Single Soil Layer Research Articles

On the reduction of FEM models dealing with vibrations propagation from ground to buildings

The problem of ground-borne vibrations in contact with a building's basement is crucial to the comfort of people living in buildings located very close to roads or railway tracks. The numerical finite elements models used to describe this situation are heavy to compute: it must combine the complexity of the building with the large dimensions of the soil. We propose a method to reduce the model computation cost while keeping accurate results. The goal of our study is to remove the ground from the model by applying efforts and boundary conditions to the building foundation to reproduce the soil/structure interactions. The full model of a simple building with a basement on a single-layer soil is studied to extract the coupling stresses. Corresponding efforts are applied to the building alone, with several boundary conditions tested. The results show similar vibration levels on the building floors, for a far lower time of computation.

A Method for Determining the Fundamental Site Period and the Average Shear Wave Velocity

The soil–structure interaction plays a crucial role in determining the displacement and internal forces of multi-story buildings subjected to strong ground motion. One of the critical dynamic characteristics influencing soil–structure interaction is the fundamental site period and the average shear wave velocity associated with it. This study introduces an original equation to determine these parameters. In addition, for the first time in the literature, the version of the Rayleigh method used for finding the fundamental periods of buildings is used to find the fundamental site period. The soil is modeled as an equivalent shear beam to obtain the proposed equation. The peak displacement is obtained by acting the soil mass as an external load on the equivalent shear beam. For single-layer soil, the fundamental site period is proportional to the square root of the peak displacement of the equivalent shear beam. The least squares method generalizes the proposed relation for single-layer soils to multi-layer soil profiles. Modified Finite element Transfer matrix method is used for calibration in the least squares method. The equations used in the literature and earthquake codes for determining the fundamental site period and average shear velocity are tested on various examples, and it is shown that the method proposed in this study, along with the Rayleigh method, gives better results than these equations. The performances of these two methods and the five commonly used equations are tested and compared on different soil profiles. Transfer functions, Finite Element Method (SAP200) and Modified Finite Element Transfer Matrix Method are used for verification. For all soil profiles, the results obtained from the transfer function, Finite Element Method (SAP200) and Modified Finite Element Transfer Matrix Method are found to be in agreement. The true percent relative error found in the results obtained with the proposed method is 4.47%.

Pullout behaviour of strip plate anchors in clay overlying sand

Plate anchors are being increasingly employed to establish mooring systems for offshore floating facilities owing to their notable efficiency and cost-effectiveness. The majority of prior studies have concentrated on plate anchors, examining the vertical to horizontal orientations, particularly when embedded in single layer clay or sand. However, it is common to encounter multiple layers of soil with varying characteristics in practical engineering, leading to inaccurate estimation of pullout capacity when based solely on the properties of a single soil layer. This paper reports pullout behaviours of strip plate anchors in clay overlying sand by adopting two dimensional finite element analysis. To simulate the hardening and subsequent softening behaviour of medium to dense sand, a modified Mohr-Coulomb model is considered. The current Finite Element (FE) results are in good agreement when compared with both previous FE simulations and physical model test data. Then, the soil flow mechanisms (e.g. the accumulated plastic shear strain, the friction angle) surrounding the anchor during pullout out are revealed. Based on a series of FE results, a calculation framework considering the effect of thickness of clay layer is designed to predict the pullout behaviour of plate anchors in clay overlying sand.

Water use characteristics and the mechanism of water uptake in two typical sand-fixing species in Mu Us sandy land

Understanding water absorption mechanisms of sand-fixing plants is important for the rational establishment of plant community structures, thereby providing a scientific basis for desertification control and the efficient utilization of water resources in sandy areas. Based on the hydrogen and oxygen isotopic compositions of precipi-tation, soil water, xylem water, and groundwater, coupled with soil water-heat dynamics, annual water consumption characteristics of vegetation, using the multi-source linear mixing model (IsoSource), we analyzed the differences in water sources between Salix psammophila and Artemisia ordosica, during winter and the growing season. We further examined the effects of groundwater depth (2 m and 10 m), soil freezing-thawing, and drought on their water utilization to elucidate water absorption mechanisms of those species. The results showed that: 1) During soil freezing-thawing period (January to March), S. psammophila mainly utilized soil water in 60-120 cm depths below the frozen layer (69.1%). In the green-up season (April and May), soil water from the 0-60 cm layers could satisfy the water demand of S. psammophila (30.9%-87.6%). During the dry period of the growing season (June), it predominantly utilized soil water at the depth of 120-160 cm (27.4%-40.8%). Over the rainy season (July and September), soil water in 0-60 cm depths provided 59.8%-67.9% of the total water required. A. ordosica, with shallow roots, could not utilize soil water after complete freezing of root zone but could overwinter by storing water in rhizomes during autumn. During the growing season, it primarily relied on 0-40 cm soil layer (23.4%-86.8%). During the dry period, it mainly utilized soil water from 40-80 cm and 80-160 cm soil layers, with utilization rates of 14.6%-74.4% and 21.8%-78.2%, respectively. 2) With decreasing groundwater depth, vegetation shifted its water absorption depth upward, with water source of S. psammophila transitioning from 120-160 cm to 60-160 cm layers, while A. ordosica shifted water absorption depth from 80-160 cm to 0-40 cm. S. psammophila's utilization of soil water is influenced by transpiration, adopting an "on-demand" approach to achieve a balance between water supply and energy conservation, whereas A. ordosica tends to utilize shallow soil water, exhibiting a higher depen-dence on water sources from a single soil layer.

Snow water equivalent retrieved from X- and dual Ku-band scatterometer measurements at Sodankylä using the Markov Chain Monte Carlo method

Abstract. Radar at high frequency is a promising technique for fine-resolution snow water equivalent (SWE) mapping. In this paper, we extend the Bayesian-based Algorithm for SWE Estimation (BASE) from passive to active microwave (AM) application and test it using ground-based backscattering measurements at three frequencies (X and dual Ku bands; 10.2, 13.3, and 16.7 GHz), with VV polarization obtained at a 50° incidence angle from the Nordic Snow Radar Experiment (NoSREx) in Sodankylä, Finland. We assumed only an uninformative prior for snow microstructure, in contrast with an accurate prior required in previous studies. Starting from a biased monthly SWE prior from land surface model simulation, two-layer snow state variables and single-layer soil variables were iterated until their posterior distribution could stably reproduce the observed microwave signals. The observation model is the Microwave Emission Model of Layered Snowpacks 3 and Active (MEMLS3&a) based on the improved Born approximation. Results show that BASE-AM achieved an RMSE of ∼ 10 cm for snow depth and less than 30 mm for SWE, compared with the RMSE of ∼ 20 cm snow depth and ∼ 50 mm SWE from priors. Retrieval errors are significantly larger when BASE-AM is run using a single snow layer. The results support the potential of X- and Ku-band radar for SWE retrieval and show that the role of a precise snow microstructure prior in SWE retrieval may be substituted by an SWE prior from exterior sources.

The Impact of Fine-Layering of Tailings Dam on the Variation Pattern of Infiltration Lines

The type of soil and its compactness significantly influence its permeability coefficient, which in turn affects the drainage difficulty of soil pore water and the distribution of the infiltration line. However, current tailings dam models typically consider only a single soil layer instead of taking into account the differences in soil types and compactness, resulting in a deviation between simulated results and actual conditions. To address this issue, this study proposes three models with a gradually increasing degree of layering refinement based on soil type and compactness. These models aim to simulate the variations in the infiltration line under three different strategies: constant head, rainfall, and drainage. The simulation results indicate that the average increase in the infiltration line of the three schemes after rainfall is 46.2%, 65.88%, 83.52%, respectively; the fitting percentages for each scheme of infiltration line after 720 days of drainage and the constant head stage are 72.38%, 88.27%, and 93.61%, respectively. It can be seen that the higher the refinement level of the layered model, the more sensitive it is to changes in the infiltration line. Furthermore, as the refinement level of the layered model increases, the simulation effect on the changes in the infiltration line improves, and the simulated results become more consistent with the actual situation. This finding provides a strategy and possibility for the study of the tailings dam’s infiltration lines, safety, and stability.

Simulating the Detection of the Global 21 cm Signal with MIST for Different Models of the Soil and Beam Directivity

The Mapper of the IGM Spin Temperature (MIST) is a new ground-based, single-antenna, radio experiment attempting to detect the global 21 cm signal from the Dark Ages and Cosmic Dawn. A significant challenge in this measurement is the frequency dependence, or chromaticity, of the antenna beam directivity. MIST observes with the antenna above the soil and without a metal ground plane, and the beam directivity is sensitive to the electrical characteristics of the soil. In this paper, we use simulated observations with MIST to study how the detection of the global 21 cm signal from Cosmic Dawn is affected by the soil and the MIST beam directivity. We simulate observations using electromagnetic models of the directivity computed for single- and two-layer models of the soil. We test the recovery of the Cosmic Dawn signal with and without beam chromaticity correction applied to the simulated data. We find that our single-layer soil models enable a straightforward recovery of the signal even without chromaticity correction. Two-layer models increase the beam chromaticity and make the recovery more challenging. However, for the model in which the bottom soil layer has a lower electrical conductivity than the top layer, the signal can be recovered even without chromaticity correction. For the other two-layer models, chromaticity correction is necessary for the recovery of the signal, and the accuracy requirements for the soil parameters vary between models. These results will be used as a guideline to select observation sites that are favorable for the detection of the Cosmic Dawn signal.

Comparative Study of the Seismic Response Characteristics of Three Special Soils

Because of its special material composition, formation environment and special structure, special soil usually shows different seismic response characteristics from general soil, and sometimes causes serious seismic disasters. Therefore, the study of seismic response characteristics of special soil has important practical significance for engineering construction and disaster prevention in special land areas, and a site seismic response analysis is an important way to study the impact of site conditions on ground motions. Based on the existing research work, the uniform and single ideal soil layer profiles of three special soils are established, and the seismic response analysis program of the soilquake soil layer is used to study the effects of the dynamic shear module ratio, damping ratio and shear-wave velocity of soft soil, loess and laterite on the characteristic period and platform value of the design response spectrum under different input ground motion intensities. At the same time, three typical actual drilling data values are selected to establish the calculation model of the site soil layer. On the basis of the seismic response analysis and calculation of the soil layer, three special soil dynamic characteristics are compared from the aspects of peak acceleration and characteristic parameters. Based on the research results of this paper, the recommended values of the dynamic shear module ratio and damping ratio of three special soils are given. This work has important reference value for seismic design in soft soil, loess and laterite areas, and also enriches the research results of soil dynamic parameters.

Permeable reactive composite approaching cathode enhanced Cr removal in soil using the byproduct of electrokinetic technology: emphasized energy utilization efficiency.

Cost-effective techniques with significant removal rates and low energy consumption are urgently required for in-situ Cr-contaminated soil remediation to reduce potential environmental toxicity to the ecosystem and human bodies. Electrokinetic technology is a valuable and promising soil remediation technology; however, the acidic and alkaline fronts evolutioninduced by the electrokinetic byproducts (H+, OH-) has significant hindering characteristics for ion removal. To effectively utilize the byproducts for enhancing Cr elimination, this paper proposed the permeable reactive composite approaching cathode with rhamnolipid-modified biochar as reactive material. Power utilization efficiency (η) was presented to comprehensively evaluate the target species elimination effect, considering removal rate and energy consumption. Results suggested that biosurfactant rhamnolipid stimulated Cr removal in acid and base fronts. Acid front induced rhamnolipid protonation reducing anolyte Cr(VI) to Cr(III), and base front induced rhamnolipid deprotonation complexing with Cr(III) and expediting Cr(VI) dissolution by electrostatic repulsion. Permeable reactive composite approaching cathode induced the maximum removal rate of Cr(VI) and Cr(III) in each section by impelling the alkaline front. Approaching cathode caused increased resistance and energy consumption in the near-anode regions, ultimately decreasing energy utilization efficiency. Optimized moving frequency and applied potential magnitude could adjust power consumption distribution in a single soil layer to obtain better electrokinetic removal performance of contaminates. This work provided essential scientific and practical importance for in-situ electrokinetic remediation of Cr(VI) and Cr(III), considering elimination efficiency and energy consumption in the future.

Prediction of nonlinear seismic response of underground structures in single- and multi-layered soil profiles using a deep gated recurrent network

A deep learning method consisting of the gated recurrent (GRU) neural network is proposed to predict the seismic responses of underground structures in single-layered soil and multi-layered soil. The proposed neural network employed ground motion as the input, and the acceleration time history of underground structure acquired by a finite element method (FEM) to be the output. The distribution of the normalized errors and the error of the peak value of the predicted acceleration time history are adopted to evaluate the prediction performance and extrapolating ability of the proposed GRU architecture. The GRU network showed better prediction performance in the seismic response of a tunnel in a homogeneous sand layer than in a clay layer, as sand has a higher shear modulus representing lower nonlinearity of the soil-structure system. The peak acceleration of a two-story three-span subway station in multi-layered soil exhibited similar prediction accuracy to the tunnel in single-layered clay. The proposed GRU neural network generally displayed satisfactory prediction performances on the acceleration responses of underground structures in various soil conditions.

Using principal component analysis to incorporate multi-layer soil moisture information in hydrometeorological thresholds for landslide prediction: an investigation based on ERA5-Land reanalysis data

Abstract. A key component for landslide early warning systems (LEWSs) is constituted by thresholds providing the conditions above which a landslide can be triggered. Traditionally, thresholds based on rainfall characteristics have been proposed, but recently, the hydrometeorological approach, combining rainfall with soil moisture or catchment storage information, is becoming widespread. Most of the hydrometeorological thresholds proposed in the literature use the soil moisture from a single layer (i.e., depth or depth range). On the other hand, multi-layered soil moisture information can be measured or can be available from reanalysis projects as well as from hydrological models. Approaches using this multi-layered information are lacking, perhaps because of the need to keep the thresholds simple and two-dimensional. In this paper, we propose principal component analysis (PCA) as an approach for deriving two-dimensional hydrometeorological thresholds that use multi-layered soil moisture information. To perform a more objective assessment we also propose a piecewise linear equation for the identification of the threshold's shape, which is more flexible than traditional choices (e.g., power law or bilinear). Comparison of the receiver operating characteristic (ROC) (true skill statistic, TSS) of thresholds based on single- and multi-layered soil moisture information also provides a novel tool for identifying the significance of multi-layered information on landslide triggering in a given region. Results for Sicily island, considering the ERA5-Land reanalysis soil moisture data (available at four different depth layers), corroborate the advantages of the hydrometeorological approach gained in spite of the coarse spatial resolution and the limited accuracy of reanalysis data. Specifically, the TSS of traditional precipitation intensity–duration thresholds is equal to 0.5, while those of the proposed hydrometeorological thresholds is significantly higher (TSS=0.71). For the analyzed region, however, multi-layered information seems not to be relevant, as performances in terms of TSS are similar to those obtained with single-layer soil moisture at the upper depths, namely 0–7 and 7–28 cm, which can imply that in Sicily landslide phenomena are mainly influenced by soil moisture in most shallow soil layers.

ANALYSING THE EFFECT OF DISCONTINUITY OF ELECTRICAL CONDUCTIVITY OF SOIL ON GROUND RESISTANCE

In addition to the direct application of the method of images the article also shows the application of complex images in the cases with two or more discontinuity boundaries of the specific electrical conductivity. The article analyzes the effect of neglected images in determining ground resistance, in a single-layer soil model, and goes on to analyse the error due to modelling single-layer soil which by its characteristics is most accurately described as double-layer. In modelling the soil the technique of simple and complex images was applied. To keep the presentation simple and make the models comparable, a normal horizontally inserted cylindrical conductor was taken as ground conductor. The results obtained are shown analytically and graphically and discussed.

Stability Analysis of 3D Tunnel Face of Shallow Rectangular Shield Tunnel

In recent years, an increasing number of rectangular excavation sections have appeared in pipe-jacking shield tunnel projects. In previous studies, calculating the stability of a tunnel face in a noncircular shield tunnel usually required a circular section. It is carried out according to the principle of equivalent areas. Although this method makes it easy to calculate the stability, deviation still occurs. To solve this issue, the rectangular shield tunnel is used as the research object. Spatial discretization technology is used to extend the rotational failure mechanism of 3D rigid blocks to the tunnel face of rectangular tunnels. Moreover, it is accomplished under the theoretical background of the upper bound method. The MATLAB calculation results were compared with FLAC3D, and the process proved to have sufficient accuracy and a high efficiency. Then, the influences of the failure modes and limit support pressure by dimensionless parameters are studied. The results show that the parameters that have a great impact on the failure region and stability of the tunnel face are H/D, C/D, and the internal friction angle ϕ, and the parameters that have little influence on them are σs/c and γD/c. Finally, a dimensionless parameter design chart that has a limit support pressure with a rectangular tunnel and a single homogeneous frictional soil layer is drawn and fitted using a ternary quadratic polynomial. Furthermore, it can be used for preliminary design.

Research on Displacement Field of Soil around Pile with Different Density Based on Particle Image Testing Technology

Particle image testing technology has the advantages of non-intervention and high precision. In this paper, the particle image testing technology is combined with the indoor model test to explore the displacement development trend of the soil around the horizontal loaded pile under the difference of soil properties between layers. The principle of PIV technology is described, and the single-layer soil test group and the layered soil test group are set up, respectively. To this end, the indoor model test is carried out by changing the soil density. The study reveals that particle image testing technology can reduce the influence of data acquisition equipment on model tests in the maximum range, and restore the development trend of surface soil displacement in the horizontal load pile test to the greatest extent. Under the same load, the displacement influence area formed in front of and behind the pile of the two groups of tests takes the shape of a spindle centred on the pile body. The influence range of surface soil decreases with the increase of density. Moreover, the results of Tecplot analysis show that the soil stiffness is ranked from small to large as follows: single layer coarse sand, upper layer large particle size and lower layer small particle size test group, upper layer small particle size and lower layer large particle size test group, single layer fine sand. The test results can provide reference for the deepening of practical engineering.

Research on Leakage Mechanism of Underwater Shield Tunnels with Different Soil Layers during Operation Period

Different soil layer properties have great influence on tunnel leakage. In this paper, the finite element software is used to analyze the homogeneous leakage model of different soil layers and different degrees of lining deterioration. The working conditions of different soil layer properties and different degrees of lining deterioration are established by means of soil layer permeability coefficient and lining permeability coefficient, and the law of tunnel leakage under each working condition is analyzed. This paper innovatively explores the relationship between the severity of tunnel seepage caused by different lining deterioration and the soil layer properties of the tunnel. Finally, by comparing the field survey data of Dinghuaimen with the leakage law and mechanism summarized by the model, the reliability and feasibility of the model method to explore the leakage mechanism are verified. The model test results are consistent with the project survey data. In this paper, the seepage law and mechanism of underwater shield tunnel are explored and the result shows: (1) The leakage laws and stress distribution laws of a single homogeneous soil layer with different strata properties are similar. The flow velocity in the lower half of the tunnel lining is greater than the upper half, and the maximum velocity occurs at the arch foot; the velocity inside the lining is much smaller than that inside the soil layer. The maximum absolute value of the axial stress of the lining occurs at the arch waist on the left and right sides, and the minimum values of the axial stress of absolute values all occur at the dome. (2) The leakage of underwater tunnels is related to the properties of soil layers. The larger the soil permeability coefficient is, the more serious the deterioration of the tunnel lining will be, and the more serious the tunnel leakage will be. (3) The leakage of complex strata follows the law of leakage in a single homogeneous stratum. The leakage of the tunnel is the most serious in the fine sand layer with the largest permeability coefficient. Moreover, when the seepage phenomenon occurs, the water flow tends to seep along the fine sand layer to the tunnel.

Modified pseudo-dynamic based soil-structure interaction of caisson with a novel 3D failure wedge

Passive resistance computation for caissons embedded in layered soil is a complicated problem. In the present study, modified pseudo-dynamic method of analysis has been used to determine both amplification of earthquake waves through the soil strata and the resulting passive earth pressure on the embedded structure. The failure wedge has been idealized based on the results of experimental and numerical studies by previous researchers as log-spiral in vertical plane and oval in the horizontal plane. Earthquake waves are assumed to propagate harmonically in vertically upward direction through layered strata considering modified pseudo-dynamic approach with the entire failure wedge assumed to be lying in a single soil layer. Both, dry and submerged soil conditions, have been considered in the present study. The effect of increase in volume of failure wedge compared to corresponding plane strain condition on earth pressure coefficient has also been discussed in the current study. The earth pressure coefficient due to unit weight component has been reported. The earth pressure coefficient obtained from the current study for structures of different widths are found to be smaller in magnitude than corresponding pseudo-static analysis results.

Functionally Graded Materials Pile Structure for Seismic Noise Cancellation

This study explores surface-wave propagation through periodic arrangements of multilayered piles in a single-layer soil medium from the viewpoint of bandgaps. The influence of the geometrical parameters of the model on the bandgaps is discussed. The periodic theory of solid-state physics is imposed to derive the dispersion equation. The finite-element method is implemented to calculate the dispersion relation and attenuation zones for surface waves in a periodic pile and soil system. The results show that the bandgaps are sensitive to the size and arrangement of the piles. The practicability of ground vibration-isolation by periodic pile barriers are verified in the time domain. The location and width of bandgaps are further authenticated through finite unit cell–based frequency response analyses. It is found that the frequency range of the Rayleigh wave reduction agrees well with the theoretical attenuation zone. This work provides new insights into the design of periodic piles as wave barriers. This approach has scope for protecting infrastructures, such as nuclear power plants, which pose high environmental risks. It is found that the dispersion analysis gives essential information for Rayleigh wave isolation using piles, including the frequency range and the form of decline.

Theoretical and numerical approaches to analyze gravity installed anchors in multi-layered clays

Gravity installed anchors (GIAs) are designed to dive into deeper seabed under cable loading to seek higher capacity, typically for OMNI-Max anchors. This feature makes the anchors more likely to penetrate through different soil layers, leading to more complicated behaviors than in single-layered soil. Furthermore, the behavior of anchor lines in multi-layered soils becomes more complicated and significantly affects the anchor behaviors. All of these bring challenges to the trajectory prediction of GIAs in the multi-layered seabed. The present work introduces theoretical and numerical approaches to predict the comprehensive behaviors of GIAs by dealing with the coupled effect of anchor lines in multi-layered clays. The theoretical and numerical models are verified by comparing with the published data of centrifuge tests and numerical simulations. The comparative study indicates that both the models have the ability to explore the effects of different factors, such as the embedment depth, the soil strength, the thickness of layers and the distribution of multi-layered soil. The complexity and variety of anchor behaviors in multi-layered clays are revealed by typical application cases, further confirming the ability and potential of the developed models.

Upscaling point-scale soil hydraulic properties for application in a catchment model using Bayesian calibration: An application in two agricultural regions of New Zealand

Hydrological modeling for landscape and catchment scale applications requires upscaling of soil hydraulic parameters which are generally only available at point scale. We present a case study where hourly root zone soil water content and drainage observations from nine flat, pastoral sites (Waikato and Canterbury regions in New Zealand) were used to develop an upscaling approach to parameterize the soil water balance module of the TopNet catchment model, based on scaling multi-layer soil profile information from the national soil data base, S-map, to the single-layer soil profile used in TopNet. Using a Bayesian calibration approach, the hydraulic behavioral parameters of TopNet's soil water balance module were identified. Of the eleven calibration parameters considered three were found to be insensitive to data (stress point, unsaturated hydraulic conductivity and infiltration rate); three were correlated and could be determined from specific soil water content observations (wilting point, field capacity and drainable water); and five were correlated and could be determined from combined specific soil water content and drainage observations (drainage rate, saturated hydraulic conductivity profile, effective soil depth, soil water holding capacity and wetting front suction). Based on the eight correlated parameters, upscaling functions were then developed to derive suitable model parameters from S-map-hydro for each site. The validity of the upscaling functions was verified at each site. The approach used in this research can be used to parameterize the TopNet model at other similar locations, and also provides a transferable framework to parameterize other catchment-scale hydrology models where point-scale soil hydraulic data available.

Installation of groups of stone columns in clay: 3D Coupled Eulerian Lagrangian analyses

This paper describes the results of three-dimensional (3D) finite element analyses investigating the installation effects of groups of stone columns in purely cohesive soils. Installation of stone columns is simplified to the insertion of rigid cylindrical elements with conical tips in a single homogeneous soil layer (Tresca plasticity and a quasi-incompressible elastic law). Installation of a single column is simulated as the reference case and the installations of two columns and a group of nine columns are considered to study the interaction between the installation of several columns and the influence of the installation sequence. The process is simulated using a Coupled Eulerian Lagrangian formulation. Stone column installation alters the surrounding soil and the numerical results show the increase in horizontal stresses and pore pressures. The installation effects of several columns at common spacings overlap between each other and accumulate, producing higher horizontal stresses and pore pressures in a larger area. The installation sequence is mainly visible around the last column installed, where the radial stresses are lower.