Deflection Ratio Research Articles

Prediction of remaining service life for flexible pavement in the Southern Central States using FWD parameters

Various Departments of Transportation (DOTs) in the South-Central States and abroad have extensively used Non-Destructive Testing (NDT) surface deflection bowl data. The primary purpose of using deflection-based NDTs in network-level assessment is to identify a section of pavement in need of further investigation at the project level. The falling weight deflectometer (FWD) test is a common NDT-based test that is used by transportation agencies to assess the performance of flexible pavement.This research concentrates on simulating the deflection produced by FWD devices using 3-D Move software. Simulations based on software will decrease the need for lengthy FWD testing in the field. In the study, ninety-seven (97) pavement sections from Arkansas, Louisiana, New Mexico, Oklahoma, and Texas are used for simulation, analysis, and verification of FWD testing. The deflection values produced from software simulations were found to be strongly correlated with field test findings. In addition, the simulated deflection values were used to develop and validate various deflection bowl parameters. In this study, the normalized comprehensive deflection ratio and the normalized comprehensive area ratio are two key characteristics that were validated and produced. Eventually, load-induced impacts using these parameters are effectively analyzed in order to anticipate the remaining service life of flexible pavement structures. The prediction of the remaining service life will be an efficient tool for different DOTs and transportation agencies to initiate the rehabilitation work in time and economically.

Prediction of remaining service life for flexible pavement in the Southern Central States using FWD parameters

Various Departments of Transportation (DOTs) in the South-Central States and abroad have extensively used Non-Destructive Testing (NDT) surface deflection bowl data. The primary purpose of using deflection-based NDTs in network-level assessment is to identify a section of pavement in need of further investigation at the project level. The falling weight deflectometer (FWD) test is a common NDT-based test that is used by transportation agencies to assess the performance of flexible pavement.This research concentrates on simulating the deflection produced by FWD devices using 3-D Move software. Simulations based on software will decrease the need for lengthy FWD testing in the field. In the study, ninety-seven (97) pavement sections from Arkansas, Louisiana, New Mexico, Oklahoma, and Texas are used for simulation, analysis, and verification of FWD testing. The deflection values produced from software simulations were found to be strongly correlated with field test findings. In addition, the simulated deflection values were used to develop and validate various deflection bowl parameters. In this study, the normalized comprehensive deflection ratio and the normalized comprehensive area ratio are two key characteristics that were validated and produced. Eventually, load-induced impacts using these parameters are effectively analyzed in order to anticipate the remaining service life of flexible pavement structures. The prediction of the remaining service life will be an efficient tool for different DOTs and transportation agencies to initiate the rehabilitation work in time and economically.

Numerical analysis and conversion of dynamic and static deflection of asphalt pavement under FWD loading

During the falling weight deflectometer (FWD) evaluation, only calculating the acceptance deflection by adopting the layered elastic system theory has its limitations. In this paper, a three-dimensional finite element method was adopted to carry out the dynamic simulation analysis of typical asphalt pavement structures under FWD test. As a result, a dynamic deflection calculation model of asphalt pavement under FWD loading was established as well as the calculating method, in which a layered elastic system theory is adopted for calculations on the basis of the dynamic-static deflection ratio. Furthermore, an equivalent conversion method of asphalt pavement was proposed based on the deflection equivalent principle. Last, the applicability of the method was examined by comparing the FWD results of the pavement sections tested on-site. The method proposed in this paper to calculate the dynamic deflection of asphalt pavement is critical for the quality acceptance of asphalt pavement construction, modulus back calculation, and asphalt pavement design.

Analytical review of design aspects of helical spring

The curvature correction factor is an important parameter for evaluating the stress of helical springs. A novel modelled curvature correction factor (KG) was proposed in terms of the shear correction factor (KS) and spring index (C). This factor (KC) falls between the Wahl and Bergstrasser correction factors, considering the stresses due to shear, torsional, and curvature effects. The ratio of the actual deflection to estimated deflection and the ratio of the actual stiffness to estimated stiffness are mirror images of each other. In addition, when C continued to decrease, the curvature correction factor increased sharply. In practical design, the actual deviation is greater than the evaluated deflection, and the evaluated deflection may need to be increased by a certain percentage to obtain the actual deflection. Therefore, a general equation was developed for this purpose. The ratios of the actual and evaluated deflections and the actual and evaluated stiffnesses were mirror images of each other. For suitable assumed data, the torsional shear stress, maximum shear stress, and modelled curvature stress were almost straight and parallel to each other.

Experimental investigation of mechanical behavior at the microstructure of copper-graphene thin films

Graphene reinforcements in the metal matrix cause improvement in mechanical properties. The interaction of graphene depends on the microstructure and deformation of the metal matrix. At the nano and micro scale, metal graphene composites are mainly evaluated by indirect techniques like nanoindentation, which only induces specific deformation and failure mechanisms. In this work, nanolayered copper–graphene composites are fabricated to study the impact of graphene particles’ reinforcements on the mechanical behavior during uniaxial tensile loading. The stress required for film cracking increases in the ten-layer copper films (channel cracks) by 50% and the four-layer copper films (microcracks) by 121% with graphene reinforcement. Electron microscopy reveals that the graphene particles’ presence at the interfaces causes deflections in the crack paths leading to improved mechanical performance. The graphene particles also affect the grain boundary sliding (cause of microcracks) in the four-layer samples, increasing the crack onset strain from 1.3% to 2.4%. Comparing the energy release rate ratio of deflection and penetration to the fracture toughness ratio of the copper–graphene interface and graphene particle shows that crack deflection is expected. Molecular dynamics simulations also show that the deflection of cracks is due to graphene stopping the growth of plastic zones, which leads to delaminations at the interface.

Dynamic Responses of Ballastless High-Speed Railway Due to Train Passage With Excitation of Uneven Trackbed Settlement

The ballastless slab track has been widely used in newly-developed high-speed railways in China as well as in other countries for its high stability and low maintenance. However, loss of track vertical alignment due to uneven trackbed settlement will bring adverse impact on train’s running safety and track serviceability. In this study, a train-track-trackbed coupling model has been proposed to investigate the dynamic responses of track structure with the excitation of trackbed settlement with varied patterns. To validate the proposed analysis model, comparisons with both the analytical solution and in- situ measures have been performed. The influences of train speeds, settlement trough amplitude and length are discussed based on this analysis model. It’s indicated that the dynamic responses of train vehicle and track structure increase with increasing in train speed and settlement amplitude within certain settlement length. By introducing the standards for train operation safety and riding comfort, a new trackbed settlement control criteria is proposed. The computation results indicate that the standard for train operation safety is found to be the dominating factor for uneven settlements with the length less than 10 m, while the standard for riding comfort dominates the settlement control criteria in other cases. To further facilitate the settlement control criteria in engineering practices, the ratio of settlement amplitude and settlement length (which is defined as deflection ratio) is adopted to depict the envelop curves for various settlement patterns.

Analysis of floating and end-bearing pile foundations affected by deep-excavations

This paper investigates the response of pile foundations to deep-excavations. An elastoplastic two-stage model is used to study the response of pile groups (with free- or rigidly capped-heads) and of piled structures (grade beams or bearing walls), considering piles embedded in either uniform or layered ground. The model is validated using results of analytical solutions, as well as data from centrifuge tests and from real case histories. Then, a parametric study investigates excavation-induced displacements and internal forces of piles, and deformations of the superstructure. Soil–pile transfer mechanisms and pile–superstructure interactions are analysed for various foundations and ground conditions, with results showing that settlements and slopes between piles are larger for floating piles than for end-bearing piles. Results show that rigidly capped piles and semi-flexible piled structures cause bending moments at the foundation heads that increase with the excavation-induced slope between piles, whereas the risk for tensile failure of piles is low. Also, results indicate that the superstructure stiffness is more relevant to decrease the slope and deflection ratio of foundations when composed of floating piles, compared to end-bearing piles. Finally, modelling end-bearing piles embedded in a stiff base using hinged connections to such stiff base may not be appropriate.

Load Test Analysis of a Long-Span Prestressed Nano-Concrete Highway Bridge.

In order to solve the problem of vehicle-bridge coupling vibration of a continuous semisteel bridge, the main bridge type of long-span prestressed concrete girder bridge, the author proposes a bridge safety test system based on the dynamic and static load test. The system combines the change of stress and deflection with the vibration amplitude of the bridge body, and using the modeling assistant in large-scale finite element software MIDAS/CIVIL, a three-dimensional finite element real bridge model is established, including input of section data, the input of boundary conditions, and the input of loads. The result obtained is as follows: the structural verification coefficient of the control strain of the main girder under each working condition is not greater than 1.0, indicating that the flexural rigidity of the structure meets the design requirements. In addition, under each working condition, the ratio of the residual strain after unloading to the measured total strain is less than 20%. Under each working condition, the deflection calibration coefficient of each control section is less than 1.0, and the ratio of residual deflection to total deflection of each measuring point is at most 3.9%; each residual deflection is small. The damping ratios are all less than 5% of the empirical damping ratio of concrete members, indicating that the bridge structure is in good condition. The result obtained by the author is compared with the standard allowable value and the theoretical calculation value, so as to provide a basis for the study of the bearing capacity of similar bridges and to verify the standardization and rationality of the existing bridge structural design.

EVALUATION AND COMPARISON OF LOAD DEFLECTION RATE OF FOUR INITIAL ORTHODONTIC ARCH WIRES: AN IN VITRO STUDY

Aim: The aim of this study was to evaluate the load-deflection rate of four different types of archwires used in initial stage of orthodontic treatment.
 Materials and methods: A modified three-point bending test was performed on the sample of 60 wires of superelastic Nickel Titanium(NiTi), everwhite esthetic NiTi, thermal NiTi and multistranded coaxial stainless steel (15 each). The load exerted by each of the wire was measured at the deflections of 2 mm and 4mm, subsequent unloading process at 37°C temperature.
 Results: Comparison of mean load-deflection values revealed that thermal NiTi wires had lowest value at both 2 and 4mm deflection when compared to other three wires which was statistically significant(p=0.009). Superelastic and esthetic NiTi showed similar values of load deflection ratios at both the deflections where as co-axial wire showed 1.89N at 2mm and 5.22N at 4mm deflection.
 Conclusion: The heat-activated NiTi wires are acceptable in severe crowding and periodontally compromised patients. Multistranded co-axial wire is acceptable when we need minimal alignment; whereas esthetic NiTi wires can replace superelastic Niti based on patient’s need.

Long-Term Loading Experimental Research of Prestressed Glulam Beams Based on Creep Influence

In this paper, long-term loading tests of ten prestressed glulam beams were carried out for 45 days, using the loading method of three-point hanging heavy objects. We analyzed the influence of prestressed steel wire numbers and total preloading force on parameters such as failure mode of beams, variation of steel wire stress, and long-term deflection of mid-span. When the total prestress was constant and the number of steel wires was 2, 4, and 6, the total stress of steel wires decreased by 33.07%, 37.26%, and 50.04%, respectively, after long-term testing for 45 days. The ratio of mid-span deflection to total deflection was 61.5%, 54.8%, and 40.9% respectively. When the number of steel wires was constant and the values of total prestress were 0, 3.079 kN and 6.158 kN, the total stress decreased by 28.90%, 36.59%, and 36.63%, respectively, after long-term loading. The ratio of long-term deflection of mid-span to total deflection was 60.7%, 54.8%, and 39.3%, respectively. The more steel wires, the greater the value of total prestress and the loss of total stress, the smaller the mid-span long-term deflection. After the test, we analyzed and fitted the test data to obtain the specific numerical of the creep coefficient θ under normal conditions, and the formula for calculating the long-term stiffness of the glulam beams based on the creep effects is proposed.

Simulation of Shear Capacity of Reinforced Concrete Column with Variation of Stirrups Using Finite Element Method Analysis

Shear failure of column causes the column to have shear reinforcement that cannot withstand shear forces so that it loses of lateral strength quickly. This research aims to see the effect of the configuration with the addition of shear reinforcement in the direction and perpendicular to the direction of the shear force on the capacity of reinforced concrete columns that are loaded with axial and lateral loads. The test was carried out by providing a constant axial load (0.3 P0) followed by a shear load until the test object failed. The numerical analysis was carried out using software based on the finite element method, namely ATENA Version 5 and GID Version 13.0.1 developed by Cervenka Consulting. This study used reinforced concrete with three variables of shear reinforcement. It can be the normal columns without stirrup reinforcement (S0P2), the addition three (3) stirrups in the direction of the shear reinforcement (S4P2) and the addition of two (2) stirrups in the direction of the shear reinforcement and one (1) stirrups perpendicular to the shear reinforcement (S5P2). After the numerical analysis is carried out, the results are verifies using experimental testing. The numerical analysis and experimental results give the load and deflection relationship results that are almost close. Therefore, the difference in shear loads compared to the experiments results and numerical analysis on columns S0P2, S4P2, and S5P2 is 0.11%, 3.95% and 1.16%, respectively, with a deflection ratio of 4.72%, 37.80% and 9.44%. The pattern of column destruction in the numerical model resembles the destruction pattern of the experimental results, both of which indicate that the column has shear cracks.

Impact of polyethylene fiber reinforcing index on the flexural toughness of geopolymer mortar

Geopolymer is a green and eco-friendly potential alternative to Portland cement. Adding fiber can overcome the brittleness and increase the toughness of Portland cement and geopolymer based composites. However, it is not clear how the characteristics of fibers affect the toughness of geopolymer composite accurately. Hence, in this paper, the influence of polyethylene (PE) fiber reinforcing index (RI) on various toughness parameters of geopolymer mortar, including toughness index (TI), flexural toughness (FT) and equivalent flexural strength (EFS) was estimated according to ASTM C1018 and JSCE-SF4, respectively. Generally, the TI, FT and EFS of geopolymer composite were all improved with the growth of PE fiber RI. Good quadratic function relationships between TI, FT, EFS and RI were developed. The RI value of 200 and 450 were thresholds for PE fiber reinforced geopolymer composite, corresponding to the loosely and the close packing conditions. With similar RI, the peak load and TI of PE fiber reinforced geopolymer composite were both higher than that of Portland cement-based composite, due to the higher bonding strength between fiber and matrix in geopolymer. When RI increased from 0 to 691.2, the quantity of cracks was increased from 1 to more than 20, and crack morphology was changed from straight to very zigzagging. The relationship between flexural toughness index and fracture fractal dimension was quadratic function, and the correlation was increased with the increase of special deflection and water-binder ratio. This study will help to predict the flexural toughness of fiber-reinforced geopolymer composites.

Seismic Response of Slab Column Connection with Pyramid Shaped Drop Panel

Both experimental and finite element analysis (FEA) was used to study the seismic response of reinforced concrete (RC) interior slab-column connection made with pyramid-shaped drop panel subjected to vertical and horizontal loads. The dimensions of the models at “¼ ” linear scale for laboratory testing and FE Analysis (FEA) are derived from rules for dimensions of column drops, given a prototype “9.60m” grid and a slab thickness of “320mm”. Lab specimens were tested with the drops (flat slab, rectangular and pyramid-shaped) facing up, with loadings (vertical down and horizontal in grid direction) applied by jacks towards the top of a central projecting “150mm” square column. One flat slab (“80mm” thick no drop), tested to failure under vertical load (80kN), provided values for setting variables used in the FEA. The remaining 5 lab specimens (1 flat and 1 each rectangular and pyramid-shaped 40mm and 30mm drop thicknesses), under a fixed vertical load (40kN), were tested to failure by increasing a moment at the column slab junction applied by a horizontal load to the column “500mm” above the slab. FEA results for the same conditions compared closely with experimental results. The pyramid-shaped drop models, with equal thickness to the rectangular drop models at the column faces (drops of “40mm” and “30mm”), exhibit similar maximum force resistances to the rectangular drop models. However, these resistances were achieved in the pyramid drops at higher maximum deflections – deflections being measured downwards at column centerline one half of slab thickness away from the face. A parametric study was conducted by FEA, at constant load, in vertical steps (10kN; 25kN 55kN), calculating deflections under increasing horizontal load. Calculations were made on the following definitions: Energy absorption is represented by the area under the deflection vs horizontal load curves; Ductility is the ratio of deflection at maximum to deflection at yield, and Stiffness and Overstrength factors are the slopes of the deflection load diagrams in the elastic and plastic zones respectively. Both drop type models exhibit significantly improved performance compared to the models without drops. The pyramid-shaped drop models exhibited improved energy absorption, ductility, and stiffness and overstrength compared to the rectangular drop models of the same column face thickness.

Optical tweezers assisted analyzing and sorting of tumor cells tagged with fluorescence nanospheres in a microfluidic chip

Due to the vital role of studying a single tumor cell, it is meaningful to establish a compatible means to realize the analysis and sorting tasks. Despite plentiful strategies have been developed, there is still a challenge to develop a fully integrated approach to be directly used in biological samples. As such, we present here a special fluorescence activated cell sorting platform assisted by optical tweezers (FACS-OT) in a microfluidic chip. To begin with, according to the significant differences in the protein expression level of cell surface, two kinds of cells are severally immunotagged with quantum dots embedded two-color fluorescent nanospheres. And then, by the home-built setup, different cells are stably and accurately detected one by one for single-cell level with two-color fluorescence resolved in the microfluidic chip. Finally, the home-built apparatus of FACS-OT is successfully used for highly precise deflection of targeted cells (deflection ratio of 95.7%) under the radiation of optical force. In addition, the results of simulation agree with our experiment, which offer a stable platform for further application. In line with above efforts, we establish a special platform by automatic analysis and deflection of single cell, offering a special strategy for studying heterogeneity in single cell.

The behavior of cross-laminated timber and reinforced concrete floors in a multi-story building

The behavior of cross-laminated timber (CLT) and reinforced concrete (RC) floors in a multi-story building is investigated in this paper. The load-bearing capacity, fire resistance, and sound insulation characteristics of the floors are the main focus of this research. In order to achieve this goal, a four-story building having RC floors is modeled, analyzed, and designed using the StruSoft FEM-Design software (FEM) following the Eurocodes and Swedish national annex. The building is considered to be in the city of Gävle in Sweden. Then, the RC floors of the building are replaced with the CLT floors, and the same process is done utilizing FEM. The utilization ratios (the ratios of the applied loads to the load-bearing capacities), vertical deflections, weights of the RC and CLT floors, and reaction forces of the buildings are evaluated and compared. The results show that the RC floors meet the deflection requirements well which contributes to the focus on their utilization ratios. The designed RC floors are acceptable from the vertical deflection and utilization ratio perspectives. However, the CLT floors cannot meet the vertical deflection requirements, and thus, need strengthening. The CLT floors are strengthened with supporting timber beams and columns which result in acceptable vertical deflections and utilization ratios. Fire resistance and sound insulation conditions of the RC and CLT floors are assessed by calculations based on the requirements of the Swedish National Board of Housing, Building, and Planning regulations (BBR) as well. The RC floors have the ability to be soundproof and have no difficulties in meeting the fire resistance requirements R60 of BBR. A cross-section is proposed for the CLT floors which can meet the fire resistance requirement R60 and sound insulation requirement C of BBR. The maximum reaction forces of the buildings and total weights of the floors are larger in the case of RC than CLT.

Experimental validation of FEM-computed stress to tip deflection ratios of aero-engine compressor blade vibration modes and quantification of associated uncertainties

Blade Tip Timing (BTT) technology is concerned with the estimation of turbomachinery blade stresses. The stresses are determined from BTT data by relating the measured tip deflection to the stresses via Finite Element (FE) models. The correlation of BTT measurements with FE predictions involves a number of uncertainties. This paper presents the process for validating the FE stress and deflection predictions of aero-engine compressor blades under non-rotation conditions as a critical preliminary step towards the complete understanding of their dynamic behaviour under rotating conditions when using BTT measurements. The process steps are described in detail, including the FE modelling and analysis of the blades and the blade-disk assembly, and the measurements of the blade tip deflection and blade stress. Furthermore, the uncertainties associated with the FE modelling and the measurement processes are quantified. The results show that the FE model is valid considering the control of most uncertainties. The experimental validation of the FE-computed stress-to-tip deflection calibration factors in the present study provides the basis for the determination of the calibration factors under rotational conditions using a previously presented BTT data simulator, and for the design of corresponding rotating experiments using BTT.

Shear and Flexural Behavior of Flat Slabs Casted with Polyolefin Fiber-Reinforced Concrete

This paper presents the influence of polyolefin fiber on the flexural and shear attitude on the flat slabs. Three slab sets (80 cm × 80 cm) were tested, each with a thickness of 10 cm. In the first set (S1), the effect of fiber content on the flexural behavior of the flat slab was considered. Therefore, four slab specimens were cast, one of which was considered as a control specimen with no fiber content, while the other three included fibers at 0.5, 1, and 1.5 percent of the total concrete volume. The second series of experiments studied the flexural behavior of flat slabs (S2) with an opening of 15 cm × 15 cm. The first specimen contained nil polyolefin, while the second included 1% polyolefin. In the third set (S3), consideration was taken for 0 and 1% of Polyolefin to realize the shear behavior of the flat slab. The increase in polyolefin fiber content from 0 to 1.5% (for slab set 1) will decrease the deflection from 4.5 mm to 2.3 mm, with an average of 3.58 mm, which is close to the deflection of a 1% polyolefin fiber specimen. Three dimensional models for the tested slabs were simulated numerically via ABAQUS software program. The ratio of the maximum deflection between the experimental and the numerical outcomes were varied with a range of 1.01 to 1.28, with an average of 1.14.

Peel-off behavior of a double-plate adhesion system

Peeling and adhesion mechanics of slender structures is of great significance in engineering and science. For a complex adhesion system with soft and slender structures, predicting its deformation can be highly difficult due to the nonlinear nature of the associated governing equations. Additionally, due to the unknown parameters in the highly nonlinear governing equations, it is impossible to solve the governing equations by the standard numerical method directly. In this paper, we perform an elaborate study on the peel-off behavior of two circular adhesive plates in the displacement-controlled cases from the theoretical and numerical perspectives. The governing equations of the system are derived using the energy method based on the finite deformation theory. Since there are many unknown parameters in the governing equations, we adopt an optimization-based approach to determine the peel-off radius as well as the motion parameters at the interface between the peel-off region and the adhesion region. The numerical examples in this work reveal that the peel-off radius becomes larger with the increase of the applied deflection ratio between two plates. We also observe that the infinitesimal deformation theory always underestimates the peel-off radius and this underestimation can lead to as high as 10% error in the predicted peel-off radius. Overall, this work proposes a novel optimization-based method to study peeling mechanics of a double-plate adhesion system and can be generalized to more sophisticated cases. The results of this work can also provide some insights for us to understand the peeling phenomena of an adhesion system.

Electric field-induced nonlinear behavior of lead zirconate titanate piezoceramic actuators in bending mode

In this article, analytical solutions of piezoelectric bimorph and unimorph actuator in cantilever configurations are developed using the second-order constitutive equation. Tip deflection ratio (TDR), a dimensionless parameter, is defined to analyze the effect of second-order coefficients of piezoelectric materials on the response of bimorph and unimorph actuators. Four piezoelectric unimorphs of varying geometries are fabricated and tested to verify the nonlinear response under applied electric field. Furthermore, second-order coefficients of lead zirconate titanate (PZT; APC 850) are derived by fitting the experimental data with nonlinear analytical solution. The nonlinear response of all the piezoelectric unimorphs compares well with the experimental results.

Fragility curves for different classes of existing RC buildings under ground differential settlements

Existing reinforced concrete (RC) buildings can be affected by different actions that can induce permanent or transient effects on them. While applications concerning the seismic vulnerability of existing RC buildings have been largely proposed in literature, the evaluation of the structural vulnerability because of hazards different from earthquake has been less dealt with. The focus of this work is to estimate the probability that the simulated RC buildings stock could reach a given Limit State for a certain intensity of imposed monotonically increasing ground differential settlements. A set of simulated FEM models, considering the geometrical and mechanical uncertainties in the representation of the existing RC frame buildings designed only for gravitational loads, has been created. The structural frames differ from each other for geometrical features and mechanical materials properties, obtained through a simulation process. The non-linear behavior of columns and beams is considered by applying a modeling approach specifically elaborated for RC members with plain bars. A FEM model for each simulated structural frame has been developed using the Open Application Programming Interface by using the programming and numeric computing platform MATLAB to run the modelling software SAP2000. Time by time, by scaling up the amplitude of the imposed base displacements, a non-linear static incremental procedure has been implemented. At each step of the analysis, a code-based seismic safety assessment has been carried out with reference to a specific ultimate Limit State considered in the Italian and European codes. The goal of the analysis has been to find the values of the significative structural response parameters (identified in this work as the maximum differential settlement and the deflection ratio) at the onset of the selected Limit State by using the critical demand to capacity ratio. Considering that these values are lognormally distributed, the structural fragility is then derived, showing how the vulnerability of the considered RC buildings stock is affected by the impact of the geometrical features and by the application direction of the differential settlements.