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Objective Dynamization of the external fixator, defined as gradually decreasing construct‐stability of the fixator, is widely accepted as a method for treatment during the late phase of the bone healing process. However, the dynamization is mostly based on the subjective experience of orthopaedists at present, without unified standards and a clear theoretical basis. The objective of the study is to investigate the influence of the dynamization operations on the tibial mechanical properties with a hexapod circular external fixator and standardize the dynamization process. Methods A 3D‐printed tibial defects model with Young's modulus of 10.5 GPa and Poisson's ratio of 0.32 simulated the clinically fractured bone. A 10 × ∅ 45 mm silicone sample with Young's modulus of 2.7 MPa and Poisson's ratio of 0.32 simulated the callus in the fracture site. Furthermore, a hexapod circular external fixator whose struts were coded from #1 to #6 was fixed on the model with six half‐pins (5 mm diameter). Corresponding to the action of removing and loosening the struts, 17 dynamization operations are designed. For each construct after different dynamization operations, the mechanical environment changes in the fracture site were recorded by a triaxle forces sensor under gradually increasing external load from 0 to 500 N. Results The results show that the bone axial load‐sharing ratio of each construct in the removal group was generally higher than that in the loosening group. The ratio increased from 92.51 ± 0.74% to 102.68 ± 0.27% with the number of operated struts rising from 2 to 6. Besides, the constructions with the same number of operated struts but with different strut codes such as constructions 3–5, had similar bone axial load‐sharing ratios. In addition, the proposed dynamization method of the hexapod circular external fixator can gradually increase the bone axial load‐sharing ratio from 90.73 ± 0.19% to 102.68 ± 0.27% and maintain the bone radial load‐sharing ratio below 8%. Conclusion The laboratory study verified the effects of the type of operations and the number of operated struts on the bone axial load‐sharing ratio, as well as the slight influence of the choice of the strut code. Besides, a dynamization method of the hexapod circular external fixator was proposed to increase the bone axial load‐sharing ratio gradually. The experimental platform. A hexapod circular external fixator was fixed on the bone model by six 5 mm half‐pins. The hexapod circular external fixator consisted of two rings, 12 hinges and six struts. All the struts were coded from #1 to #6. The tensile testing machine was used to apply axial extral load and the triaxial forces sensor was used to record the force condition of the silicone sample simulated the callus.

One of the major disadvantages of micropiles is their low lateral stiffness and flexural rigidity due to the small diameter. This limitation can be handled in current practice, by installing the micropile with inclined condition or providing a steel casing. Additional steel casings will increase the lateral load capacity of micropiles but increase the project cost as well. Thus, inclination of micropile which is relatively simple and cheap is recommended. In this paper, a comprehensive numerical analysis is conducted on the behavior of micropiled rafts installed with inclined condition under combined vertical and lateral loading. A FEM calibrated against full-scale axial and lateral field tests is used to conduct the analysis. The soil profile is soft clay soil underlain by a layer of dense sand. The study investigates the impact of several parameters which are as follows: magnitude of vertical loading, reinforcement type, inclination angle of micropiles, and number of inclined micropiles. The study reveals that increasing vertical loads causes continuous decrease in the lateral load capacity of micropiled rafts. When all micropiles installed are inclined, the positively inclined micropiles carry 79–86% of the total lateral load carried by micropiles, whereas the negatively inclined ones carry 14–21%. Inclined micropiles offer greater lateral load sharing ratio (α h ) than that of vertical ones, largest at θ = 45°. The effect of micropile reinforcement on improving the lateral performance is low compared to the effect of micropile inclination angle.

If the rigidity and the bearing capacity of the soil under a superstructure are not efficient to bear loads of structures, a common remedy is to increase the depth of the footing to transmit loads to soil layers having high bearing capacity (well graded dense gravel, gravelly sand, hard clay, rock, etc.) by using the pile group. Piled raft foundation (PRF) has come a significant footing system of late years due to that it combines load-carrying capacities of piles and raft. Therefore, extensive empirical, numeric and analytical studies have been carried out for reliable design of these footing system. Nonetheless, the load sharing ratio (LSR) between the driven piles and the raft received no attention from researchers. It is aimed to examine the LSR between the driven pile group and the raft in this study. Therefore, a testing apparatus was set up, and loading tests were carried out including the raft and the piled raft cases. Thus, the LSR of the piles and the raft were measured by means of the tests, and the effect of the pile length and relative density on this ratio was also investigated. The model of the test setup was determined numerically for same loading conditions and the material properties by using ABAQUS software. From the test and finite element analysis results, it has been found that rafts share foundation loads at such levels that should not be ignored. Vertical settlements of raft foundations at certain loads are found to be greater than the settlements of piled raft foundations at the same loads. Relative density was observed to be effective in the range of 1–2% on the LSR of the piles in PRFs. In addition to this, the length of the pile was found to be more effective on this ratio in the range of 11–14%.

Piled raft foundations, wherein a small number of connected piles are utilized as settlement reducers, have been widely used for high-rise buildings. Recently, a new technique has been introduced by disconnecting the piles from the raft and inserting a cushion layer between them. In such cases, the piles are considered as soil reinforcement components rather than structural members. To explore the feasibility of utilizing the disconnected piled raft foundation, a series of experimental model tests were conducted to examine the load–settlement behavior and pile load sharing ratio of the connected piled raft (CPR) and disconnected piled raft (DCPR) foundation systems using cushions of different thicknesses and stiffnesses. In addition, ABAQUS 3D finite element analyses were performed to analyze the axial stress along the piles and the bending moments along the raft. The results indicated that the total settlement of the system was minimized significantly when disconnected piles were used. In addition, the disconnected technique provided a significant reduction in the axial stress along the piles and the bending moment along the raft compared with that of the CPR. These findings may be accompanied by economic and environmental benefits.

Piled raft foundations are a reliable solution for improving load distribution and minimizing settlement, particularly in soils where shallow foundations are inadequate. This study focuses on the performance of floating piled raft systems in sandy soils, where controlling settlement is critical. A calibrated three-dimensional finite element (FE) model was developed and validated using experimental load–settlement data to investigate the effect of key parameters, including the number of the pile and the stiffness of the piled-raft foundations. The results show that an optimal configuration of 10 piles achieves a balanced load-sharing ratio of approximately 50% between the raft and piles, which effectively minimizes the settlement without any unnecessary structural redundancy. Beyond this point, additional piles reduce settlement by only 3–5%. The stress distribution analysis highlights the importance of raft–soil interactions, while parametric studies demonstrate how pile numbering and piled-raft stiffness affect the performance of the foundations. This research reinforces the value of numerical modeling as a predictive tool and offers practical design recommendations for cost-effective and sustainable foundation systems in sandy ground conditions.

Purpose Defects and cyclic loads often lead to tooth-root cracks in spur gear transmission systems, affecting system stiffness, vibration patterns, and lifespan. Traditional methods using straight limiting lines and parabolic curves to assess reduced load-bearing areas due to cracks have limitations, including substantial errors with deep cracks and incompatibility with semi-analytical techniques. Methods This paper introduces a novel approach: a modified limiting line for calculating gear mesh stiffness over a broader range of crack depths. Gear body is treated as rigid to avoid error in gear-body deflection estimates. The modified limiting line is defined by minimizing the difference between mesh stiffness obtained using analytical and finite element methods at a particular mesh position. Moreover, the orientation is used to derive mesh stiffness at additional mesh sites for a given crack configuration. Also, an optimization problem involving a compatibility condition is proposed to determine the load-sharing ratios during double tooth pair engagement. Results The optimization problems, featuring nonlinear constraints, are solved using sequential quadratic programming. The mesh stiffness and load-sharing ratios are obtained for various crack configurations and are verified using the finite element method. Moreover, the dynamic responses at different crack levels are obtained. Conclusions The current approach demonstrates better accuracy at higher crack levels than the existing analytical methods and is computationally less expensive than finite element methods.

Undertaking new foundation pit excavation in a congested urban dwelling is characterized by the associated unfavourable outcomes in the surrounding area and hence continues to evolve a performance problem involving intricate soil–structure interactions. Despite decades of effort to analyse the response of conventional pile foundations to nearby excavations, performed experiments were limited to either single and group piles or elevated connected piled rafts. This paper intends to collate and examine the in-house 1-g experimental results from the past few years on the performance of supported excavations in close proximity to composite piled rafts, as well as the excavation-induced changes in the load-carrying capacity of foundations with multi-type piles. First, the additional earth pressure on the retaining wall is introduced under the mode of wall translation and/or rotation about the base, taking into account the stress redistribution and shielding effect of the piles, which leads to a reduction of the lateral pressure as compared to estimations from the traditional procedures. Second, the influence of wall movement progression on the load-bearing capacity of the foundations with varying pile lengths/stiffness is compared, demonstrating the reduction of the load borne by the soil beneath the cushion to proportionally transfer onto the piles. Experimental results from centrifuge tests are then compiled to shed light on the influence of excavation execution sequence. Furthermore, parametric numerical analysis findings on the load-sharing and lateral response of the piles are included. The article would assist researchers and practicing engineers to comprehend the mutual interaction between composite pile foundations and new excavations.

Pile composite foundations (PCFs) have been commonly applied in reinforcement engineering to adjust the vertical stiffness of foundations, due to the displacement control design criteria for foundations. PCFs that have dissimilar pile lengths, located over inclined bedrock, have shown significantly different vertical behaviors from PCFs with equal pile lengths, placed over a semi-infinite medium. However, the vertical behaviors of dissimilar PCFs over inclined bedrock cannot be predicted with the current theoretical methods, although they have been widely adopted in engineering. An analytical method is proposed in this investigation to analyze the vertical bearing characteristics of dissimilar PCFs over inclined bedrock. A pile–soil system is decomposed into fictitious piles and extended soil, and then a control equation to determine the axial force along the fictitious piles is established, stemming from the compatibility conditions between them. The vertical behaviors of dissimilar PCFs can be obtained by solving the control equation with iterative procedures, and the equation is verified by two field load tests of single piles from the Honghe bridge and a numerical case. Then, the settlement and load transfer behaviors of 3 × 1 dissimilar PCFs and their influence factors are analyzed, and the results are as follows. (1) Obvious differences can be observed concerning the axial force distribution, settlement w, and load-sharing ratio (LSR) of each pile element for different pile–soil stiffness ratios (Ep/Es). (2) The LSR of pile 1 increases from 0.074 to 0.253 for the rigid pile and from 0.062 to 0.161 for the flexible pile condition when the cushion stiffness Kc changes from 1 × 104 kN/m to 3 × 108 kN/m. The non-dimensional vertical stiffness of the foundation, N0/wdEs, increases from 10.21 to 28.95 for the rigid pile condition and increases from 8.69 to 14.44 for the flexible pile condition, when Kc increases from 1 × 104 kN/m to 4 × 105 kN/m. (3) The neutral layer depth of the pile zn, the average settlement w, and the differential settlement wd of each element head decrease with Kc, and no negative friction zone exists (zn = 0 m) for all the pile elements when Kc> 2 × 105 kN/m. (4) The N0/wdEs decreases with the distance between the pile bottom and the inclined bedrock Δ. For the rigid and flexible pile conditions, the N0/wdEs is 22.16 and 13.48 for Δ = 1 m, and 13.13 and 10.10 for Δ = 8 m. The wd reaches 16.7 mm and 4.0 mm for Δ = 1 m and Δ = 8 m, respectively. (5) The N0/wdEs increases almost linearly with an increase in l/d for the rigid pile condition, and it gradually decreases for the flexible pile condition. The developed model can improve the design and analysis of PCFs located over inclined bedrock under vertical loading.

This research aims to investigate the applicability and performance of piled rafts in soft clay. This aim has been achieved by studying how the pile length, pile number, raft-soil relative stiffness, and presence of a sand cushion beneath the raft would affect piled raft settlement, differential settlement, and load sharing. Piled rafts have been numerically simulated using PLAXIS 3D software. Experimental testing results were used to verify the numerical simulation. The portion of the load carried by the piles to the total applied load was represented by the load sharing ratio (GPR). The results indicated that with increasing pile length and number, settlement and differential settlement decreased. It was also noticed that with increasing raft-soil relative stiffness, the differential settlement decreased. The GPR decreased with increasing thickness and relative density of the sand cushion, whereas it increased with increasing pile length and number. This increase in GPR was 13.7, 36, and 58% with an increase in pile length to diameter ratio from 10 to 30 for the number of piles 4, 9, and 16, respectively. Additionally, the raft-soil relative stiffness was observed to have a marginal effect on the GPR.

As a new type of foundation, the nodular diaphragm wall (N-D wall) has large transverse stiffness and high bearing capacity, with low noise and low vibration, which is suitable for high-rise buildings in cities with limited land area. The reduction coefficient of each load composition under the same displacement conditions and the ABAQUS finite element numerical analysis software are introduced to analyze the group effect of N-D wall foundations. The results show that the compressive group wall effect coefficient is greater than 1, while the uplift group wall effect coefficient is less than 1. Under the same displacement condition, the group effect of the compressive wall is more obvious than that of the uplift wall, and the group effect of the middle wall is more obvious than that of the sidewall. The wall group effect gradually develops downward with the increase in displacement. The ultimate compressive capacity is mainly controlled by the friction resistance, which is especially obvious in the sidewall. The cap resistance load-sharing ratio decreases first and then increases with the settlement. The cap resistance is not evenly distributed, the stress at the corner is the lowest, and the stress is mainly concentrated in the middle. The influence of wall spacing, length, and width on the uplift bearing capacity is highly significant, while the influence of nodular part angle is slightly significant. The influence of wall width, length, and spacing on compressive bearing capacity is highly significant, while the influence of nodular part angle is weak. The influence of nodular part angle on the uplift bearing capacity of group wall foundation is stronger than that of the compressive bearing capacity.