the grout first and then stress redistribution occurs in the anchor, resulting in cracks in the concrete. A simple initial inspection is possible if the crack width of the concrete is relatively predictable through the grout crack. In other words, the degree of cracking of the concrete underneath can be inferred from the degree of cracking of the grout. In this study, the concrete was completely fixed by applying hydraulic pressure and no movement of the substructure occurred, as measured by LVDT. The displacements of the left and right points 100 mm away from the predicted failure line of the front center part of both the concrete pedestal and grout bedding were measured using LVDTs. As an example, the load displacement curve of the LN-3.2d-15 specimen for the grout and concrete pedestal is shown in Fig. 58. A bridge bearing anchor adopts the method of stirrup reinforcement, which extends to the substructure reinforcement. The ACI 318 simply increases the strength through a breakout cracking factor ψc,V for an anchor with reinforcement based on the breakout strength, rather than considering the resistance by the reinforcement38. Whereas, EN 1992-4 considers the effect of supplementary reinforcement in the form of stirrups and edge reinforcement on shear performance by presenting equation3. Eligehausen et al. reported that a narrow stirrup spacing with large edge distance increases the restraint effect and evaluated the resistance strength of the stirrup reinforcement by applying the concept of the strut-tie model44. Sharma et al. developed a model for single and multiple row anchorage with supplementary reinforcement by improving the formula proposed by Schmid62.Few studies have been conducted on anchors reinforced by a straight reinforcement commonly used in construction, while there are some experimental studies on the hairpinThe details of the stirrup reinforcement and strain gauge locations are shown in Fig. Figure 50. In the bridge bearing anchor, the upper part of the anchor bolt in the load plate resists the shear load first, and then the load is transmitted to the concrete through the anchor socket combined with the anchor bolt. Because the diameter of the socket is relatively larger than that of the anchor bolt, ductile behavior of the anchor socket cannot be expected in the shear load. Therefore, brittle fracture occurs due to stress concentration at the contact point between the socket top and the bolt, which is not directly embedded in the concrete. It can be confirmed that the bolts were broken and bent at the contact point, as shown in Fig. 63.Anchor sockets are used for the convenience of construction in bridge bearing anchors. In the current design codes, diameter of anchor socket is simply considered as diameter of anchor. However, the behavior of anchor socket is quite different from general anchors, which fail as a result of anchor shaft fracture without any bending64. Therefore, the analysis of the design formula for the breakout strength was confirmed based on the results.A bridge bearing anchor is generally composed of anchor groups, whose number is determined according to the bearing type, and mostly comprises four anchors. The anchor should be designed based on the steel strength of the anchor, breakout strength, and pryout strength. Because anchor bolts are determined according to the bearing type, both the general diameter and strength have already been generalized. The pryout strength of a general anchor embedded up to the substructure reinforcement is generally higher than the breakout strength in shearψh,V and projected concrete failure area AVc among the variables failed by breakout failure. The concrete breakout strength was shown to be almost proportional to the square root of the compressive strength, as previously described. Therefore, the compressive strength was not considered as a variable in the regression analysis. A regression analysis with two independent variables, which are edge distance and embedment depth, was performed. The breakout strength of the bridge bearing anchor can be expressed as follows:Multiple nonlinear regression analysis was performed on variables of low concrete pedestal to avoid considering the effects on the breakout thickness factor 65. The power of 66. As the edge distance increases, the shear capacity may decrease because of the effect of the level arm. A comparison with the load predicted by Eq. (The derived design equation showed that the power of d by Eq.  and the For simplicity of the design equation, Eq.  can be m68. The coefficient of 5% fractile, F5%, was calculated as 0.884 using the mean, COV, and number of specimens. Consequently, the nominal concrete breakout strength of the bridge bearing anchor in shear can be obtained as follows18:The ACI 318 for the strengths of anchors adopts the 5% fractile concept for the safety of the structure. The concept of 5% fractile indicates a 90% confidence that the actual strength exceeds the nominal strength with 95% probabilityThe breakout strength Three types of failure modes were observed according to the edge distance, embedment depth, and compressive strength. If the breakout strength was much greater than the steel strength of the anchor, the bolt showed brittle failure under load higher than the predicted strength. In case of a short embedment depth, such as the LN-4.5d-7 specimen, failure load occurred near the pryout strength; however, no large spalling was observed on the rear part of the anchor due to the bearing effect of the reinforcement.The shear capacities of the anchors were different from the strengths obtained by design equation in the ACI 318 and EN 1992-4; in particular, the embedment depth had a greater influence on shear resistance than that considered in the current codes due to the existence of both surface and substructure reinforcements. As the height of the concrete pedestal increased, the stress distribution from the bearing to the substructure was not well-transmitted, especially with shallow embedment depth specimens.The grout bedding on the concrete pedestal was locally damaged before serious damage was caused to the concrete, forming a level arm, which induced a decrease in shear capacity. The effect of grout on shear resistance increased as the grout height decreased, and was influenced by the edge distance rather than the embedment depth. Through the analysis of displacement behavior of grout bedding and concrete pedestal, an equation of curve was proposed to predict the relative cracking degree of the concrete under the grout.The strain of the surface stirrup reinforcement was measured, and a high strain occurred in the rebar close to the anchor. The behavior of the strain was more influenced by the embedment depth than the edge distance; thus, increasing the embedment depth up to the substructure reinforcement was found to be effective in improving the resistance of the stirrups against shear load.The comparison of experimentally obtained and analytically evaluated failure loads by calculations according to EN 1992-4, Schmid model and Sharma model was conducted to consider the effect of supplementary reinforcement. The failure loads of the bridge bearing anchor were higher than those calculated by the EN 1992-4 and Schmid model except for specimens with embedment depth of 70. The failure loads calculated by the Sharma model were lower than the experimental failure load according to a decrease in edge distance and increase in embedment depth.Multiple nonlinear regression analysis was performed for anchors with low concrete pedestals where breakout failure occurred, and a design equation was derived to enable a more precise prediction of the bridge bearing. The power of compressive strength showed a tendency similar to that of the code, and the powers of the embedment depth and edge distance were modified. The 5% fractile concept was also introduced into the equation to ensure safety of the structure.This research investigated the shear capacities of cast-in-place single anchors simulating the characteristics of bridge bearing anchor under quasi-static loads. Twenty-one anchor specimens with different edge distance, embedment depth, and compressive strength of the concrete were fabricated and tested. Based on the results and analysis detailed above, the following conclusions were drawn:Supplementary Information.


Based on engineering practice and practical needs, this paper takes ordinary concrete specimens as the research object, and adopts a high-temperature true triaxial loading test system to carry out high-temperature uniaxial and true triaxial static compression tests of concrete under high-temperature conditions. By comparing with normal temperature conditions, this paper analyzes the influence of the coupling effect of high-temperature and biaxial unequal lateral pressure on the static mechanical properties of concrete. By analyzing the experimental data, we reached a series of conclusions and carried out theoretical research on this basis. High temperatures can significantly affect the uniaxial static pressure strength characteristics, deformation characteristics, and failure mode of concrete. When the temperature exceeds 400 °C, the compressive strength decreases significantly, the peak strain increases sharply, and the plasticity of concrete is further enhanced. The coupling effect of high-temperature deterioration and lateral pressure strengthening makes the true triaxial mechanical properties of concrete change significantly; 0.6:0.2 and 400 °C are the turning points of side pressure ratio and temperature that affect the change law of the true triaxial mechanical properties of concrete, respectively. Based on the study of the high-temperature deterioration factor and lateral pressure strengthening factor, this paper further puts forward a concrete strength formula under the coupling action of high temperature and biaxial unequal lateral pressure. It was verified that the formula has a high accuracy. As the most common building material, concrete is widely used in both industrial and civil buildings and protection engineering . During In order to evaluate the safety status of buildings after fire and improve the fire resistance of concrete components, researchers from various countries have carried out high-temperature mechanical tests of concrete since the 1960s. The researchers found that the mechanical properties of high-strength concrete deteriorate with the increase of heating temperature. With the increase of heating temperature, the peak stress, peak strain, and elastic modulus of concrete decrease, and the change range is small when the temperature is lower than 400 °C. After the temperature exceeds 400 °C, its properties deteriorate rapidly . In a hiThe spatial scale characteristics of concrete structures determine that concrete materials are often, not only subjected to the force in one direction, but are in the state with three forces, which is particularly obvious at the joints of concrete components. By studying the mechanical characteristics of concrete under triaxial stress, this can help to understand the mechanical behavior of concrete components in the actual working environment. Research on the true triaxial static compression mechanical properties of concrete is often transformed into research on the uniaxial static compression mechanical properties of concrete under biaxial unequal stress. In this field, scholars from various countries have carried out a large number of experimental studies and preliminarily established the theoretical basis of concrete triaxial tests.x-axis and z-axis were linear during the loading process [Through a triaxial static mechanical property test of high-strength concrete, researchers found that the axial compressive strength of high-strength concrete increases with the increase of confining pressure, but compared with ordinary concrete, its strength is less affected by confining pressure . Girgin  process . In 2021 process .It can be seen from the above that, at present, research on the mechanical properties of concrete at high temperature mainly focuses on the mechanical properties of uniaxial static compression at high temperature, while research on the mechanical properties of concrete under true triaxial static compression at high temperature is relatively scarce. With fire and deep-underground environments, concrete members are often in the coupling state of high temperature and three-dimensional complex stress. Therefore, it is necessary to study the high-temperature true triaxial mechanical properties of concrete.In this paper, a high-temperature true triaxial loading test system was used to carry out high-temperature uniaxial and true triaxial static compression tests of concrete. By comparing the mechanical properties of concrete under uniaxial static compression at high temperature, the effects of different temperature levels and different lateral pressure ratios on the strength characteristics, deformation characteristics, and failure modes of concrete under high-temperature true triaxial static compression were systematically analyzed. Combined with the test results and relevant research theories, the internal influence mechanism was analyzed, and a concrete strength formula under the coupling action of high temperature and biaxial unequal lateral pressure is put forward.Xi’an Lantian Yaobai Cement Co., Ltd.,  and its specific chemical composition and relevant performance indexes are shown in −3. The fine aggregate was Bahe medium sand, with an apparent density of 2650 kg/m3, bulk density of 1490 kg/m3, and mud content of 1.3%. The water used for the preparation of the test piece was tap water, cleaned in the laboratory. JKPCA-02 polycarboxylic acid high-performance water reducer produced by Shaanxi Jingcheng building materials Co., Ltd.  were used to improve the workability of the mixed concrete. The water reduction rate was 26%, and the gas content was 2.8%.In this paper, the specimen was poured with ordinary concrete, and the raw materials required for its preparation included: cement, aggregate, water, and water reducer. The cement selected, P.O42.5, was produced by Code for Mix Proportion Design of Ordinary Concrete (JGJ 55-2011) [The mix proportion of concrete required for this test was designed according to the provisions of 55-2011) . After cGB/T 50081-2019 Test Method Standard for Physical and Mechanical Properties of Concrete [According to Concrete  and testLuoyang tengyang Machinery Technology Co., Ltd.,  and the applicable specimen size is a 70.7 mm × 70.7 mm × 70.7 mm cube. The test system is divided into a high-temperature heating system, static loading system, dynamic loading system, and data acquisition system. It can be used for true triaxial static compression tests of concrete, rock, and other materials at room temperature and high temperature, as shown in In this paper, a HYY electro-hydraulic servo material test system was used to carry out a uniaxial static compression test of concrete at room temperature, as shown in Standard for Test Methods of Physical and Mechanical Properties of Concrete [(GB/T 50081-2019), a HYY electro-hydraulic servo material test system was used to carry out uniaxial static compression tests at room temperature on 150 mm × 150 mm × 150 mm cube concrete specimens aged 28 days, and the test data were recorded. The main purpose of this test was to calibrate the concrete strength, to check whether the concrete strength met the requirements. In this paper, according to the Concrete  , and the test data were recorded. The high-temperature true triaxial loading test system was used to conduct high-temperature true triaxial static compression tests on 70.7 mm × 70.7 mm × 70.7 mm cube concrete specimens. The equipment can apply a constant lateral pressure to the concrete specimen in the Z and X directions using a hydraulic device. The lateral pressure ratio is the ratio of the lateral pressure applied in the Z and X directions. The greater the lateral pressure ratio, the greater the lateral pressure in the Z-direction. Four different side pressure ratios were set, and five temperature grades  were set under each side pressure ratio. xσ and zσ represent the specific values of the side pressure, and the side pressure settings of the other test groups were similar. In this paper, tσ is defined as the uniaxial compressive strength of concrete at the corresponding temperature. For example, “the lateral pressure in Z direction is 0.4tσ“ means that the lateral pressure in the Z direction is equal to 0.4 times the uniaxial compressive strength at this test temperature. The average value of three test data was taken as the test result for each group of tests above. The specific test process is shown in See y in the Y direction of a concrete specimen under the condition of constant lateral compressive stress σz and σx. Static compressive strength is an important index to characterize the static compressive strength characteristics of concrete under the condition of true triaxial loading. In the actual service environment, concrete is often in complex stress conditions, and different stress conditions have different effects on the true triaxial static compressive strength of concrete. Therefore, this paper studied the true triaxial static compressive strength of concrete under four side pressure ratios at each temperature level.The true triaxial static compressive strength of concrete is essentially the peak stress reached by the compressive stress σThe results of the high-temperature uniaxial static compression test and high-temperature true triaxial static compression test of concrete are shown in gf was introduced, and its expression is shown in Formula (1).yσ is the true triaxial static compressive strength, and 0σ is the uniaxial compressive strength at room temperature.The 150 mm × 150 mm × 150 mm cube concrete specimen poured in the test was tested for compressive strength, which was used to determine the cubic compressive strength of the concrete, and did not participate in the subsequent test. The strength of the cube concrete specimens with an uniaxial compressive strength of 70.7 mm × 70.7 mm × 70.7 mm described in this paper was measured using uniaxial compression in a high-temperature true triaxial loading test system. In order to facilitate the research, the concrete strength retention rate As can be seen from the figure:At the same temperature, the true triaxial static compressive strength of concrete was significantly higher than that of the uniaxial static compressive strength, and increased with the increase of the side pressure ratio. When the side pressure ratio was 0.8:0.2, the true triaxial static compressive strength of concrete at 20 °C~800 °C reached the maximum, which was 243.09%, 248.30%, 239.79%, 280.45%, and 295.53% higher than the uniaxial static compressive strength at each test temperature. This shows that lateral pressure can significantly improve the true triaxial static compressive strength of concrete, and the influence law of lateral pressure on the compressive strength of concrete at different temperatures is similar. At the same temperature, with the increase of side pressure ratio, the true triaxial static compressive strength of concrete did not show a linear growth trend, and its growth rate was first large, then small, and then large. It can be seen from the figure that under the same side pressure ratio, the static compressive strength of concrete decreased with the increase of temperature. When the temperature was 20~400 °C, the overall change range of concrete compressive strength was small. At 400 °C, the strength was slightly higher than that at 200 °C, but still lower than that at normal temperature, indicating that when the temperature was lower than 400 °C, the static compressive strength of concrete was less affected by temperature. When the temperature exceeded 400 °C, the static compressive strength of the concrete decreased sharply, and reached the minimum value at 800 °C. Under the condition of 800 °C, the compressive strength of concrete with each side pressure ratio only accounted for 28.41%, 29.45%, 31.27%, 32.16%, and 32.75% of the compressive strength under normal temperature, indicating that a high temperature, above 400 °C, can significantly reduce the static compressive strength of concrete, and that the effect on concrete under different side pressure ratios is similar.As can be seen from the figure:Under each test condition, the strength retention rate of the concrete changed greatly. The lower the temperature and the greater the side pressure ratio, the greater the strength retention rate of the concrete and, on the contrary, the smaller the strength retention rate. According to the strength retention rate, the influence of the coupling action of high temperature and biaxial unequal lateral pressure on the strength characteristics of concrete can be divided into three stages: saturation stage, strengthening stage, and deterioration stage. In the saturation stage, when the temperature does not exceed 400 °C and the side pressure ratio is greater than or equal to 0.6:0.2, the strength retention rate of concrete fluctuates slightly, but basically remains above 300%; indicating that, in this case, the temperature has little effect on the compressive strength of concrete, and the strengthening effect of side pressure tends to be saturated. In the strengthening stage, when the temperature is 400 °C~600 °C and the side pressure ratio is less than 0.6:0.2, the strength retention rate of concrete is still greater than 100%, and the increase of strength retention rate is larger with an increase of side pressure ratio; indicating that at this time, temperature has a certain deterioration effect on the compressive strength of concrete, but the side pressure effect is dominant. In the deterioration stage, when the temperature exceeds 600 °C, the strength retention rate of concrete decreases sharply. Increasing the lateral pressure ratio has little effect on the strength retention rate of concrete, indicating that temperature degradation is dominant and the reinforcement effect of lateral pressure is hidden.In conclusion, the coupling effect of high temperature and biaxial unequal lateral pressure can significantly affect the strength characteristics of concrete, but the dominant position of temperature deterioration and lateral pressure strengthening is different in the coupling range of different temperatures and lateral pressure ratios.sf is introduced, and its expression is shown in Formula (2).The strain of concrete during compression failure is an important factor reflecting the mechanical properties of concrete. Therefore, it is necessary to explore the effects of temperature and side pressure ratio on the deformation characteristics of concrete under triaxial compression. Among these, the strain characteristics in the failure direction of principal pressure are the focus of research. Similarly, in order to facilitate this research, the concrete strength retention rate yε is the peak compressive strain of concrete in Y direction, and ε0 is the uniaxial static pressure peak strain at room temperature.In the formula, The relationship between the peak static pressure strain of concrete under high temperature and the side pressure ratio is shown in As can be seen from the figure:At the same temperature, the peak strain of the true triaxial static pressure of concrete is significantly higher than that of the uniaxial static pressure. With the increase of lateral pressure ratio, the peak strain of concrete first increases and then decreases. When the side pressure ratio is 0.6:0.2, the peak strain reaches the maximum value, which increases by 113.83%, 926.4%, 718.65%, 518.26%, and 365.53% compared with the peak strain of concrete under uniaxial compression at various temperatures, indicating that a bidirectional side pressure can significantly improve the peak strain of concrete. When the side pressure ratio is 0.8:0.2, the peak strain of concrete is less than that when the side pressure ratio is 0.6:0.2. This shows that compared with the side pressure ratio of 0.6:0.2, when the side pressure ratio is 0.8:0.2, the concrete has obvious internal damage under the side pressure, and the internal damage expands rapidly during the compression process, resulting in the peak stress of the concrete.The relationship between concrete static pressure peak strain and temperature under different lateral pressure ratios is shown in As can be seen from the figure:With the increase of temperature, the peak strain of concrete under the same side pressure ratio increases, and the growth rate also increases, indicating that temperature can significantly affect the peak strain of concrete, and that the effect increases with the increase of temperature. When the temperature is 20 °C~400 °C, the peak strain of concrete increases slowly with the increase of temperature under the same lateral pressure ratio. However, when the temperature is 400 °C~800 °C, the peak strain of concrete under the same side pressure ratio increases rapidly with the increase of temperature, indicating that 400 °C is the turning point of the influence of temperature on the variation law of peak strain.The relative peak strain of concrete under the coupling action of high temperature and biaxial unequal lateral pressure is shown in As can be seen from the figure:It can be seen that under the coupling action of high temperature and lateral pressure, the relative peak strain of concrete increases significantly, and is significantly higher than that of concrete under uniaxial static pressure at room temperature.In general, the higher the temperature and the greater the side pressure ratio, the greater the relative peak strain. According to the variation law of relative peak strain, the influence of high temperature and biaxial unequal lateral pressure coupling on the deformation characteristics of concrete can be divided into three stages: stress plasticization stage, stress deterioration stage, and temperature plasticization stage. In the stress plasticization stage, when the temperature is lower than 400 °C and the side pressure ratio is less than or equal to 0.6:0.2, the relative peak strain of concrete increases slightly with the rise of temperature, but increases significantly with the increase of side pressure ratio, indicating that the side pressure plays a leading role in the deformation of concrete at this time. In the stress deterioration stage, when the temperature is lower than 400 °C and the side pressure ratio is greater than 0.6:0.2, the relative peak strain of concrete still increases significantly and is less affected by temperature, but it decreases with the increase of side pressure ratio. This shows that at this time, the lateral pressure causes some pre-damage in the concrete, resulting in the strain in the process of concrete compression failure reaching the peak strain earlier. In the temperature plasticizing stage, when the temperature is higher than 600 °C, the peak strain of concrete at the same temperature still increases at first, and then decreases with the increase of side pressure ratio. However, the variation range is small, and the relative peak strain remains in the range of 12~17 as a whole. This shows that high-temperature plasticization plays a leading role in the deformation of concrete, and the stress plasticization is covered up.To sum up, the coupling effect of high temperature and biaxial unequal lateral pressure can significantly change the deformation characteristics of concrete, but within the coupling range of different temperatures and lateral pressure ratios, the dominant position of stress plasticization and high-temperature plasticization is dynamic.The failure mode can directly describe the propagation law of internal cracks in concrete during loading, and it is an important index for the analysis of concrete mechanical tests. High temperature and lateral pressure have important effects on the mechanical properties of concrete, which can not only significantly affect the strength and deformation characteristics of concrete in a uniaxial static compression test, but also significantly change the failure mode of concrete. As can be seen from Under the condition of 20 °C~600 °C, the uniaxial static pressure failure mode of concrete has little change, and the specimen has serious collapse failure. Its main body is two quadrangular cones separated from each other, while under the condition of 800 °C, the compression failure of concrete is only lateral spalling, and its main body is wedge-shaped and not separated into two quadrangular cones. In the range of 20 °C~800 °C, the color of concrete changes with the increase of temperature. There is little difference between 200 °C and normal temperature. The color of concrete changes to a light reddish brown at 400 °C and further lightens at 600 °C. At 800 °C, the color of concrete becomes gray white, the aggregate is white, the cement hydration product is gray powder, and the aggregate and hydration product are obviously separated. In the range of 20 °C~800 °C, with the increase of temperature, the average particle size of concrete crushing and spalling decreases progressively. Under the condition of 20 °C~400 °C, the concrete shows obvious brittle failure, and the failure process is accompanied by an obvious fragmentation sound. At 600 °C, the concrete is in the transitional stage of brittle failure and plastic failure, and there is no obvious fragmentation sound in the failure process. Under the condition of 800 °C, the concrete shows obvious crushing failure, significant plastic deformation, and there is no cracking sound in the failure process. It can be seen that high temperature can significantly affect the uniaxial static pressure failure mode of concrete, and with the increase of temperature, the failure mode of concrete gradually changes, from brittle failure to plastic failure.As can be seen from When the specimen was damaged at different temperatures, the main pressure surface remained flat and intact without cracks. Only the color changed significantly with the increase of temperature, and the change law was the same as that of concrete in the uniaxial static pressure test. The specimen was obviously compressed along the main pressure direction at different temperatures. The specimen bulged laterally to varying degrees, and the edges and corners of the side pressure surface peeled off seriously, with multiple cracks parallel to the main pressure direction appearing on its surface. As the concrete specimen expanded significantly at 800 °C and shrank after cooling, many intersecting cracks appeared on its surface, covering up the cracks parallel to the main pressure direction. Under the condition of 20 °C~600 °C, the crushing shape of the concrete specimens was basically the same, and the main pressure direction was similar to that of the uniaxial static pressure test. Two forward and backward separated quadrangular cones were formed during failure, but four small quadrangular cones with distinct shape were formed in the two lateral pressure directions, which increased with the increase of lateral stress. The crushing shape of the concrete specimen along the main pressure direction at 800 °C was similar to that of concrete under the uniaxial static pressure test at the same temperature. The specimen was wedge-shaped during failure and did not form two separate quadrangular cones. This was similar to the true triaxial test of concrete at 20 °C~600 °C in the two lateral pressure directions, forming four small quadrangular cones, but it was significantly smaller than the latter under the same lateral pressure ratio, and the specimen spalled obviously. In the high-temperature true triaxial static pressure test of concrete, the plasticity of concrete was obviously enhanced and the brittleness was lessened in the failure process, and this failure characteristic was strengthened with the increase of temperature and lateral stress. Especially at 800 °C, the concrete had significant plastic deformation.To sum up, the coupling action of high temperature and biaxial unequal lateral pressure can cause obvious plastic failure of concrete and greatly change the failure mode of concrete. Compared with the uniaxial static pressure test of concrete at high temperature, the dual action of high temperature and biaxial unequal lateral pressure further enhances the plasticity of concrete and leads to significant plastic deformation during concrete failure.By comparing and analyzing the strength characteristics, deformation characteristics, and failure modes of concrete in the high-temperature uniaxial and high-temperature true triaxial static compression tests, it was found that different temperature levels and different stress conditions can have a profound impact on the static mechanical properties of concrete, and the two factors are coupled and affect each other, which makes the static mechanical properties of concrete change more significantly under different conditions. Its mechanism of influence can be explained from the following three perspectives:Under the condition of high temperature, the complex physical and chemical reactions of each component in concrete will significantly change the material composition and structure of concrete, which will directly affect the mechanical properties . When th2 crystals are decomposed into CaO, resulting in the expansion of the matrix, the continuous expansion of cracks, and the destruction of C-S-H gel. At the same time, the cracks in the cement paste and its cementation interface with aggregate continue to expand. Therefore, the compressive strength of the concrete decreases sharply.When the temperature is 400 °C, C-S-H gel combines with water to evaporate. On the one hand, the shrinkage of cement paste leads to the increase of internal micro cracks. On the other hand, the cementation between cement paste and aggregate is further enhanced, which makes the concrete structure more compact, and the integrity is enhanced. Moreover, it effectively relieves the stress concentration at the tip of microcracks. Therefore, the compressive strength of concrete increases slightly compared with that at 200 °C, but it is still lower than that at room temperature. When the temperature is 600 °C, the hydration products of the concrete are decomposed by heat, and the Ca(OH)2 are almost decomposed. The pores in the concrete increase obviously, and the cracks continue to expand and penetrate. Therefore, the compressive strength of concrete is seriously reduced [When the temperature is 800 °C, the cement paste becomes loose and crisp, and the internal cracks are intertwined. The adhesion between the slurry and the aggregate is seriously reduced, and the hydration products and Ca(OH) reduced . In the tσ. When the Z-direction stress was small (0.2tσ~0.6tσ), the concrete was basically in the elastic stress stage. On the one hand, the pre stress in X and Z directions could close some pores and micro cracks of the concrete and improve the compactness and integrity of concrete. On the other hand, the “hoop effect” in the compression process of concrete was caused by the pre-stress in the X and Z directions. The two factors worked together to significantly improve the compressive strength of the concrete [X-axis and Z-axis directions, which limited the deformation of the specimen in these two directions, delayed the development of internal cracks in the concrete, and improved the strength of the concrete.In the true triaxial test described in this paper, the X-direction Lateral pressure of concrete specimen was always 0.2concrete . “Hoop etσ, the concrete was in a state of conventional triaxial stress during compression. With an increase of Y-direction stress, the X and Z direction strains gradually changed from compressive strain to tensile strain. Since the pre-stresses in the X and Z directions were the same, the tensile strains in the X and Z directions occur at the same time and remained basically the same. After the tensile strain in the X or Z direction reached the ultimate tensile strain, the concrete was damaged. When the lateral pressure in the Z-direction was 0.4tσ and 0.6tσ, the concrete was in a state of true triaxial stress during compression. With the increase of the Y-direction stress, the X-direction produces tensile strain before the Z-direction and accumulates continuously. After the tensile strain in X-direction reached the ultimate tensile strain, the concrete was damaged [In addition, the lateral deformation of concrete was restrained by the pre-stress in the X and Z directions. At the same time, it also limited the generation and expansion of micro cracks in the concrete under Y-direction loading, resulting in obvious compression deformation in the y-direction when concrete was damaged, so as to significantly increase the peak strain of the concrete. In the true triaxial static pressure test of the concrete, when the lateral pressure in Z-direction was 0.2 damaged . tσ, the concrete began to enter the plastic damage stage under the condition of pre-stress, and micro crack propagation and pore penetration occurred in it. Therefore, when the lateral pressure in the Z-direction increased from 0.6tσ to 0.8tσ, the compressive strength of the concrete still increased under the influence of the “hoop effect”, but the increase was significantly less than that when the lateral pressure increased from 0.4tσ to 0.6tσ. In addition, the occurrence of pre-damage led to early peak stress in the compression process of concrete, so the peak strain of the concrete decreased. The existence of preloading load on the end face of the concrete loaded in the X and Z directions and friction effect made the failure mode of the concrete along the X and Z directions similar to that of under uniaxial static pressure. Therefore, after the failure of the concrete under true triaxial static pressure, its main body formed six quadrangular cones, which increased with the increase of the preloading load.When the Z-direction lateral pressure was 0.8In the true triaxial static compression test of concrete at high temperature, the concrete was subjected to the double coupling effect of high-temperature deterioration and lateral pressure strengthening at the same time. When the temperature was low (20 °C~400 °C), the high temperature increased the micro-cracks and pores in the concrete, and the concrete softened as a whole. However, at this time, the hoop effect caused by lateral pressure masked the deterioration of high temperature, and the static pressure strength and peak strain of the concrete were significantly higher than those of the uniaxial compression strength and peak strain. At this stage, the strengthening effect of lateral pressure was dominant. When the temperature gradually rose above 600 °C, a series of physical and chemical reactions occurred in the concrete, resulting in a significant increase in the number and size of micro cracks and pores in the concrete. The whole concrete became “soft and crisp”. The destructive damage of high temperature in the interior of concrete was dominant. In this case, the strengthening effect of lateral pressure on the concrete became very small.In short, the high-temperature deterioration and lateral pressure strengthening were superimposed and offset each other. The change of the two under different coupling conditions has different effects on the static compressive mechanical properties of concrete. By comparing and analyzing the mechanism of influence of single factor and two factor coupling, the effects of high temperature and side pressure under different coupling conditions can be explained.TK which was used to quantitatively describe the weakening effect of high temperature on concrete strength, and the lateral pressure strengthening factor CK, which was used to quantitatively describe the effect of lateral pressure on concrete strength. They can be used to accurately describe the effects of different factors and analyze the mechanical behavior of concrete under triaxial static compression in a high-temperature environment. Furthermore, a formula for predicting the static pressure strength of concrete under the coupling action of high temperature and biaxial unequal lateral pressure was proposed.High temperature and biaxial unequal stress can have different effects on the stress–strain relationship of concrete during loading, and the effects are different. Based on the strength theory established by predecessors, this paper introduced the high-temperature deterioration factor Concrete is a complex multiphase system, mainly composed of inorganic materials such as cement, water, coarse aggregate, and fine aggregate. Its properties are jointly affected by its own factors, such as the aggregate, water cement ratio, and age, as well as environmental factors, such as the temperature, humidity, and pH. After 28 days of maintenance, the concrete specimens mainly contained coarse aggregate, fine aggregate, and cement gel. Under the condition of high temperature, complex physical and chemical changes took place in each group, resulting in the continuous development of inherent defects in the concrete, such as micro crack propagation and deepening, pore penetration, etc. Therefore, the physical and chemical properties of the concrete changed significantly, so that the mechanical behavior of the concrete at high temperature was different from that at room temperature ,28,29.Related research  has showBased on thermodynamic theory, Li Liang  introducLi Rongtao  considerIn Johnson–Cook (JC) model, in order to describe the stress-strain relationship of metal materials under high strain rate and high-temperature conditions, and considering the joint action of high strain rate and high-temperature conditions, the stress–strain relationship of materials is established as follows:0C, 1C, 2C, m, and n, are the parameters characterizing different properties of the material. rT is the reference temperature of the material , mT is the melting point temperature of the material.In the formula, TK is defined as the ratio of the uniaxial compressive strength of concrete at t temperature to the compressive strength at room temperature. Based on the above theoretical research and referring to the temperature degradation effect in JC model, it is proposed that the high-temperature degradation factor of concrete under the coupling action of high temperature and biaxial unequal lateral pressure is:In this paper, the high-temperature deterioration factor T refers to different temperature grades, taking the absolute temperature as K; T0 is the normal temperature, taking 20 °C, i.e., 293 K. In the JC model of metal material, mT is the melting point temperature of the material. Compared with ordinary concrete, its strength is almost 0 at 1000 °C, so mT is taken as 1000 °C, i.e., 1273 K.In the formula, α is the material parameter; TK formula and the test data. The fitting equation is shown in Formula (8). It can be seen from the figure that the curve is in good agreement with the test data, which proves the rationality of the formula of the high-temperature deterioration factor TK.Concrete is a very common building material, which is widely used in all kinds of engineering constructions. It can be seen everywhere, in both industrial and civil buildings, as well as military protection projects. In practical engineering, the stress of concrete is often not a simple one-way stress state, but a complex multi-directional stress state. However, complex stress conditions often have a significant impact on the strength of concrete. In order to approximate the real stress environment of concrete in service and determine its mechanical properties under complex stress conditions, many scholars have carried out extensive research on the biaxial and triaxial mechanical properties of concrete. Due to the difficulty of concrete true triaxial static compression testing and high requirements for test equipment, most of the existing studies are concrete conventional triaxial static compression tests, while there are relatively few studies on concrete true triaxial static compression testing.In terms of the formula of concrete triaxial static compressive strength, a large number of scholars have made important contributions to the establishment and modification of the formula ,34. Baseσmax, 0σ and σ3 is the same as above, and A and B are empirical parameters.In the formula, the definition of Wang  conducteotcτ is octahedral shear stress, otcσ is octahedral normal stress, and σ0 is the uniaxial compressive strength of concrete; while σ1, σ2, and σ3 are the three-dimensional unequal stress of concrete.In the formula, Therefore, whether under conventional triaxial conditions or true triaxial conditions, lateral pressure can produce a “hoop effect”, to limit the lateral deformation of concrete, so as to significantly improve the triaxial static compressive strength of concrete. Although different researchers have established different strength formulas, the strength formula has changed from linear to nonlinear and from simple to complex, which makes scholars better able to accurately describe the relationship between concrete triaxial static compressive strength and lateral pressure.CK as the ratio of concrete compressive strength σmax and uniaxial compressive strength σ0 under triaxial compression, which can be expressed as:Based on the above research, this paper defines the lateral pressure strengthening factor Based on the formula of triaxial static compressive strength of concrete under equal lateral pressure proposed by Newman et al. and Wang Chuanzhi et al., and combined with the research content, this paper reasonably deforms and modifies the formula, and establishes a formula used to describe the true triaxial static compressive strength of concrete under unequal lateral pressure:0σ is the uniaxial compressive strength of concrete, Xσ and Zσ are the preloading static load applied to the concrete in the X and Z directions, respectively, Yσ is the true triaxial static compressive strength of concrete, and A, B, C, and D are empirical parameters.In this formula, Since the static load applied to the concrete in the X direction remains unchanged in this test, and the influence of the static load in the X direction on the true triaxial strength of the concrete can be regarded as a constant, it is proposed that the lateral pressure strengthening factor of the concrete under the coupling action of high temperature and biaxial unequal lateral pressure is:σ0 and Zσ is the same as above, and A, B, and C are empirical parameters.In the formula, the definition of Zσ to σ0 in Formula (13).TK and the side pressure strengthening factor CK. The experimental data were used to fit the equations of TK and CK, and the results showed that the fitting was good. On this basis, a concrete strength formula under the coupling action of high temperature and biaxial unequal lateral pressure is proposed, as shown in Formula (24). In the formula, yσ is the true triaxial compressive strength of concrete, and 0σ represents the uniaxial compressive strength of concrete. The significance of this formula is that the true triaxial compressive strength of concrete can be predicted according to the uniaxial compressive strength of concrete specimens under the condition of a given temperature and lateral pressure static pressure ratio.Based on the previous research results and theoretical derivation, this paper puts forward the high-temperature deterioration factor Substitute into Formulas (7) and (18):It can be seen from The strength and deformation characteristics of concrete under true triaxial static compression at high temperature are significantly higher than those under uniaxial static pressure. With the increase of lateral pressure in the Z direction, the compressive strength of concrete increases continuously, and the peak strain first increases, and then decreases. When the side pressure ratio is 0.2:0.6, the peak strain reaches the maximum. With the increase of temperature, the compressive strength of concrete generally decreases and the peak strain increases. When the temperature exceeds 400 °C, the compressive strength decreases significantly, and the peak strain increases sharply.Compared with the high-temperature uniaxial static pressure failure mode, the high-temperature true triaxial static compression failure mode of concrete changes significantly. When the temperature is 200 °C~600 °C, the main body of concrete failure under different lateral pressure ratios is six mutually separated quadrangular cones. The two pyramids in the main pressure direction are larger, and the four pyramids in the side pressure direction are smaller, but they increase with the increase of side pressure. When the temperature is 800 °C, the main compression direction of concrete is wedge-shaped, and the lateral compression direction is four small quadrangular cones. The plasticity of concrete is further enhanced and significant plastic failure occurs.The coupling effect of high-temperature deterioration and lateral pressure strengthening makes the static mechanical properties of concrete change significantly. When the temperature is lower than 400 °C, the strengthening effect of lateral pressure is dominant, which shows that the strength and deformation characteristics of concrete are significantly enhanced. When the temperature is higher than 600 °C, the high-temperature deterioration is dominant. At this time, the strengthening effect of lateral pressure is covered up, which shows that the strength characteristics of concrete are reduced and the deformation characteristics are enhanced. It was found that 0.2:0.6 and 400 °C are the turning points of side pressure ratio and temperature that affect the change law of static mechanical properties of concrete, respectively.TK and lateral pressure strengthening factor CK were proposed, and then the concrete strength formula under the coupling action of high temperature and biaxial unequal lateral pressure was proposed. Based on the previous theories, the empirical equations of TK and CK were put forward through derivation, and the equations were fitted using the experimental data. The fitting results showed that the equation was in good agreement with the experimental data. On this basis, a strength equation was proposed, and it was verified that the formula has a high accuracy.A high-temperature deterioration factor In this paper, high-temperature uniaxial static compression tests and high-temperature true triaxial static compression tests of concrete were carried out. The variation laws of concrete strength characteristics, deformation characteristics, and failure modes under different temperatures and side pressure ratios were analyzed. In this paper, the uniaxial static compression mechanical properties of concrete at high temperature and the true triaxial static compression mechanical properties at high temperature were compared and studied. Combined with relevant theories, the mechanism of influence of high temperature and bidirectional side pressure was systematically analyzed. The main conclusions are as follows:


The objective of this study is to review, evaluate, and compare the existing research and practices on electrical resistivity as a nondestructive technique in evaluating chloride-induced deterioration of reinforced concrete elements in buildings and civil infrastructure systems. First, this paper summarizes the different measurement techniques for gathering electrical resistivity (ER) values on concrete. Second, comparison analyses are performed to review the correlation of ER to different parameters representing corrosive environment and activity of steel corrosion in concrete, such as degree of water saturation, chloride penetration and diffusivity, and corrosion rate. In addition, this research enumerates and individually discusses the different environmental and interference factors that are not related to the electrochemical process of steel corrosion in concrete but directly affect the ER measurements, including temperature, the presence of steel reinforcement, cracks and delamination defects, specimen geometry, and concrete composition. Lastly and most importantly, discussions are made to determine the current gap of knowledge, to improve the utilization of this method in field and laboratory measurements, and future research. When either the pH of concrete decreases and reaches a certain level or the chloride ion concentration in concrete exceeds a threshold level, the protective film becomes unstable ; R is gas constant (=8.314 J/mol K); T is absolute temperature [K]; iZ is ionic valence i; F is Faraday constant ; it is transfer number of ions i; γi activity coefficient for ion i; ic is ion concentration in the pore water [mol/cm3]; and ρ is electrical resistivity [Ωcm].In this regard, chloride diffusivity/diffusion coefficient is one of the most commonly used parameters in quantifying chloride ingress/penetration as it controls the transport of chloride ions in saturated concretes ,72,125. 2) of the values gathered from different references ranges from 0.60 to 0.99, denoting a positive correlation. Different methods were used to measure the electrical resistivity of concrete, which will be described in In order to visualize the relationship between chloride diffusivity and electrical resistivity, this review paper summarized 11 experimental works in the literature see , as show2, the material composition, and the experimental condition of the concrete specimens of the cited references.cR, the charge transfer resistance involved in the corrosion mechanism, as follows,α is the surface area of steel contributed to current flow and β is known as the Stern–Geary constant [pR [cR value can be determined by subtracting the contribution of bulk concrete, sR, from pR as follows,The corrosion initiation and activity of steel reinforcement in concrete have been correlated to the severity of deterioration in concrete ,135,136.constant ,82,142. tant [Rp ,139. TheR1 and R2 are resistance components related to bulk concrete, corresponding to sR, in Equation (4), and cZ is frequency-dependent electrical resistance (or impedance) related to electrical properties of steel and steel–concrete interface, which can be expressed ascR is charge transfer resistance, C is the capacitance of the electrical double layer in the steel–concrete interface, j is the unit imaginary number, and f is frequency. Therefore, it can be inferred that the contribution of concrete to electrical resistivity values, which is not really related to the kinetics of steel corrosion in concrete, can explain the large variations in the corrosion rate and electrical resistivity relation from different researchers. As will be discussed in more detail in Prior researchers demonstrated that the electrical resistivity of concrete is correlated with the rate of corrosion of concrete structures once corrosion of steel in concrete initiates ,144,145.Nevertheless, under common environmental exposure, corrosion rate has a decreasing relationship with electrical resistivity . BecauseIn this section, a summary and comparison of findings in the literature are made on the variation of electrical resistivity values with different factors that are not really related to the electrochemical process of steel corrosion in concrete. It is necessary to consider the effect of such parameters to better interpret the electrical resistivity values for condition assessment of chloride-induced deterioration in reinforced concrete. Several previous research works describe how temperature can influence ER measurements ,69,158. Liu and Presuel–Moreno ,90, in tT (in Kelvin), R is the gas constant, and Previous researchers suggested several ways to compensate for the temperature effect for more consistent ER measurements. First, Presuel–Moreno and Liu  suggeste Millard  establisA number of published papers studied the influence of reinforcement steel on the electrical resistivity (ER) of concrete analyzed through experimental and numerical investigation. It is discussed that the presence of rebar in concrete results in disruptions of the electrical current fluxes when an external current is applied ,147. BecAccording to Sengul and Gjorv , increasPolder et al.  reportedSalehi , in his In the numerical investigation conducted by Salehi , variatiThe derivation of Equation (1) for the computation of the apparent electrical resistivity considers a semi-infinite and very large medium; therefore, the geometrical composition of concrete can be disregarded . HoweverFor concrete slabs, only limited published papers discussed the effect of its geometric composition on ER measurements. Garzon et al. , in theiIt is noteworthy that the method of measurement also has an effect on the ER measurements. Using a two-point method, the electric current flows at the whole geometry of the specimen. This is not the case in a Wenner probe configuration, where the electrical resistivity depends both on the specimen geometry and electrode spacing, whereas the larger the spacing of probes, the deeper the current . AccordiThe presence of cracks in concrete structures usually indicates that there is a deterioration in the concrete. Chloride ions penetrate the concrete through voids and cracks that can result in reinforcement corrosion . With reAs for crack location, according to Otieno et al. , cracks Currently published papers only explain that the delamination defects cause variation in ER values. However, to the authors’ knowledge, no systematic approach was studied to quantify such ER measurements. Morales , in her Lataste , in his The water-to-cement (or binder) ratio is one of the most important parameters in concrete mixture proportion that influences the mechanical and durability properties of concrete. Numerous researchers concluded that the water-to-cement (w/c) ratio has an inverse relationship to concrete resistivity measurements. While existing standards, measurement procedures, and the majority of published research papers are focused on the electrical resistivity of normal concrete, wide-ranging research has been conducted to analyze the effect of substituting geopolymers to cement without compromising the compressive strength and concrete durability ,186,187.In addition, a study showed that bacterial concrete demonstrates higher electrical resistivity values than normal concrete, considering fresh and seawater curing conditions . Similar2 = 0.60) samples in the paper have different ages, ranging from 90 days to 2 years, whereas, Isfahannni [2 = 0.93) after four months at a constant temperature. 2 = 0.99), verified the linear relationship between electrical conductivity and chloride diffusivity by testing a concrete sample at different ages. In addition, for the influence of corrosion rate on ER measurement, Gonzales [2 = 0.95, by testing a concrete sample at different ages. On the other hand, Morris (2004) [2 = 0.53) used four different kinds of concrete mixtures exposed to the marine environment. Research by Otieno et al. [However, variation in values is still observed in the relationships reported by different researchers in the literature. As described in fahannni , tested Gonzales  correlats (2004)   level under similar test conditions. Test regions with relatively low ER values can be interpreted as a higher corrosive environment in the initiation period of corrosion and can be further used to estimate corrosion activity and kinetics of steel corrosion in concrete. The latter application could gain more reliability in the context of combined NDE methods such as half-cell potential measurement that more directly informs corrosion activity (or corrosion risk) of steel in concrete. Furthermore, it can be concluded that more studies are still needed to consolidate the standard test method for electrical resistivity measurements for the evaluation of chloride-induced deterioration in concrete structures. The standards set by AASHTO ,193 and Another interesting finding is that majority of the research and studies cited in this review focused on the influence of one specific parameter  on electrical resistivity values. There are very limited studies that discuss and evaluate the combined effect of two or more parameters on ER measurements. Ahmad , in his It can be derived through the limitations discussed in this review regarding the use of electrical resistivity for the evaluation of chloride-induced deterioration of concrete that ER measurement cannot be a stand-alone method in conducting durability inspections and in acquiring accurate results. Gucunski et al.  mentioneIn addition to discussion regarding the use of combined NDT methods, recently published papers conducted studies relating to data fusion of multiple NDT data by machine and deep learning to forecast concrete behavior using electrical resistivity and other NDT data ,204,205.TM) in the long-term bridge performance program supported by the federal highway administration in the US (FHWA), which integrates multiple NDT methods . The robotics-assisted technology provides rapid, fully autonomous, and real-time data collection [Another direction that recent studies took related to the use of NDT for concrete durability evaluation is the application of smart technologies such as real-time structural health monitoring and robotics-assisted autonomous measurements. As for real-time structural health monitoring, Kan et al.  used an llection ,216,217,(1)After conducting an extensive literature review, this study was able to review and evaluate the correlation of electrical resistivity (ER) to critical parameters related to the electrochemical processes of steel in concrete, such as degree of water saturation, chloride diffusivity and chloride penetration, corrosion risk, and corrosion rate. It was observed that ER values showed a downward trend as the value of the three critical parameters increased. Therefore, it can be inferred that ER measurements are effective for condition assessment of chloride-induced deterioration in reinforced concrete materials. Furthermore, ER measurements could be used to evaluate the activity of corrosion after the propagation of rust in corroded steel is initiated, though there is a lack of a strong theoretical link between ER and corrosion damage;(2)However, variations in values are still observed in the relationships reported by different researchers in the literature. The variations are generally attributed to the fact that ER values are affected by various material and environmental parameters that are not really related to the corrosion process of steel in concrete. This study reviewed and summarized the effects of temperature, presence of rebars, delamination defects, presence of cracks, concrete composition, compressive strength, and specimen geometry, among others;(3)Therefore, it can be concluded that, based on the current studies in the literature, electrical resistivity evaluation is recommendable to be used at a project (or site) level under similar test conditions. Test regions with relatively low ER values can be interpreted as a higher corrosive environment in the initiation period of corrosion and can be further used to estimate corrosion activity and kinetics of steel corrosion in concrete;(4)It was also recommended that more studies are needed using electrical resistivity (ER) values to compare the conditions of reinforced concrete structures distributed at national-network levels. This research recommended four directions of future research toward the use of ER evaluation as an NDE tool for network-level application: (1) consolidation of the standard test method for electrical resistivity measurements, (2) more systematic studies to investigate the effects of combined parameters on electrical resistivity measurements values, (3) more study to use the ER in the context of combined NDE methods for comprehensive evaluation of chloride-induced deterioration in concrete structures, in which advanced data fusion techniques by machine learning and deep learning models could be useful, and (4) further developing ER data collection methods using advanced smart technologies such as real-time health monitoring technique and robotics-assisted autonomous data measurements, which enable more reliable, consistent, and rapid data collection in large concrete structures in the field.A comprehensive review study was performed to review, evaluate, and compare the existing research and practices on electrical resistivity as a nondestructive technique in evaluating chloride-induced deterioration of reinforced concrete elements in buildings and civil infrastructure systems. Specific findings and conclusions can be drawn as follows: In summary, future researchers, engineers, and practitioners can use this review in conducting future studies, experimental investigations, field inspections, and monitoring relevant to the application of electrical resistivity to concrete durability evaluation. The limitations of this method, including its sensitivity to different environmental factors and concrete parameters, should be strictly taken into consideration to make an accurate, logical, and appropriate conclusion.