L9 Orthogonal Array Research Articles

Examination of mechanical properties of 3D printed geopolymer mortar using the Taguchi method

This study examined the strength features of 3D printed fly ash-based geopolymer mortar with silica fume using the Taguchi and ANOVA methods. This study used the Taguchi L18(21 × 32) orthogonal array. Silica fume was used in the mixtures at 0% and 10% of the binder weight. 40 × 40 × 160 mm specimens were manufactured by a 3D printer. After the specimens were produced, they were cured at 80 °C for 24, 48, and 72 h. Then, these specimens were kept at 20 ± 2 °C for 3, 7, and 28 days. Lastly, the microstructural features, compressive strength, and flexural strength of the samples were determined. The ANOVA results found that the most affecting parameter for the strength properties of geopolymer mortars was found to be silica fume. Also, the Taguchi method found that optimum values of silica fume, curing time, and curing day for strength properties of geopolymer mortar were 10%, 48 h, and 28 days, respectively.

Multi-Objective Welding Optimization for AA5052 Using Taguchi-Fuzzy Approach

<div>This study investigates the influence of tungsten inert gas (TIG) welding parameters on the dilution and hardness of AA5052 aluminum alloy. Employing Taguchi’s L27 orthogonal array, the research systematically explores the effects of current, voltage, and welding speed. Analysis of the experimental data utilizes signal-to-noise ratio, analysis of variance (ANOVA), and regression techniques. The study compares a traditional regression model with a fuzzy logic approach for result validation, finding that the latter exhibits marginally better predictive accuracy. Optimal welding parameters are identified as 150 A current, 20 V voltage, and 45 mm/s welding speed, yielding a maximum dilution of 52.81% and hardness of 145.3 HV 0.5. Current emerges as the most significant factor influencing both dilution and hardness. Microstructural examination, hardness profiling, and tensile testing of specimens welded under optimized conditions reveal a characteristic hardness distribution across the weld zones and ductile fracture behavior.</div>

Optimizing proinsulin production in E. coli BL21 (DE3) using taguchi method and efficient one-step insulin purification by on-column enzymatic cleavage.

Diabetes is a critical worldwide health problem. Numerous studies have focused on producing recombinant human insulin to address this issue. In this research, the process factors of production of recombinant His-tagged proinsulin in E. coli BL21 (DE3) strain were studied. Bacterial culture factors with significant effects on the amount of produced recombinant proinsulin were screened using a Taguchi L8 orthogonal array. Proinsulin expression was conducted under predicted optimal conditions. The folded impure His-tagged proinsulin was purified using immobilized metal ion affinity chromatography (IMAC). A novel IMAC sequence order combined with the use of non-His-tagged C-peptide cleavage enzymes followed by His- tagged enterokinase enzyme enabled simultaneous protein purification and elimination of C-peptide and His-tag in just one step. Statistical analysis revealed that the amount of produced proinsulin was significantly affected by several factors including the post-induction incubation temperature, Isopropyl ß-D-1-thiogalactopyranoside (IPTG) concentration, pre-induction incubation temperature, the glucose concentration, bacterial cell population at induction step, and the time of harvesting. The optimized model resulted in an empirical maximum proinsulin concentration of 254.5 ± 11.7 µg/ml. The high purity of the purified insulin (> 96% by SDS-PAGE) indicated that applied IMAC sequence order could be considered an efficient technique for on-column cleavage and insulin purification.

Optimization of 3D Printing Nozzle Parameters and the Optimal Combination of 3D Printer Process Parameters for Engineering Plastics with High Melting Points and Large Thermal Expansion Coefficients

Three-dimensional printing is a transformative technology in the manufacturing industry which provides customization and cost-effectiveness for all walks of life due to its fast molding speed, high material utilization, and direct molding of arbitrary complex structural parts. This study aims to improve the molding accuracy of 3D printed polyether ether ketone (PEEK) samples by systematically studying key process parameters, including printing speed, layer thickness, nozzle temperature, and filling rate. The 3D printing nozzle has an important impact on the extrusion rate of the melt, and the fluid simulation of the nozzle was carried out to explore the variation characteristics of the melt flow rate in the nozzle and optimize the nozzle structure parameters. In order to effectively optimize the process, considering its inherent efficiency, robustness, and cost-effectiveness, the L9 orthogonal array experimental design scheme was used to analyze the effects of printing speed, layer thickness, nozzle temperature, and filling rate on the molding accuracy of the test sample, and the optimal combination of process parameters was optimized through the comprehensive weighted scoring method so as to improve the molding accuracy of the 3D printed PEEK sample; finally, the molding accuracy of the components printed using the Sermoon-M1 3D printer with the optimized nozzle structure was printed. The results show that the nozzle structure is optimal when the convergence angle is 120° and the aspect ratio is 2, and the outlet cross-section velocity is increased by 2.5% and 2.7%, respectively. The order of influence strength on the dimensional accuracy of the test sample is layer thickness > filling rate > nozzle temperature > printing speed. The optimal combination of parameters is: a printing speed of 15 mm/s, a layer thickness of 0.1 mm, a nozzle temperature of 420 °C, and a filling rate of 50%. The insights derived from this study pave the way for predicting and implementing the selection of optimal process parameters in the production of 3D printed products, with important implications for the optimal molding accuracy of printed components.

Investigation on geometric, dimensional accuracy and surface roughness for 3D printed PLA via fused deposition modelling (FDM) process

Fused deposition modeling (FDM) is an advanced additive manufacturing technique known for its precision and repeatability, extensively applied in producing automotive and industrial components. This study employs the Taguchi L9 orthogonal array (OA) approach to optimize process parameters for minimizing dimensional inaccuracies, geometric deviations, and surface roughness (Ra) in polylactic acid (PLA) specimens fabricated as per ASTM D638 Type V standards. Four critical printing parameters: extrusion temperature (ET), infill pattern (Ip), print rate (Rp), and layer height (LH) are investigated, focusing on specimen thickness (Ts), width of the grip section (Wgs), overall length (OL), circularity (Circ), cylindricity (Cyl), surface roughness (Ra), and waviness (Wa). Signal-to-noise (S/N) ratio analysis identified optimal parameter combinations, revealing that Ip, ET, and Rp significantly influence circularity by 39.24%, 37.34%, and 15.19%, respectively. One of the important factors that affect the degree of inaccuracy in cylindricity is the Ip. Gyroid pattern generated the least amount of inaccuracy out of all the patterns that were tested. Layer height (LH) at 0.1 mm was the most critical factor affecting Ra and Wa, while an extrusion temperature of 215°C predominantly influenced Ts. The Ip has the most affected the grip section width. In contrast to expectation, the triangle Ip achieved the minimum width error that was 0.3384%. The Rp of 40 mm/s has the highest impact on the OL deviations. Out of all the other patterns, the Tri-Hexagon (Ip) has made the least contribution to the OL deviations. Rp exhibited a lower contribution to Ra (2.35%) and Wa (12.45%). The results demonstrate the effectiveness of the Taguchi approach in identifying optimal process setups for enhancing the precision, geometric accuracy, and surface quality of 3D-printed specimens.

Green dyeing of cellulose diacetate fabric with disperse dyes in a liquid paraffin medium.

The conventional method of dyeing cellulose diacetate (CDA) fabric with disperse dyes consumes significant amounts of fresh water and dispersants, contributing to environmental pollution and health hazards. This study explored the use of liquid paraffin as an alternative to aqueous mediums for dyeing CDA fabric with Disperse Blue 56 dyes, eliminating the need for dispersants. An L16 orthogonal array was used to optimize dyeing conditions based on the color strength values. The fabric properties were evaluated through several techniques. These include tensile strength, colorfastness to washing and rubbing, Fourier-transform infrared spectroscopy, thermogravimetric analysis, scanning electron microscopy, and X-ray diffraction. These findings highlight that the textile industry can adopt a practical and environmentally friendly technique for dyeing CDA fabric, leading to a significant reduction in pollution.

Multioptimization analysis of machining characteristics on spark electrical discharge machining of Al/SiC and Al/SiC/B4C composites

Abstract This study examines the machining characteristics of sintered aluminium composites, including Al+6% SiC and Al+4% SiC+2% B4C, utilising electrical discharge machining (EDM) by changing the input machining factors like current (C) in amperes, Pulse-OFF and Pulse-ON time in µs, at three distinct levels. The L9 Orthogonal array was employed to examine the influence of process factors on output variables, including Surface Roughness (SR), Material Removal Rate (MRR), and Hole Circularity (HC). An Analysis of Variance (ANOVA) was conducted to determine the percentage contribution of the input factors to the output variables. Observation implies that the GRG ANOVA for Al+6%SiC composite has achieved the most significant contribution to the total GRG, with the current contributing 86.66%, followed by the Pulse-ON at 8.52% and the Pulse-OFF at 3.63%. In contrast, the Al+4%SiC+2%B4C composite shows the current contributing 74.07%, followed by the Pulse-ON at 15.25% and the Pulse-OFF at 9.82%. The ideal input levels for Al+6%SiC and Al+4%SiC+2%B4C composites were found to be A3B3C1 and A3B3C3, correspondingly.

Optimizing process parameters for enhanced formability and fracture behavior in single point incremental forming of SS310 sheets

This research investigates the forming and fracture behavior of stainless steel 310 Grade sheets using the single point incremental forming (SPIF) process under various parameters: ball diameter, spindle speed, feed rate, and vertical step down. Employing an L9 orthogonal array suggested by Taguchi, the study evaluates formability through stress and strain-based forming limit diagrams (FLD). Structural changes were analyzed using scanning electron microscopy fractography and optical microscopy. The highest level of formability was identified at the spindle speed of 100 rpm, feed rate of 600 mm/min, ball diameter of 12 mm, and a vertical step-down of 0.3 mm. Formability analysis is given variations with a maximum of 0.931 at a wall angle of 72.71°, and minimum and medium values of 0.423 and 0.63 at all angles of 60° and 66.24°, respectively. The least and most moderate formability levels showed an 11% variation, and the least and highest formability limits had a 21% higher formability limit. The stress-based limits also increased by 10% for moderate to better formability. The findings indicate that formability increases with lower vertical step down and feed rate, as well as higher spindle speed and ball diameter. This study provides valuable insights into optimizing SPIF process parameters to enhance the quality and structural integrity of formed SS310 components.

Efficient hole extraction by doped-polyaniline/graphene oxide in lead-free perovskite solar cell: a computational study

Abstract The intriguing behavior of doped polyanilinine/graphene oxide (PANI/GO) offers a solution to the pivotal problem of device stability against moisture in perovskite solar cell (PSC). Tunable bandgap formation of doped PANI/GO with an absorber layer allows effective flexibility for charge carrier conduction and reduced series resistance further boosting the cell performance. Herein, the L9 Orthogonal Array (OA) Taguchi-based grey relational analysis (GRA) optimization was introduced to intensify the key output responses. Furthermore, this work also delved into incorporating a Pb-free absorber perovskite layer, formamidinium tin triiodide (FASnI3), and concomitantly eluding the environmentally hazardous substance. The numerical optimization supported by statistical analysis is based on experimental data to attain the utmost peak cell efficiency. Taguchi’s L9 OA-based GRA predictive modeling recorded over one-fold enhancement over experimental results, reaching as high as 20.28% power conversion efficiency (PCE). Despite that, the PCE of the structures is severely affected by interface defects at the electron transport layer/absorber (ETL/Abs) vicinity, which is almost zero at merely 1 × 1014 cm−2, manifesting that control measures need to be taken into account. This work deduces the feasibility of ETL/Abs stack structure in replacing the conventional Pb-based perovskite absorber layer, while maximizing the potential use of doped PANI/GO as a hole transport layer (HTL).

Effect of FFF parameters on PLA/WD composite properties: Comparative analysis using Taguchi and GRA approach

This article explores the optimization of 3D printing parameters of PLA/wood dust (PLA/WD) composite material for enhanced physical properties, including density, surface roughness, water absorption, and Shore D hardness. The study employs a Taguchi-based L27 orthogonal array design for experimentation, with mathematical models created using grey relational analysis (GRA) to predict the material’s performance by obtaining a grey relational grade (GRG). The obtained GRG was further optimized using ANOVA. The FFF input parameters analyzed include nozzle temperature (190–200°C), layer height (0.12–0.28 mm), print speed (30–50 mm/min), infill density (80–100%), and raster angle (0–90°). The results indicate that a printing temperature of 195°C, a layer thickness of 0.12 mm, a print speed of 30 mm/sec, 100% infill density, and a raster angle of 45° yield the highest GRG, signifying the best overall performance. Furthermore, the data obtained from Analysis of Variance (ANOVA) indicated that, raster angle has the most substantial influence on physical characteristics, followed by infill %, print speed, print temperature, and layer thickness. The investigation of the sample using Scanning Electron Microscopy (SEM) revealed aspects of the sample morphology, including layer bonding irregularities and empty spaces, which impact the density and hardness of the material.

Experimental-design-based optimization of dispersive liquid-liquid microextraction coupled with gas chromatography–negative-ion chemical ionization–mass spectrometry for the determination of pyrethroids in agricultural products and drinks

Pyrethroids are synthetic chemicals that account for 16% of the international insecticide market and have been shown to be of varying toxicity to different species. There are various methods available for detecting pyrethroids in agricultural products, but these products must be pre-treated to remove interference from the food matrix, such as through dispersion liquid-liquid microextraction (DLLME). This study employed two experimental design methods to optimize the continuous and discontinuous experimental parameters of DLLME and investigated whether DLLME combined with GC-NICI-MS is effective for detecting pyrethroids in agricultural products. The Taguchi design with an L9(34) orthogonal array and response surface methodology were employed to optimize the discontinuous and continuous parameters of the DLLME process, respectively. To validate the performance of GC-NICI-MS after optimized DLLME, pyrethroids in mixed standard solutions at levels ranging from 0.02 to 50.00 µg/L were measured, and the resultant calibration curves were fitted. Adequate linearity was found for the six investigated pyrethroids (r = 0.9908–0.9960). The limits of detection and quantification ranged from 0.005 to 0.035 µg/L and 0.02 to 0.1 µg/L, respectively. The proposed approach simplifies the optimization of parameters compared to reported methods and achieves considerably lower limits of detection. The concept of mixed application based on the dual experimental design method can be applied to other regulated compounds to enhance the safety of agricultural products. The feasibility of the method was confirmed by successfully detecting pyrethroids in 13 types of teas, fruit, and vegetables.

An experimental and modelling approach to proclaim sustainable machining using avocado oil-based nano-cutting fluids

Higher-end science and technology facilitate the human community with a sophisticated life despite it curses by abundant pollution. The alarming demand for sustainability pressurizes the manufacturing sector to ensure sustainable manufacturing. Since Molybdenum di sulfide (MoS2) and avocado oil are known solid and liquid lubricants respectively, hence, it is a worthwhile attempt to implement the bio-based degradable avocado oil enriched with nano Molybdenum di sulfide (nMoS2) particles as a potential machining fluid for CNC-end milling. Different proportions of avocado oil and nMoS2 were used to synthesise four distinct machining fluids to assess the individual impact of avocado oil and nMoS2 particles. The emulsification and sonication were employed to synthesise the fluids. A hybrid Grey Relational Analysis (GRA) coupled with Principal Component Analysis (PCA) was followed to scrutiny the effect of novel machining fluid on machining objectives. The experimental results of physio-chemical properties revealed that avocado-rich 0.5% nMoS2 excels among others. The L16 orthogonal array experiments associated with statistical analysis explored the developed machining fluid (A6W4/0.5) that significantly impacts the machining objectives. The experimental results manifest that nearly 64.87% of surface roughness and 93.3% of tool wear have been reduced during machining in the presence of A6W4/0.5 fluid than A4W6/0.75. The improved performance of the novel machining fluid upholds its potential to replace conventional fluids and ensure green manufacturing.

Artificial neural network-based predictive models for analyzing the flexural and compressive strength of PLA/carbon parts fabricated via material extrusion-based 3D printing

This study focuses on material extrusion-based (MEX) 3D printing of PLA reinforced with milled carbon fiber composite using the fused deposition modeling technique, structured through an L16 orthogonal array design. The effects of key 3D printing input parameters (print temperature, layer thickness, infill pattern, and print speed) on flexural and compressive properties were recorded, including flexural force and stress and compressive force and stress. Levenberg-Marquardt (LM) and Scaled Conjugate Gradient (SCG) algorithm was developed to predict and evaluate the accuracy of the experiment. Regression analysis showed strong correlation between predicted and actual values, with LM recoding R-squared values of 0.99,983, 0.9809, and 0.98,968 for training, validation, and testing, respectively and 0.99,446, 0.98,119, and 0.98,876 for the SCG model. Both models effectively captured the relationships between input parameters and fracture toughness, with overall R-squared values of 0.99,506 for LM and 0.98,863 for SCG, indicating robust predictive performance across all datasets.

Investigation of the Effect of Cutting-Edge Rounding on Surface Quality in Milling of Al 7075 and Al 6082 Alloys

Al 7075 and Al 6082 alloys are alloys that are widely used in many sectors, especially aviation and automotive. During their processing along with the widespread use of those alloys, significant machinability problems such as low surface quality due to chip accumulation (Built Up Edge-BUE) on the cutting edge are observed. In this study, the effect of cutting-edge corner rounding and machining parameters on surface roughness in milling of Al 7075 and Al 6082 alloys were experimentally investigated. To determine the effect of cutting-edge rounding, two different corner rounding values (5.5-6 µm and 7-9 µm) were applied and compared with standard/coated and standard/uncoated tools in terms of machining performance. In the experimental studies, cutting parameters were determined as two different cutting speeds (300 m/min, 400 m/min) and two different feed rates (0.085 mm/tooth, 0.11 mm/tooth). With each tool, peripheral milling was performed on four sides of the prismatic test specimens under dry machining conditions. Taguchi L8 orthogonal array experimental design was used as the experimental design. Analysis of variance (ANOVA) was performed to evaluate the effects of cutting parameters on surface roughness and the reliability of all results was above 85%. The results of the analysis of variance revealed that the alloy type was more effective on the surface roughness. In the surface roughness measurements, the best surface roughness values (Ra=0.14 µm) were obtained in the experiments performed with a standard/coated cutting tool using a cutting speed of 300 m/min and a feed rate of 0.11 mm/tooth.

Optimizing conventional machining process parameters for A713 aluminum alloy using Taguchi method and passive optical network for data transmission

Abstract This study focuses on optimizing machining parameters for A713 aluminum alloy, renowned for its high strength-to-weight ratio but challenging to machine with precision. Using the Taguchi method, key parameters – cutting speed, feed rate, and depth of cut – are optimized to improve surface finish, tool life, and dimensional accuracy. An L9 orthogonal array is applied to enhance experimental efficiency. Furthermore, the integration of Passive Optical Network (PON) technology facilitates real-time data monitoring and transmission, enabling continuous feedback and timely adjustments. This hybrid approach of Taguchi optimization and PON technology achieves superior machining performance, boosting surface quality and operational efficiency. The research highlights how modern data transmission solutions like PON can enhance traditional optimization methods, providing a scalable framework for advanced machining processes in industrial applications.

OPTIMIZATION OF FDM 3D PRINTING PARAMETERS FOR TENSILE STRENGTH OF PETG CARBON FIBRE USING TAGUCHI METHOD

Fused Deposition Modeling (FDM) has become one of the most prevalent technologies in the field of additive manufacturing (AM). Nonetheless, polyethylene terephthalate glycol (PETG), a polymer renowned for its mechanical strength, has been significantly employed in 3D printing as an alternative to traditional materials. The incorporation of fibers renders PETG-based composites viable for a diverse range of applications. However, the tensile strength of PETG carbon fibre developed using FDM depends on multiple printing conditions. Therefore, this work aims to examine the impact of printing parameters (layer thickness, infill density, and printing speed) at three individual levels on the tensile and structural characteristics of PETG carbon fibre. A total of nine print runs were executed by manipulating the three parameters. Three samples were produced for each run to ensure consistency in the results. Tensile tests on the samples were carried out, and a scanning electron microscope (SEM) was used to examine the structure of the printed parts. Finally, L9 (33) orthogonal arrays were developed for the experiment. Following that, an analysis of variance (ANOVA) was conducted to determine the crucial factors and their ideal levels. The results showed that the infill density parameter significantly influenced the optimization of the tensile strength of PETG carbon fibre. The optimal value for this parameter was found to be 80%. Increasing the density of the infill improves the tensile strength by reducing the air gaps and decreasing deformation, leading to a solid and tightly packed structure. Thereafter, the most effective settings were identified as a layer thickness of 0.4 mm, an infill density of 80%, and a printing speed of 30 mm/s.

Surface Characteristics and Performance Optimization of W-Doped Vanadium Dioxide Thin Films

This study explores the surface characteristics evaluation and performance optimization of tungsten (W)-doped vanadium dioxide (VO2) thin films. W-doped vanadium dioxide films were deposited on B270 glass substrates using an electron beam evaporation technique combined with the ion beam-assisted deposition (IAD) method. The Taguchi method was used to analyze the performance optimization of VO2 thin films, and L16 orthogonal array design and Minitab software were used for optimization calculations. The surface roughness, visible light transmittance, infrared transmittance, and residual stress of un-doped and tungsten-doped (3–5%) VO2 thin films are set as the quality performance indicators of thin films. The goal is to identify the key factors that affect the performance of VO2 thin films during deposition and optimize their process parameters. The experimental results showed that a VO2 thin film with 3% tungsten doping, an oxygen flow rate of 60 sccm, a heating temperature of 280 °C, and a film thickness of 60 nm exhibited the lowest surface roughness of 2.12 nm. A VO2 thin film with 5% tungsten doping, an oxygen flow rate of 0 sccm, a heating temperature of 280 °C, and a film thickness of 60 nm had the highest visible light transmittance at 64.33%. When the oxygen flow rate was 60 sccm, the heating temperature was 295 °C, the film thickness was 150 nm, and the tungsten doping was 5%, the VO2 thin film showed the lowest infrared transmittance of 31.34%. A thin film with 5% tungsten doping, an oxygen flow rate of 20 sccm, a heating temperature of 265 °C, and a film thickness of 120 nm exhibited the lowest residual stress of −0.195 GPa.

Exploration of Engine Parameters for Emission Reduction in Gasoline-Ethanol Fueled Engines

The main objective of this study is to develop spark ignition engine parameters that allow complete combustion while reducing dependence on fossil fuels. To achieve this goal, optimization of compression ratio, gasoline-ethanol mixture, ignition timing, and spark plug type was used. In addition, this study used water injection that continuously injects water before the intake manifold. In this study, the Taguchi method with the L9 orthogonal array was applied. According to the experimental verification results, the best combination to reduce exhaust emission levels is to utilize gasoline-ethanol (E70), a compression ratio (CR) of 15.6:1, an ignition degree of +4°, and a platinum spark plug. Meanwhile, the presence of water injection at 1.45 ml/s helps reduce vehicle exhaust pollutants.

A Study on Electroless Copper Deposition for Desktop Stereolithography 3D Printing Materials

Electroless deposition is a method of metallizing parts without needing for an electrical source that can be performed on electrically conductive and non-conductive materials. Adhesion quality is an essential aspect of the electroless deposition process that determines the metal deposition conditions. The properties of stereolithography (SLA) 3D printed parts can be improved through the metallization process for various applications. In this study, optimization through the orthogonal design method was used to obtain the optimal processing parameters of electroless copper deposition on desktop SLA material with respect to adhesion quality. Experimental work was carried out according to the L9 (34) orthogonal array, followed by an evaluation of the signal-to-noise (S/N) ratio and analysis of variance (ANOVA). Based on the S/N ratio results, the optimal processing parameters for adhesion quality were potassium hydroxide concentration (400 g/L), etching time (30 min), formaldehyde concentration (3.75 mL/L) and deposition time (30 min). The results of the study are useful for industries such as rapid tooling, rapid prototyping, and semiconductors.

Numerical Simulation of Uplift Behavior of a Rock-Socketed Pier Anchored by Inclined Anchors in Rock Masses

The rock-socketed pier anchored by inclined anchors (RPIA) is a new type of foundation developed by combining a rock-socketed pier and inclined anchors. Current research on RPIA is relatively limited, and the impact of design parameters on its bearing performance remains unclear. To investigate the uplift-bearing performance of RPIA, a finite-element model that considers the nonlinear properties of materials and multidirectional interactions was developed and verified. Based on this model, numerical simulations were performed on twenty-five RPIA that were designed using the L25 orthogonal array proposed by the Taguchi method, and the uplift load–displacement curve for each RPIA was obtained. Based on the interpretation of the elastic limit, uplift resistance, initial stiffness, and the ductility index for each simulated RPIA, the sensitivity of each factor was examined by analyzing the signal-to-noise ratio and variance. The results indicated that rock strength and pier diameter were the main factors determining the uplift performance of the RPIAs, while the angle of inclined anchors is the most influential factor affecting the ductility of RPIA. The primary role of the inclined anchor is to reduce the extraction of the pier after failure of the side resistance between the pier and rock mass, thus significantly enhancing the ductility of the uplift-loaded RPIA. The addition of reinforcements around the connection joints of the pier and anchors may prevent concrete failure and to fully execute the role of inclined anchors.