Arch Shape Research Articles

Compressive load-dominated concrete structures for customized 3D-printing fabrication

Existing approaches from design to concrete 3D-printing fabrication can customize the shapes of compression-dominated concrete arches and vaults but has limited applications due to high facility requirements such as a robotic arm and a reconfigurable print bed for fabricating overhanging geometries. Therefore, there is a need to develop an alternative design-to-fabrication approach for 3D printers without such facility requirements. In this paper, concrete blocks were designed as prismatic shapes which could be customized by a most basic, gantry-based 3D printer with a flat print bed and could be assembled to a larger 3D arch structure designed based on stability and strength analyses. The feasibility of such approach was demonstrated by lab prototyping. Reduced facility requirements in this approach allow 3D-printing to be more widely applied for customizing compression-dominated structures. With further design method innovation in the future, this design-to-fabrication approach can be extended for compression-dominated structures with more complex geometries.

Comparative Evaluation of the Surface Area of the Maxillary and Mandibular Denture Bearing Area According to Arch Shapes Obtained Through A Manually Molded Impression.

Objective:This study was done to compare the surface area of the maxillary and mandibular denture bearing area obtained through a manually molded impression in an open mouth selective pressure technique.Methodology:Final impression was made in 60 patients with zinc oxide eugenol impression paste, poured in dental stone to get master cast. Denture bearing area was marked with an indelible pencil. The number of squares were calculated which constituted the denture bearing area.Results:Square arch form provides more surface area than ovoid and tapering which in turn increases the retention and support.Conclusion:The variance and standard deviation of the surface area of square, ovoid, and tapering arch shapes of maxillary dentures were very much significant and in case of Mandibular dentures were less significant.

UAV-based bridge geometric shape measurement using automatic bridge component detection and distributed multi-view reconstruction

UAV cameras combined with image-based reconstruction are promising non-contact tools for bridge shape inspection while computational efficiency is low, particularly on large-scale image sets. This paper describes an efficient image-based reconstruction pipeline for bridge geometry measurements. A full bridge three-dimensional reconstruction task is decomposed into multiple distributed tasks of reconstructing bridge sub-models using sub-image sets. A deep learning-based object detection method combined with Euclidean clustering is proposed to automatically generate cropped sub-image sets. An image mask generation technique based on 3D-to-2D mesh projection is used to keep valid pixels for camera pose estimation. The proposed method was validated in a laboratory test for arch shape measurement and in a field test for suspension cable shape measurement. The results show significant improvement about computational efficiency without accuracy reduction, compared with conventional image reconstruction methods.

Correlations of Alveolar Bone Surrounding Central Incisors in Adults

To find correlations between alveolar bones of central incisors with gender, age, central incisor shape, dental arch shape, buccolingual inclination, and effective length of premaxilla/length of the mental protuberance. We selected 36 out of 308 CBCT patients’ cases (18 males & 18 females, aged 18-38 years), and measured crest height, plate thickness, and ridge width at 1) coronal third, 2) middle third, 3) apical third of the root. We identified significant differences between many sites of alveolar bones according to the abovementioned factors. Alveolar crest height was greater in males. In the mandible, alveolar bone was thinner than in the maxilla and the lingual plate at third 1 was thin (<1 mm) in most cases. We found: a) Moderate positive correlations: 1. In maxilla: Between crest height and age. Between buccal plate thickness and ELP. Between lingual plate thickness at third 2&3 and inclination. 2. In mandible: Between buccal crest height and age / LMP. Between buccal plate thickness at third 2&3, ridge width and inclination; b) Moderate negative correlations: 1. In maxilla: between buccal plate thickness, lingual plate thickness at third 1, and age. Between buccal plate thickness at third 3 and inclination. Between lingual plate thickness at third 3 and ELP. 2. In mandible: Between buccal plate thickness at third 3, lingual plate thickness, ridge width, and LMP. Between lingual plate thickness at third 1, ridge width at third 2&3, and age. No strong correlations were found between the alveolar bone and studied variables. However, this topic needs further studying.

Effect of Earthquake on Pressure Arch above the Tunnel

Abstract In this paper, the changes in the pressure arch height above the tunnels subject to earthquake were analyzed by using theoretical, numerical, and experimental ways, respectively, and then, a corresponding formula was derived. The phenomenon of stress rotation and pressure arch around the tunnel under earthquake was found by illustrating the stress vector around tunnel. The force transmission method was used to analyze the change in pressure arch height of rectangular, horseshoe-shaped, and circular tunnels before and after earthquake, and then, a new method was presented to determine the pressure arch height above the tunnel under earthquake according to stress changes in surrounding rock. Then, the two methods were jointly used to analyze the pressure arch height above the tunnel. The results show that the tunnel shape has great effect on the shape of pressure arch, and the pressure arch height of deep tunnel varies little with depth. The changes in the shape and height of tunnel pressure arch before and after earthquake obtained from theoretical analysis and numerical simulation were finally verified by shaking table model tests. The research results in this paper may provide practical significance in seismic design of tunnel structures.

DEM simulations of agglomerates impact breakage using Timoshenko beam bond model

Attrition and breakage of agglomerates are prevalent during production and handling processes in many industries. Therefore, it is highly desirable to be able to model and analyse the agglomerate breakage process under various loading conditions. The ensemble strength and breakage patterns of agglomerates are still not well understood despite a significant amount of research being carried out. In this study, three-dimensional discrete element method (DEM) simulation of the impact breakage behaviour of agglomerates were performed using a Timoshenko beam bond model which considers axial, shear, twisting and bending behaviours on the bonds. An advantage of the Timoshenko beam bond model is the pertinent parameters of the bond contact have clear physical meaning and therefore could be determined through corresponding experimental characterisations. The mechanical properties of the bonds in this study were firstly calibrated using experimental measurements. The validation of the Timoshenko beam bond model was then undertaken by direct comparisons between the numerical simulation and experimental results of impact tests. It was shown that the time evolution of the agglomerate breakage process obtained from simulation had good agreement with experimental observations. Numerical results indicate that most of the damage happens at the early stage of the impact and a cone shape fracture zone is formed quickly inside the agglomerate where strong compressive stresses are concentrated. It is found that the exterior of the fracture zone is surrounded by an arch shape tensile stress which dominates the fracture propagation.

Effect of tunnelling-induced ground loss on the distribution of earth pressure on a deep underground structure

This paper investigated the stress-transfer mechanisms in soil around a circular tunnel (CT) and a rectangular tunnel (RT) using the finite element method (FEM). Compared with the CT, there was a self-weight stress zone in the local soil above the RT, and the shear stress was concentrated only near the sliding surface, which caused the trajectory of the minor principal stress in this area to take an inverted arch shape. Then, a multi-arch model consisting of the end-bearing arch and the friction arch was proposed for estimating the distribution of the vertical earth pressure on a deep RT in dry sand. Unlike the CT, the friction arch in the RT was based on the assumption that the minor principal stress was a circular arc. The distribution factor of the vertical earth pressure on the RT was obtained. Note that a modified coefficient in the distribution factor was introduced, which was obtained by numerical simulation at different cover depth ratios and internal friction angles. Finally, the theoretical, experimental and numerical results were compared to evaluate the validity of the proposed model. The theoretical results in this paper were in good agreement with the experimental and numerical results.

Vibration characteristics of submerged floating tunnels with suspension cables according to wave periods

The tension leg method is typically used for the mooring of submerged floating tunnels (SFTs). These tunnels may have mooring lines and foundations installed very close together, depending on the wave conditions. Sometimes, the construction cost can be increased by the foundation design. To overcome these weaknesses, a suspension SFT using the mechanism of a suspension bridge has been proposed. In this approach, the tunnel body is connected to fixed towers at both ends. Two main cables are installed for controlling the tunnel motion. The main cables are connected to the tunnel using hangers. The main cable is a steel pipe and filled with water to increase its weight. The main cables are arranged in an arch shape for controlling the buoyancy weight ratio (BWR) of the tunnel body. The present study analyzed the vibration characteristics of a suspension SFT using the free vibration analysis and time-domain analysis techniques. The study demonstrates that the SFT has excellent self-vibration control. The suspension SFT affected tuned mass damping via the interaction between the tunnel body and main cables.

Individual anatomical variability of dental arches in the period of mixed dentition with optimal occlusal ratios

Based on the results of a biometric study of plaster models of the jaws obtained in 84 children in the period of mixed dentition (8–12 years old) with a neutral location of the first permanent molars and optimal incisal overlap corresponding to the optimal functional occlusion of this age category, the main linear and angular parameters of the dental arches were determined with taking into account the trusive position of the incisors. Patients, taking into account the size of the inter-incisal angle, were divided into three groups. The first group (n=33) consisted of children with a mesotrusion position of the incisors (the value of the inter-incisor angle was 125–140°), the second group (n=27) consisted of children whose incisors were located protrusive (the value of the inter-incisor angle was less than 125°), the third group (n=24) – children with retrusion position of the incisors (the value of the inter-incisal angle is more than 140°). It has been established that in the period of mixed dentition, the main linear morphometric parameters of the dental arches are determined by the trusive types of the dental system and the vestibular-lingual inclination of the incisors. A diagnostically significant characteristic of the conjugation of the shape and size of the dental arches in the period of mixed dentition is the dental-diagonal coefficient, as the ratio of the length of the dental arch to the total component of the incisor-molar diagonals, the value of which for all types of dental systems is: for the upper jaw – 1.06 ± 0 .01; for the lower jaw – 1.09±0.01. It has been proven that in the period of mixed dentition the value of the incisal angle of the pentagon formed by the incisal diagonal and the width between the incisors is the smallest in children with protrusive incisors, while the parameters of the canine angle of the pentagon formed by the canine diagonal and the intercanine width are the largest in children with retrusion position of the incisors.

Morphometric features of dental arches in the period of mixed dentition

Based on the results of a biometric study of plaster models of the jaws obtained in 38 children in the period of early mixed dentition (8–9 years old) with a neutral location of the first permanent molars and optimal incisal overlap corresponding to the optimal functional occlusion of this age category, the limits of variability of the dental arcade index were calculated arcs with macro-, micro- and normodental type of the dental system. The total value of the width of the crowns of 12 teeth in children in the period of early mixed dentition from 92 mm to 97 mm in the upper jaw and from 85 mm to 90 mm in the lower jaw is an indicator of the normodontic type of the dental system, while the length of the dental arch is less than 92 mm in the upper jaw and 85 mm on the lower jaw indicates that such arches belong to microdont ones, and more than 97 mm on the upper jaw and 90 mm on the lower jaw – to macrodont ones. In the early period of mixed dentition, the value of the arcade index, as the ratio of the width of the dental arch to its length, in the range from 0.57 c.u. up to 0.64 c.u. is an indicator of the mesoarcade type of dental arches, and an increase (more than 0.64 a.u.) or a decrease (less than 0.57 a.u.) of this value indicates that the dental arches belong to the brachiarcade or dolichoarcade types, respectively. When constructing a dental diagnostic triangle in children with anomalies in the shape of the dental arches in the early removable dentition, it is advisable to take into account that the value of the incisor-molar diagonals is established not by determining linear parameters, but by calculating the ratio of the length of the dental arch to the value of the diagonal correction factor (upper jaw – 1 .05; lower jaw – 1.07).

Classification of the loosening zones and estimation of the loosening pressures of tunnels in layered jointed rock strata.

Due to the complexity of tunnels, accurate prediction of their loosening pressures in layered jointed rock strata is a very difficult engineering task. To recognize loosening patterns and estimate loosening pressures, numerical tests were employed in areas where tunnels were excavated in layered jointed rock strata. A total of 12 influential factors, including joints, tunnel depth, and strata, were considered in each of the numerical models. Three loosening patterns were found in the numerical testing: a ringent trumpet-shaped boundary, an arch-shaped boundary, and a closing-trend trumpet-shaped loosening zone. Empirical expressions for the loosening zone boundaries were further established and, in the form of the 12 influential factors, considered in the simulation. Given the boundary function, the loosening pressures were further deduced, which were categorized according to loosening pattern, i.e., ringent trumpet shape or arch shape, and the excavation condition of whether or not the embedded depth was deeper than the soft layer. Two case studies were used to test this method. The newly-proposed method was found to perform better than existing methods, with loosening pressure values that were slightly larger than, but very close to, actual measured field data.

Force-Chain-Based Analysis of Factors Influencing Pressure Arch Around Tunnel Under Earthquake

The force chain method is a powerful tool to analyze the pressure arch of a tunnel, which has important influence on the seismic stability of tunnel structures. The force distribution around the tunnel before and after an earthquake was observed with numerical simulation and shaking table test, and then some parameters related to the pressure arch around the tunnel were analyzed. The discrete element method software PFC was used to numerically simulate the variation of shape and height of pressure arch with tunnel depth before and after an earthquake. The effect of tunnel depth, span, section shape, lining stiffness, seismic spectrum, and seismic amplitude on the shape and height of pressure arch was numerically simulated. The numerical results show that the tunnel depth, span, section shape, and seismic amplitude have great effect on the pressure arch shape, while the lining stiffness and seismic spectrum has little effect on the pressure arch shape. In addition, the shaking table tests were conducted to observe the pressure arch shape before and after an earthquake, and the experimental results were applied to verify the numerical simulation results.

VARIANT ANATOMY OF TRANSITIONAL OCCLUSION DENTAL ARCH AT OPTIMAL OCCLUSAL RELATIONSHIPS

Through the transitional bite period, the variability of the dental arch shape and size is due to the replacement of milk teeth with permanent ones, which feature different odontometric values. The aim of this study was to identify the main linear and angular parameters of dental arches, in view of the trusive position of the incisors with optimal functional occlusion. A stratified study was involved 76 children ages 8–12 years old, who were divided into three groups (protrusive, retrusive and mesotrusive dental arches). An analysis of cone-beam computed tomograms and plaster models of jaws was carried out, which was preceded by obtaining informed consents according to the Ethics Committee requirements. The study revealed certain features of the variant anatomy of transitional occlusion dental arch. The calculated factors allowed identifying the proportionality of the dental arch parameters to odontometric indicators. During that, the dental-diagonal factor (the ratio of the dental arch length to the incisor-molar diagonals) for the upper jaw was 1.06±0.01, for the lower arch being equal to 1.09±0.01, in all types of dental arches, which is a fact to be used in clinical orthography to predict the location of the dental arch incisor (central) point in case of shape anomalies, specifically in the anterior part. The angular parameters of the diagnostic dental pentagon will allow simulating the geometric and graphical construction of arches through the transitional occlusion period.

Are facial, maxillary arch and incisor dimensions related in patients with a unilaterally impacted palatal canine? A prospective investigation

Abstract Objective To identify and determine the relationship between facial, maxillary arch and incisor dimensions of patients presenting with a unilaterally impacted palatal canine. Methods Prospective referrals over one calendar year of patients identified with a unilaterally impacted palatal canine were compared with prospectively recruited control subjects. Canine location was determined radiographically and re-confirmed two weeks later. Facial, maxillary arch and incisor dimensions were assessed. Intra-examiner reproducibility was re-assessed using randomly selected images (20%, n = 40). General linear models were applied for inter-group comparisons incorporating Bonferroni adjustment with categorical parameters assessed using Fisher’s exact test (SAS®, Version 9.4, SAS.com). Inter-class correlation coefficients were calculated for relationships between the variables. Results Fifty-four patients (37 females; 17 males) presenting with a unilaterally impacted palatal canine [mean age 14.5 (SD 1.7) years] and 54 control subjects (37 females, 17 males) [mean age 14.3 (SD 2.2) years] were recruited. Measurement error was small for landmark data (0.58 mm), palatal depth (0.09 mm), palatal area (0.42 mm²) and Bolton ratio (0.14%). For facial, maxillary arch and tooth shape assessments, landmark error was 0.05 mm with complete agreement for classification. The mean nasal basal width was smaller in the unilaterally impacted palatal canine group compared with the control group (P &lt; 0.0001) but face shape distribution and face ratio were similar (both P &gt; 0.05). The mean anterior Bolton ratio was larger in the impacted canine group (P &lt; 0.01). No differences were recorded between groups for other parameters (all P &gt; 0.05). No positive correlations were identified between the variables. Conclusions Patients with a unilaterally impacted palatal canine had a narrower mean nasal basal width and a larger mean anterior Bolton ratio compared to a control group but the clinical significance of the differences was considered minor. Facial, maxillary arch and incisor dimensions were neither individually nor collectively correlated with a palatal canine which may lend support to a genetic aetiology.

GENERAL CHARACTERISTICS OF RENAL CALICES OF A MATURE AND ELDERLY HUMAN

The use of non-invasive and minimally invasive diagnostic and treatment methods in modern urological practice dictates the need to study the location of the initial section of the extrarenal urinary tract. The aim of the study was to describe general characteristics of renal calices of a mature and elderly human. Material and methods. The study included 175 corrosive preparations of human pyelocalyceal complexes. Organometric study of number, shape of arches, linear parameters, volumes, ranking place in the ranking distribution of renal calyces volumes was performed. Results. The upper renal is characterized by a large height (14.8±9.2 mm) and a wide neck (7.2±2.3 mm) and the largest volume 1202-1246 mm3. The anterior superior renal calyx has round vault of medium diameter (6.7±2.3 mm) and medium height (7.2±3.1 mm), a narrow neck (5.0±1.6 mm) and a small stable volume (14.8 mm3). The anterior middle calyx has a round vault of medium diameter (7.4±2.2 mm) and height (10.7±5.1 mm) and a narrow neck (4.8±1.6 mm); its volume is 348.4 mm3. The anterior inferior renal calyx has medium diameter (7.2±2.3 mm) and height (8.9±4.6 mm) with a narrow neck (4.8±1.8 mm); its volume is 275.2-307.1 mm3. The posterior superior renal calyx has medium arch diameter (8.4±3.0 mm) and height (8.6±4.5 mm) with a narrow neck (5.7±2.1 mm) and a small stable volume (less than 500.0 mm3). The posterior middle renal calyx has medium diameter (7.2±2.3 mm) and height (10.7±5.1 mm) with a narrow neck (5.1±1.9 mm), medium volume (402.1 mm3). The posterior inferior renal calyx has medium diameter (7.2±2.2 mm) and height (7.0±3.6 mm) with a narrow neck (5.3±2.3 mm), small stable volume (402.1 mm3). The lower renal calyx has medium diameter (7.4±2.4 mm) and height (8.6±4.6 mm) with a narrow neck (5.7±2.2 mm) and medium volume (402.1 mm3). Conclusions. As a result of the study, we determined the general characteristics of the renal calyces of a person of mature and elderly ages. New morphological information about the structure of the pyelocalyceal complex can be used to improve the diagnosis and treatment of the kidneys extrarenal urinary tract.

The Effect of Arch Cartilage Graft and Tajima Reverse U Approach in the Secondary Reconstruction of Unilateral Cleft Lip Nasal Deformity.

Secondary cleft lip nasal deformity is complicated with wide spectrum of defect and varied reconstructive procedures. There has been no unanimous solution for a given problem. In case of a localized alar depression in unilateral cleft lip nasal deformity, the conchal cartilage applied as arch graft was proposed. Patients were recruited from database of craniofacial center who received Tajima method and arch cartilage graft. Inclusion criteria were patients with unilateral cleft lip nasal deformity after skeletal maturity. Through a reverse U incision, the lower lateral cartilage was dissected and released from the skin and the contralateral cartilage. The harvested conchal cartilage graft was trimmed to 25 to 30 by 8mm in size, and inserted as arch shape overlying the cleft side lower lateral cartilage. Transdomal fixation sutures were made. Outcome assessment was performed, and the nostril and alar dimensions were measured. Thirty-nine patients were eligible for evaluation of the surgical outcome. Majority of patients underwent simultaneous lip revision (97%). No surgery-related complications were noted in this series. Satisfaction to the nasal reconstruction was reported in 85% of patients. Further minor nasal revisions were performed in 6 patients (15%). Quantitative measurement showed statistically significant improvement in nostril height, alar height and alar width after the surgery. It is concluded that the Tajima reverse U approach plus arch cartilage graft is an effective method for secondary reconstruction of the unilateral cleft lip nasal deformity in selected patients presenting with cleft side alar depression.5.

Characteristics and Evolution of Tunnel Collapse in Fully-Weathered Coastal Red Sandstone Strata

Xu, H.; Shao, Z.; Chen, C.; Wang, Z.; Cai, L.; Li, Z., and Huang, C., 2022. Characteristics and evolution of tunnel collapse in fully-weathered coastal red sandstone strata. Journal of Coastal Research, 38(2), 289–301. Coconut Creek (Florida), ISSN 0749-0208. Understanding characteristics of tunnel collapse and its evolution is the premise of effective prevention and control. Fully-weathered coastal red sandstone is widely distributed in coastal areas, and the characteristics of tunnel collapse under this stratum are not clear. This paper studies characteristics of tunnel collapse and its evolution by conducting a model test of tunnel excavation in fully-weathered coastal red sandstone with digital image processing, where the whole process of rock mass failure, displacement, and strain variations are studied. The results show that: (1) the instability failure of the fully-weathered coastal red sandstone rock mass is a progressive process under the load. Three major collapses occur consecutively, where the first and the second start at the arch foot and arch waist, respectively; both manifested as cracks developing upward to the middle until the cracks penetrate. The third is mainly manifested as the collapse of rock mass block above the tunnel crown. (2) The displacement and shear strain around the tunnel increase first with the load and then stabilize. The vertical displacement is more significant than the horizontal displacement. Tunnel crown is where the vertical displacement increases the fastest and accumulates the most, which directly threatens the rock mass stability and thus deserves special attention. The arch waist has the most intense change of shear strain. (3) All three collapses end up forming a stable balanced arch. The three collapses show the evolution that the foot of the balanced arch gradually moves horizontally outward, and the height of the balanced arch gradually expands upward. The shape of the balanced arch can be well fitted by a parabolic function. Practical suggestions on tunnel collapse prevention and control of fully-weathered coastal red sandstone are also put forward.

Optimal arch forms under in‐plane seismic loading in different gravitational environments

AbstractThis paper is motivated by the renewed interest in space exploration and the need to provide structurally sound and resource‐efficient shielding solutions for valuable assets and future habitable modules. We present, implement and test a methodology for the preliminary design and assessment of optimal arch forms subjected to self‐weight as well as seismically induced loads. The numerical framework, built around a limit thrust‐line analysis, previously published by the authors, is summarized first. This is followed by a detailed account of the form‐finding algorithm for arches of variable thickness. Special attention is placed on the physical feasibility of our assumptions and the justification of the engineering inputs adopted. The newly form‐found arches achieve material efficiencies between 10% and 50% in comparison with their constant minimum‐thickness circular or elliptical counterparts, depending on the relative intensity of the seismic action. The influence of the initial input geometry and the stabilising presence of additional shielding material against extreme radiation are also evaluated with emphasis on the effects of low‐gravity conditions. Finally, a case study is presented and Discrete Element Models of constant and varying thickness arches (VTAs) are assessed under a set of representative ground‐motions on a lunar setting. The significant over‐conservatism of constant thickness arches (CTAs) is made manifest and potential improvements of the optimally found arch shape are highlighted. Although developed with extraterrestrial applications in mind, the results and methods we present herein are also applicable to terrestrial conditions when material efficiency is of utmost concern.

Effect of beam configuration on its multistable and negative stiffness properties

Multistable and negative stiffness mechanical metamaterials are promising and gain great attention recently. Beam structure is the most commonly used negative stiffness element in these metamaterials’ designs. The tilted beam element (V-shape) and the curved beam element are frequently exploited, but their difference is almost neglected. In this study, we investigated the mechanical properties of the beam structures with different configurations (the tilted, the curved, and the arched shapes) and the influence of the variable cross-section design using a combination of analytical, numerical and experimental methods. We draw the geometric parameter boundary of positive stiffness, negative stiffness, and bi-stable regions for these beam structures, and compare their basic mechanical properties as well as energy trapping capacity. Research results indicate that the curved beam and the tilted beam respectively show better performance in different parameter regions, and are both more suitable than the arched beam in constructing the metamaterials. The variable cross-section design can be applied to tune the basic mechanical properties and shift the boundary for various mechanical behaviors. The obtained results are also verified in different material systems and can be a reference to the design of multistable and negative stiffness mechanical metamaterials.

Experimental Study on Temperature Field Evolution Mechanism of Artificially Frozen Gravel Formation under Groundwater Seepage Flow

Artificially ground freezing method is increasingly applied in formations with high permeability. The groundwater seepage flow should be considered because an excessive groundwater seepage flow would make the merging of the frozen wall challenging. Therefore, in this study, we investigate the temperature field and frozen wall merging characteristics at varying groundwater seepage flow rates in gravel formation. Results show that the heat exchange between the seepage flow and freezing pipes delays the merging of the frozen wall and reduces its total thickness. The groundwater seepage flow restricts the freezing of the upstream zone and accelerates the freezing of the downstream zone. The upstream and downstream temperature fields are symmetrical in nonseepage flow conditions but are asymmetrical in the presence of seepage flow. The merged frozen wall presents an arched shape and shifts to the downstream zone. The “scouring effect” and “water barrier effect” simultaneously act on the merging process of the frozen wall. The total thickness of the frozen wall decreases by more than 30% when the flow rate increases from 0 to 5.0 m/d. Optimising the layout of the freezing pipes in gravel formations is a reasonable solution for a safe and economical design.