Nothing Special   »   [go: up one dir, main page]
Next Article in Journal
Assessing the Moisture Resilience of Wood Frame Wall Assemblies
Previous Article in Journal
Applying Analytical Hierarchy Process (AHP) to BIM-Based Risk Management for Optimal Performance in Construction Projects
You seem to have javascript disabled. Please note that many of the page functionalities won't work as expected without javascript enabled.
 
 
Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
Journals
Buildings
Volume 14
Issue 11
10.3390/buildings14113633
buildings-logo
Submit to this Journal Review for this Journal Propose a Special Issue
► Article Menu

Article Menu

share Share announcement Help format_quote Cite question_answer Discuss in SciProfiles thumb_up
...
Endorse textsms
...
Comment
first_page
settings
Order Article Reprints
Font Type:
Arial Georgia Verdana
Font Size:
Aa Aa Aa
Line Spacing:
Column Width:
Background:
Article

Mechanical Characteristics of Grillage Root Foundation for High-Voltage Tower Under Horizontal Conditions

by
Zehui Ma
1,
Junjie Wang
2,
Xuefeng Huang
2,*,
Kun Sun
3,
Senlin Yang
4 and
Jun Yuan
5
1
School of Civil Engineering, Chongqing Jiaotong University, Chongqing 400074, China
2
School of Materials Science and Engineering, Chongqing Jiaotong University, Chongqing 400074, China
3
Wuhan Hanyang Municipal Construction Group Co., Ltd., Wuhan 430050, China
4
Qinghai Power Transmission and Transformation Engineering Co., Ltd., Xining 810000, China
5
Northwest Electric Power Design Institute Co., Ltd. of China Power Engineering Consulting Group, Xi’an 710075, China
*
Author to whom correspondence should be addressed.
Buildings 2024, 14(11), 3633; https://doi.org/10.3390/buildings14113633
Submission received: 30 September 2024 / Revised: 7 November 2024 / Accepted: 10 November 2024 / Published: 15 November 2024
(This article belongs to the Section Building Structures)
Browse Figures
Figure 1
<p>Site plan of root foundation.</p> "> Figure 2
<p>Site construction.</p> "> Figure 3
<p>Field installation diagram: (<b>a</b>) field drawing; (<b>b</b>) schematic drawing.</p> "> Figure 4
<p>Load–displacement curve of test foundation.</p> "> Figure 5
<p>m variation with displacement.</p> "> Figure 6
<p>TF<sub>1</sub>: (<b>a</b>) bracket numbering and position; (<b>b</b>) load–stress curve of bracket.</p> "> Figure 7
<p>RF<sub>2</sub>: (<b>a</b>) bracket numbering and position, (<b>b</b>) load–stress curve of bracket.</p> "> Figure 8
<p>TF<sub>1</sub>: (<b>a</b>) position diagram of base plate strain gauge; (<b>b</b>) load–stress curve of plate.</p> "> Figure 9
<p>RF<sub>2</sub>: (<b>a</b>) position diagram of base plate strain gauge; (<b>b</b>) load–stress curve of plate.</p> "> Figure 10
<p>TF<sub>1</sub> and RF<sub>2</sub> fracture distribution map of test foundation: (<b>a</b>) TF<sub>1</sub>; (<b>b</b>) RF<sub>2</sub>.</p> "> Figure 11
<p>Finite element model.</p> "> Figure 12
<p>Comparison of measured and simulated results.</p> "> Figure 13
<p>Different base plate sizes: (<b>a</b>) load–displacement curves; (<b>b</b>) fitting curve.</p> "> Figure 14
<p>Load–displacement curves of foundations with different lengths of root.</p> "> Figure 15
<p>Load–displacement curves of foundations with different numbers of roots.</p> "> Figure 16
<p>Load–displacement curves of foundations with different spacing of root.</p> ">
Versions Notes

Abstract

:
In response to the issue of reduced horizontal bearing capacity due to inadequate compaction of backfill soil in traditional grillage foundations, a novel grillage root foundation is proposed in this study. That is, the root is introduced into undisturbed soil at a traditional grillage foundation base plate. To assess the applicability of this innovative foundation under horizontal loading conditions, on-site experimental research was conducted. It was employed to comparatively analyze the load–displacement curves, changes in internal forces of steel components, and the development patterns of soil cracks around the foundation between traditional grillage foundations and various sizes of grillage root foundations subjected to horizontal loading. The results indicate that the horizontal bearing capacity of the grillage root foundation increased by 1.3 times compared to traditional grillage foundations, with economic benefits surpassing those of the traditional counterparts. The determination of the “m” value serves as the proportional coefficient of the horizontal resistance coefficient of the foundation soil, and the synthesis of the reactive force provided by the soil to the roots contribute to enhancements in soil resistance and the horizontal bearing capacity of the foundation. The horizontal load at which cracks appear in the grillage root foundation exceeds that of the traditional metal grillage foundation, with a slower rate of development. Finite element analysis was conducted to optimize the arrangement of roots, maximizing the foundation’s bearing capacity. This research provides certain references in terms of enhancing foundation bearing capacity, reducing ground treatment costs, and promoting sustainable development.

1. Introduction

As is widely acknowledged, the underpinning infrastructure of transmission lines assumes a pivotal role in ensuring the resilience of transmission networks [1,2]. When conveying power resources across extensive distances through transmission lines, the inherent limitations of low transmission lines, characterized by substantial power and voltage losses, render them unsuitable for protracted and expansive transmission endeavors. In contrast, high-voltage transmission lines exhibit the capacity to markedly diminish losses during power transmission. Consequently, the dimensions of high-voltage foundations must undergo continual augmentation to accommodate the escalating load demands [3,4]. Additionally, the bearing capacity of shallow foundations has proven a challenging task in geotechnical engineering [5,6,7]. Research substantiates that the ultimate bearing capacity of a foundation is intricately influenced by factors such as its dimensions, burial depth, and the density of the surrounding soil [8,9,10]. Owing to constraints associated with the concrete curing period, conventional foundations for transmission towers face challenges in promptly meeting elevated bearing capacity and stability requisites. Nevertheless, grillage foundations have gained widespread adoption owing to their attributes of factory prefabrication and abbreviated construction cycles [11,12,13]. In practical engineering applications, grillage foundations supporting transmission towers often experience horizontal loads induced by wind and water flow [14]. However, existing research on these foundations predominantly concentrates on individual vertical and combined loads. For instance, Sieira A [15] conducted an analysis of load–displacement, transmission mechanisms, and stress mechanisms in grillage foundations. Nevertheless, investigations into the effects of isolated horizontal loading conditions are notably scarce. Preliminary research indicates that foundations for transmission line towers not only endure vertical tensile and compressive loads but also experience significant horizontal load effects. Xue [16], employing the Monte Carlo simulation method, investigated the reliability of shallow foundations in sandy soil under various loads. Their findings suggested that the influence of compressive loads on the failure of shallow foundations is less pronounced than that of horizontal loads. Additionally, Halder and Chakraborty [17], utilizing finite element limit analysis, explored the bearing capacity of strip foundations, and observed a decrease under inclined and eccentric loads in reinforced cohesionless soil strip foundations. A study by Achmus [18] delved into the bearing performance of foundations under combined loads, revealing enhanced performance when compressive loads were less than 1256 kN, surpassing that under a solitary compressive load. This improvement was attributed to larger horizontal loads generating bending moments, augmenting front friction resistance and offsetting the combined compressive effect. However, when horizontal loads surpassed a certain threshold, they proved detrimental to the longitudinal bearing capacity, causing premature reaching of the soil’s bearing limit and a reduction in the foundation’s ultimate bearing capacity [19,20]. Grillage foundation research predominantly encompasses experiments, numerical simulation analyses, and theoretical derivations. Throughout the research process, numerical simulations effectively complement model and on-site experiments [21]. Scholars have employed indoor model tests, numerical analyses, and on-site tests to investigate the bearing mechanism of windblown sand foundations, deriving theoretical calculation formulas for ultimate bearing capacity [22,23,24,25]. Enhancing foundation-level bearing capacity at a reasonable cost remains a pertinent focus in geotechnical engineering.
Against this backdrop, this study introduces a novel grillage root foundation as an enhancement to traditional transmission line foundations. This foundation utilizes the favorable mechanical properties of undisturbed soil around it by incorporating roots, thereby enhancing the foundation’s horizontal bearing capacity. To verify the foundation’s applicability and reliability, on-site horizontal static load tests were conducted on the new root foundation, with comparisons made against traditional grillage foundations. The objective was to investigate its horizontal bearing capacity and stress mechanism. Employing numerical simulation analysis, the roots were optimized and arranged to fully distribute the root effect, thereby mobilizing the surrounding undisturbed soil to maximize the foundation’s horizontal bearing capacity. This research provides an experimental basis and data reference for the foundation’s application in transmission line tower engineering. However, the test site was predominantly composed of silt and silty clay, which has certain limitations.

2. Overview of Field Tests

2.1. Testing Program

The novel grillage root foundation configuration is illustrated in Figure 1. To assess both the horizontal bearing capacity and the economic advantages of this grillage root foundation, three distinct foundation types were chosen for on-site horizontal static load testing. The dimensions of these foundations are presented in Table 1. These foundations were chosen to investigate the influence of root dimensions and configurations on the overall performance of grillage foundations under horizontal loading conditions. Physically, the traditional foundation TF1 lacks root reinforcement and relies solely on its structural resistance to withstand horizontal loads, which represents the conventional approach to grillage foundation design. In contrast, the 0.8 m root foundation RF1 and 0.6 m root foundation RF2 incorporate roots of different dimensions, which enhance their horizontal bearing capacity by utilizing both the structural resistance of the foundation and the shear strength of the surrounding soil. The roots provide additional reaction forces from the soil, thus improving the overall stability of the foundations. RF1 and RF2 represent innovative designs that incorporate root reinforcement to improve performance. These foundations were chosen to investigate the influence of root dimensions and configurations on the overall performance of grillage foundations under horizontal loading conditions.
The foundation loading procedure adheres to the specifications outlined in JGJ106-2014, “Technical Code for Testing of Building Foundation Piles” [26]. Throughout the testing process, a jack is employed to apply incremental loading through a hydraulic oil pump. The initial level loading is set at twice the graded load, followed by gradual loading in accordance with the specified graded amounts. Subsequently, load equalization is executed at each level in alignment with the graded loading criteria. Post-application of each load level, the displacement at the foundation’s top is measured at intervals of 5, 10, 15, 15, and 15 min, with subsequent measurements taken at 30 min intervals. Per DL/T 5219-2014, “Technical Code for Design of Foundation of Overhead Transmission Line” [27], the loading process is halted when the horizontal displacement at the foundation’s top surpasses 10 mm under a given level of load, provided that the change in displacement within one hour remains within permissible limits.

2.2. Grillage Root Foundation Construction Technology

The primary distinguishing feature of the grillage root foundation lies in the incorporation of I-shaped steel roots into the undisturbed soil surrounding the base plate of a conventional foundation. This is achieved by effectively interconnecting all I-shaped steel roots using high-strength bolts. This innovative foundation design harmonizes the advantageous attributes of traditional foundations, such as light weight and facile assembly, with the heightened stability afforded by the surrounding undisturbed soil. The construction process of the grillage root foundation, as elucidated through the field test construction procedure, is delineated into the following six sequential steps: (a) Layout planning: This initial phase involves the precise determination of the foundation’s location, dimensions, and orientation based on engineering specifications and site conditions. It ensures that the foundation is positioned correctly to support the intended structure while minimizing impact on surrounding soil and structures. (b) Foundation excavation: Once the layout is finalized, excavation commences to create the foundation pit. This process must be carefully monitored to maintain the integrity of adjacent soil and underground utilities. Excavation depth and dimensions are tailored to accommodate the specific design of the grillage root foundation. (c) Placement of the baseplate: Following excavation, the baseplate is positioned at the bottom of the foundation pit. This component serves as the foundational support for the grillage structure and must be installed with precision to ensure stability and alignment. (d) Insertion of the steel roots: The steel roots, which are integral to the grillage root foundation’s design, are then inserted into predefined positions around the baseplate. These roots provide additional horizontal bearing capacity and stability to the foundation. Their installation requires careful alignment and securing to prevent displacement during subsequent construction phases. (e) Positioning of the support bracket: The support bracket is placed on top of the baseplate. It serves as a transitional component, connecting the grillage structure to the superstructure. Proper positioning and alignment of the support bracket are crucial for load transfer and overall stability. (f) Incremental layered backfilling: The final phase involves backfilling the foundation pit with soil in incremental layers. This process ensures that the grillage root foundation is gradually compacted and stabilized, reducing the risk of settlement or heave. Each layer of soil is carefully placed and compacted to meet engineering standards. Refer to Figure 2 for a visual representation of the construction process.

2.3. Loading and Data Acquisition Device

As depicted in Figure 3, the loading apparatus comprises a 200 t hydraulic jack, a 100 t dynamometer, one reaction steel beam, two concrete reaction piles, four high-strength threaded steel bars, and steel pads. The displacement measurement system utilized in the field test involves two electronic displacement meters symmetrically affixed to the reference beam. During the installation of the reference beam, careful consideration is given to ensuring that the installation point is positioned sufficiently far from the plastic zone of the soil surrounding the foundation. Additionally, the reference beam is securely installed to prevent potential soil-induced displacement or other factors leading to its oscillation, which could introduce errors in the displacement meter readings. The stress data of the steel members constituting the test foundation are gauged using resistive strain gauges, specifically, model BX120-3AA, static resistive strain gauges (model DH3816), and a computer for data acquisition and analysis.

2.4. Engineering Geological Conditions

The testing site is situated in Qinghai Province, China, falling within the expansive loess region characterized by substantial sedimentary deposits. The geological stratum in this locale exhibits stability and is predominantly constituted of silt and silty clay. Additionally, the groundwater level extends below 20 m from the ground surface, rendering its influence on the on-site testing foundation negligible. Indoor geotechnical tests such as compaction tests and direct shear were systematically conducted by acquiring soil samples from the on-site testing area, and the pertinent physical parameters are detailed in Table 2.

3. Testing Results and Analysis

3.1. Comparison of Load–Displacement Curves

The horizontal load–displacement curves for three foundation groups are presented in Figure 4. The horizontal bearing capacity was determined as the maximum horizontal load that the foundation could withstand without experiencing excessive displacement, and the maximum horizontal displacement specified in this manuscript is 10 mm. Therefore, the first-level load before the displacement reaches 10 mm is the maximum horizontal bearing capacity of the foundation. At lower loads, the foundation’s load–displacement curves generally overlap, exhibiting linear growth. As the load incrementally escalates, the horizontal displacement of the test foundation increases, and the curve disparities progressively manifest a non-linear development trend. Under equivalent horizontal loads, the hierarchy in the relationship between horizontal displacements at the top of the test foundation is typically observed as TF1 > RF2 > RF1. This observation suggests that the arrangement of steel roots around the base plate effectively mitigates the rise in horizontal displacement at the foundation’s top. For a more in-depth analysis of the bearing advantages conferred by the inclusion of roots as compared to traditional foundations, the corresponding horizontal bearing capacity at 10 mm displacement is extracted for comparison. The comparative evaluation of the ultimate horizontal bearing capacity for the three foundation types is summarized in Table 3. As depicted in the Table 3, under identical horizontal load effects, the grillage root foundation exhibits reduced displacement. Conversely, under equivalent displacement, the grillage root foundation demonstrates a higher bearing capacity. This underscores that the addition of roots significantly enhances the foundation’s horizontal bearing capacity, with RF1 showing a 133% increase compared to TF1, and RF2 demonstrating a 100% increase compared to TF1. The horizontal bearing capacity of experimental foundations TF1, RF1, and RF2 primarily derives from soil resistance and foundation structural resistance. However, owing to the incorporation of roots, RF1 and RF2 leverage the stability of the surrounding undisturbed soil to augment the foundation’s horizontal bearing capacity.
Further comparative analysis was undertaken using the same class comparative analysis method to evaluate the engineering economic benefits of the experimental foundations TF1, RF1, and RF2 under extreme horizontal loads. Key parameters including construction time, material consumption, and horizontal bearing capacity are summarized in Table 4. A scrutiny of the table reveals that, for foundations of identical size and burial depth, while the horizontal bearing capacity of the RF1 foundation increased by 80 kN relative to the TF1 foundation, its steel consumption concurrently rose by 0.4 t, and the construction time increased by approximately 1 h in comparison to TF1. This comparison does not clearly highlight the advantages of the grillage root foundation. To better delineate the advantages of the grillage root foundation, a comparison between the experimental foundations TF1 and RF2 was conducted. It was observed that, despite RF2 and TF1 sharing the same construction time, RF2 exhibited a reduction in earthwork excavation volume by 15.76 m3 compared to TF1. Moreover, the steel consumption was diminished by 0.4 t. Under extreme load conditions, RF2 demonstrated an increased horizontal bearing capacity by 60 kN. Although the grillage root foundation introduced an additional step of pushing the roots during construction, this process was executed through hydraulic jacks, rendering it straightforward and easy to operate, without extending the construction period. In summary, the economic efficiency of the grillage root foundation surpasses that of the traditional foundation, exhibiting greater application potential. When horizontal bearing capacity requirements are identical, the grillage root foundation not only accelerates the foundation construction period but also reduces the consumption of foundation materials and the excavation area of the foundation pit.

3.2. Comparison of the Proportional Coefficient m Values of the Horizontal Resistance Coefficient

The geometric intricacies inherent in the grillage root foundation design discussed in this paper necessitate fundamental simplifications for analytical purposes. To streamline the analysis, the influence of bolted connections on horizontal bearing capacity is disregarded. Taking into account the force characteristics of the foundational components, a methodology employing weight and cross-sectional area equivalence is adopted for the support element. Concurrently, weight equivalence and bending stiffness equivalence methodologies are applied to both the foundation base plate and the root. In the analysis, the cross-section is treated as equivalent to a rectangular cross-section. The equivalent [26] formulas are expressed as follows:
ρ d A d = ρ s A s
E d A d = E s A s
I = B e 1 3 − b H 3 + a e 2 3 3
Within these equations, ρd, Ad, and Ed denote the density, cross-sectional area, and elastic modulus of the equivalent foundation, respectively. Similarly, ρs, As, and Es represent the density, cross-sectional area, and elastic modulus of the original foundation, respectively. The variable I signifies the basic cross-sectional moment of inertia, while B corresponds to the width of the base plate, and b is the equivalent cross-sectional width of the support. The parameter H designates the burial depth of the foundation, and e1 and e2 represent the distances from the center of gravity of the T-shaped section foundation to the base plate and the distance from the center of gravity to the top, respectively.
In the context of horizontally loaded foundations, the parameter m assumes significance in their design, and on-site testing is deemed the most reliable method for its determination. In accordance with the Technical Specification for Building Pile Foundations, the derivation considers several factors, including the properties of the soil, the geometry and dimensions of the foundation, and the applied horizontal load. Equation (4) incorporates these relationships and provides a means to calculate m based on the specific characteristics of the foundation and the surrounding soil. The calculation formula for m is expressed as follows:
α = m b 0 E I 5
m = ( v x H c r Y 0 ) 5 3 b 0 ( E I ) 2 3
b 0 = 1.5 B + 0.5 ,   B ≤ 1 B + 1 ,   B > 1
In the presented equation, α represents the horizontal deformation coefficient of the foundation, while m serves as the proportional coefficient of the horizontal resistance coefficient of the foundation soil. The variable vx denotes the horizontal displacement coefficient at the top of the foundation, and EI is the basic bending stiffness. Furthermore, b0 signifies the calculated width of the foundation, and Y0 corresponds to the horizontal displacement.
Equation (5) is a further development or variation of Equation (4), which may account for additional factors or specific conditions related to the foundation design. The derivation of Equation (5) is similarly based on empirical data and testing, taking into account the unique characteristics of the foundation and the surrounding environment. This equation provides a refined means to calculate the horizontal resistance coefficient, taking into account a broader range of variables that may affect foundation performance.
The Y0-m curves for the two experimental foundations are illustrated in Figure 5. The trend of the Y0-m curve for the foundation under combined load aligns with that under a single horizontal load. At small horizontal displacements, m experiences rapid decay with increasing displacement, and the rate of m attenuation is faster for smaller displacements. Conversely, at larger horizontal displacements, the m value gradually approaches stabilization with increasing displacement. The threshold value for Y0 can be considered as 3 mm. When the displacement is less than this value, the m value rapidly decays; when the displacement exceeds this value, the m value tends to stabilize. Importantly, under combined loading, the m values for both sets of test piles are smaller than those under single horizontal loading. The m value reflects the magnitude of the horizontal resistance coefficient of the foundation. Consequently, the coupling effect of combined loading results in a weakened horizontal resistance coefficient of the foundation, leading to a reduction in the foundation’s horizontal bearing capacity. This analysis suggests that under combined loading, the foundation pile diminishes the resistance of the surrounding soil to horizontal loads, and it reduces the soil resistance around the foundation during the process of driving the soil around the pile. In contrast, the grillage root foundation enhances the m value through the incorporation of roots, thereby improving the soil resistance and horizontal bearing capacity of the foundation. This effectively controls the horizontal displacement of the foundation.

3.3. Internal Force Analysis of Steel Components

The horizontal loading direction applied to the experimental foundation RF1 deviates from that of the other two foundations, resulting in a notable influence on the stress transfer dynamics between the support and the base plate. Consequently, to facilitate a comparative analysis of the disparities in the internal force transfer patterns of foundation steel components under horizontal loading between the traditional metal grillage foundation and the grillage root foundation, we focus on the experimental foundations TF1 and RF2, both subjected to the same horizontal loading direction, for an in-depth examination.

3.3.1. Internal Force Analysis of Support Components

Figure 6a and Figure 7a illustrate the locations where strain gauges were affixed to the test bases of TF1 and RF2. The designation “B” represents the support, while the letters “a”, “b”, and “c” correspond to the upper, middle, and lower sections of the support, respectively. Figure 6b and Figure 7b present the stress variations in the support under horizontal loads.
With the application of horizontal load, the support stress for both TF1 and RF2 exhibits gradual increments proportional to the horizontal load, displaying a stepwise progression. At the positions of horizontal loading, namely, TF1B1 and RF2B1, the stress on the support is tensile, whereas at positions opposite to the horizontal loading, specifically TF1B3 and RF2B3, the stress is compressive. At smaller loads, tensile and compressive stresses are comparable. However, as the load intensifies, compressive stress gradually surpasses tensile stress, with the disparity widening. The stress values on the supports of TF1 and RF2 remain relatively low, indicating that the primary material of the foundation support experiences elastic deformation throughout the loading process until its completion.

3.3.2. Internal Force Analysis of Base Plate Components

The strain gauge placements on the base plates TF1 and RF2 are depicted in Figure 8a and Figure 9a, while the load stress curves are presented in Figure 8b and Figure 9b, with “P” denoting the base plate. Under the influence of horizontal loads, the load stress on the base plates of the experimental foundations TF1 and RF2 gradually increases with the augmentation of horizontal load, maintaining the base plate components in a safe operational state. A more detailed analysis reveals that the stress at position TF1P4 on the base plate of foundation TF1 is relatively high, whereas the stress at positions TF1P1 and TF1P3 is comparatively low. Conversely, the stress at position RF2P4 on the base plate of foundation RF2 is the highest, primarily attributable to the direct connection of the H-shaped steel at RF2P4 to the support RF2B3 at the horizontal loading position, as well as its connection to the root RF2R8. The stresses at positions RF2P2 and RF2P3 on the base plate are relatively low, and for horizontal loads below 20 KN, these positions experience minimal force. This phenomenon arises from the fact that at lower loads, the horizontal bearing capacity is primarily provided by the support, base plate, and root closer to the horizontal load. As the load exceeds 20 KN, the base plates RF2P2 and RF2P3 begin to bear force. Comparing the stresses on base plates RF2P2 and RF2P3, it is evident that the stress on RF2P2 consistently remains lower than that on RF2P3. This discrepancy is primarily attributed to the deformation of steel components and the presence of bolts, which mitigate stress during transmission. At a load of 90 KN, the horizontal load is predominantly borne by the root at the RF2P3 position on the base plate, resulting in a sharp increase in the stress curve at the RF2P3 position.

3.4. Analysis of the Development Law of Cracks Around the Foundation

Figure 10 illustrates the eventual distribution of cracks in the traditional metal grillage foundation TF1 and the root foundation RF2. Under horizontal loading, the width and length of cracks in the traditional metal grillage foundation TF1 increase proportionally with the load, primarily manifesting at the position of horizontal loading. Conversely, under horizontal loading, the cracks in the soil surrounding foundation RF2 predominantly propagate outward in a direction perpendicular to the loading direction. As the load incrementally rises, the length and width of these cracks in the soil surrounding the foundation continue to expand, with their development primarily exhibiting a radial pattern. The crack development process adheres to a pattern where the main crack drives the progression of surrounding smaller cracks. Throughout the horizontal loading process, cracks in TF1 manifest earlier and exhibit a swifter development compared to RF2. These cracks typically initiate in a direction perpendicular to both the foundation’s center and the horizontal force, with their development being most comprehensive in this direction. This phenomenon stems from the horizontal load on the foundation inducing soil movement on the side perpendicular to both the foundation’s center and the horizontal force, resulting in tensile forces within the soil in that direction. Besides tension-induced cracks, other cracks mainly arise from the compression of the foundation by the soil on the right side in a divergent manner under horizontal load. In practical engineering, enhancing the cross-sectional size of the root in this direction can effectively improve the horizontal bearing capacity of the grillage root foundation.

4. Numerical Simulation

4.1. Model Validation

Due to the distinctive construction process of the grillage root foundation, on-site testing inadequately addresses the intricacies of root layout types. To advance the practical application of the grillage root foundation and optimize root arrangement, this section conducts numerical simulations corroborated by experimental results. The model encompasses detailed representations of the foundation components, including the base plate, steel roots, and supporting structure. To mitigate boundary effects, the size of the soil surrounding the foundation is set at 10 times the diameter of the root foundation and 2 times the burial depth of the foundation. It employs an elastic material model for the foundation and adopts the Mohr–Coulomb constitutive model for the soil [28]. To accurately simulate crack development, the model incorporates surface-to-surface contact with tangential contact properties, enabling the capture of crack initiation, propagation, and interaction within the soil surrounding the foundation, employing surface-to-surface contact with tangential contact as a “penalty” contact featuring a friction coefficient of 0.5. Normal contact is established as a “hard” contact [29,30]. The model employs a hexahedral mesh, and horizontal loading is applied through the displacement control method. This comprehensive setup allows for an in-depth analysis of the factors influencing the bearing capacity of the grillage root foundation, including the base plate size, number of roots, and the length and spacing of roots, aiming to elucidate the optimal root arrangement scheme and the factors influencing the bearing capacity of the grillage root foundation. The finite element mesh division of the model is depicted in Figure 11, and the material parameters of the model are presented in Table 5.
Horizontal static load tests were executed to validate the performance of the traditional grillage foundation and two distinct sizes of root foundations during on-site examinations. The comparison between test and simulation results is presented in Figure 12. Observably, the simulation outcomes marginally underestimate the on-site test results. This discrepancy may be attributed to the omission of the squeezing effect induced by the roots penetrating the surrounding soil in the simulation. Utilizing a 10 mm horizontal displacement as the fundamental failure criterion, the horizontal loads of each foundation under this displacement were extracted and juxtaposed. It was discerned that the simulated horizontal bearing capacity decreased by 7.5%, 7.9%, and 7.1%, respectively, in comparison to the experimental results. Despite this minor divergence, the numerical simulation results for the three experimental foundations align well with the trajectory of on-site test results. This indicates that the aforementioned models capture the real conditions on-site. To assess the influence of different working conditions on foundation bearing capacity, the horizontal bearing capacity was extracted for displacements of 10 mm and 30 mm, respectively.
The specific simulation working conditions are delineated in Table 6.

4.2. Impact of Base Plate Size on Bearing Capacity

The impact of varying base plate sizes on bearing capacity with increasing load is illustrated in Figure 13. Analogous to the traditional grillage foundation, the horizontal bearing capacity of the grillage root foundation escalates with the augmentation of the base plate size, exhibiting a linear increase trend. According to the outcomes of linear fitting, the horizontal bearing capacity registers an increment of approximately 20 kN for every 0.2 m increase in base plate width. However, an indiscriminate augmentation of the base plate width to enhance the horizontal bearing capacity necessitates extensive soil excavation, undermining the economic and environmental viability of the foundation. Consequently, the ensuing discussion centers on examining the influence of alterations in roots on the horizontal bearing capacity of grillage foundations.

4.3. The Influence of Root Parameters on Bearing Capacity

Under the influence of varying root lengths, the alterations in the horizontal bearing capacity of the foundation are depicted in Figure 14. As the horizontal load intensifies, the foundation’s horizontal bearing capacity gradually rises. For instance, when the root length is 0.4 m, the growth rate reaches 70.5% compared to traditional foundations. However, as the root length extends to 0.9 m and 1.0 m, the growth rates diminish to 108.2% and 109.8%, respectively, indicating a diminishing growth trend. Excessive root length may complicate construction and potentially lead to root failure due to increased bending moments at the connection between the root and the base plate. Consequently, it is recommended that in the design of grillage root foundations, the selection of root length should be judiciously made based on the specific engineering context to enhance the ultimate bearing capacity of the foundation.
The load–displacement curve of the assembled root foundation under varying numbers of roots is illustrated in Figure 15. The horizontal bearing capacity of the root foundation consistently rises with an increasing number of roots. In comparison to traditional foundations, the introduction of roots augments the horizontal bearing capacity, attributed to the roots sharing a portion of the horizontal load. Initially, the increase in the number of roots results in a substantial enhancement of horizontal bearing capacity; however, this increment diminishes progressively. Excessive roots may cause the plastic zones of the soil above them to overlap, forming a continuous plastic zone. This overlapping adversely affects their individual contributions. Therefore, in the construction of grillage root foundations, economic considerations should guide the selection of an appropriate number of roots. This ensures optimal utilization of the soil surrounding the roots while mitigating any undesirable interactions between closely spaced plastic zones.
Figure 16 illustrates the variation curve of the horizontal bearing capacity of the foundation under different root spacings, displaying a gradual growth trend. While keeping other parameters constant, changes in root spacing have minimal impact on the horizontal bearing capacity of the grillage root foundation. Data analysis from Table 6 supports this observation, indicating that when the displacement is 10 mm and the distance between roots increases from 0.4 m to 1.4 m, the horizontal bearing capacity only experiences a modest rise from 110 kN to 121 kN. In the range of 0.6 to 1.2 m, the increase is approximately 5% compared to a distance of 0.4 m. In conclusion, when optimizing the design of grillage root foundations based on root arrangement, the influence of root spacing can be disregarded. Root spacing can be reasonably selected considering the construction convenience of the foundation base plate.

5. Conclusions

This study demonstrates that grillage root foundations significantly enhance stability and bearing capacity compared to traditional metal grillage foundations. By utilizing both structural resistance and the shear strength of surrounding soil, these innovative foundations exhibit improved performance, especially under horizontal loads. Additionally, finite element analysis confirms that optimizing root characteristics effectively maximizes the bearing capacity.
  • Root implantation in grillage foundations effectively reduces horizontal displacement and enhances overall stability. Compared to traditional metal grillage foundations, grillage root foundations demonstrate an up to 130% increase in horizontal bearing capacity while maintaining economic efficiency.
  • Traditional grillage foundations rely solely on their structural resistance for horizontal loads. In contrast, grillage root foundations benefit from both their structural attributes and the shear strength of the undisturbed soil around the roots, leading to superior horizontal bearing capacity.
  • Cracks under horizontal loads typically develop in a direction perpendicular to the foundation’s center and the applied force. The metal grillage root foundation shows more substantial crack formation at higher loads, but with a slower rate of development compared to traditional foundations, indicating better load distribution capabilities.
  • Analysis reveals that the m value, reflecting the soil resistance and horizontal bearing capacity, is higher in grillage root foundations than in traditional ones. This indicates that grillage root foundations utilize additional reaction forces from the soil on the roots. Factors such as root density and arrangement further influence this value and overall foundation performance under varying loading conditions.

Author Contributions

Conceptualization, J.W. and X.H.; methodology, Z.M.; software, K.S.; validation, J.W. and X.H.; formal analysis, Z.M. and K.S.; investigation, Z.M. and K.S.; resources, X.H.; data curation, Z.M., X.H., K.S. and J.Y.; writing—original draft preparation, Z.M., J.W., X.H., K.S., J.Y. and S.Y.; writing—review and editing, Z.M.; visualization, Z.M. and K.S.; supervision, J.Y. and S.Y.; project administration, S.Y.; funding acquisition, J.W. and X.H. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by the National Natural Scientific Foundation of China (52378327) and the State Grid Qinghai Electric Power Company Technology Project (52283820000A).

Data Availability Statement

The data used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest

Author Kun Sun was employed by the company Wuhan Hanyang Municipal Construction Group Co., Ltd. Author Jun Yuan was employed by the company Northwest Electric Power Design Institute Co., Ltd. of China Power Engineering Consulting Group. Author Senlin Yang was employed by the company Qinghai Power Transmission and Transformation Engineering Co., Ltd. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

References

  1. Mozakka, I.; Zeynalian, M.; Hashemi, M. A feasibility study on construction methods of high voltage transmission towers’ foundations. Arch. Civ. Mech. Eng. 2021, 21, 41. [Google Scholar] [CrossRef]
  2. Zeynalian, M.; Khorasgani, M.Z. Structural performance of concrete poles used in electric power distribution network. Arch. Civ. Mech. Eng. 2018, 18, 863–876. [Google Scholar] [CrossRef]
  3. Kishore, T.S.; Singal, S.K. Optimal economic planning of power transmission lines: A review. Renew. Sustain. Energy Rev. 2014, 39, 949–974. [Google Scholar] [CrossRef]
  4. Zucca, M.; Franchi, A.; Crespi, P.; Longarini, N.; Ronca, P. The new foundation system for the transept reconstruction of the basilica di collemaggio. In Proceedings of the International Masonry Society Conferences, Milan, Italy, 9–11 July 2018. [Google Scholar]
  5. Ghazavi, M.; Eghbali, A.H. A Simple Limit Equilibrium Approach for Calculation of Ultimate Bearing Capacity of Shallow Foundations on Two-Layered Granular Soils. Geotech. Geol. Eng. 2008, 26, 535–542. [Google Scholar] [CrossRef]
  6. Luo, Z.; Ding, X.; Zhang, X.; Ou, Q.; Yang, F.; Zhang, T.; Cao, G. Experimental and numerical investigation of the bearing capacity and deformation behavior of coral sand foundations under shallow footing loads. Ocean Eng. 2024, 310, 118601. [Google Scholar] [CrossRef]
  7. Sasso, L.F.; Wagner, A.C.; Ruver, C.A.; da Silva Lopes, L.; Consoli, N.C. Pile Groups and Piled Footings Bearing in Weakly Cemented Residual Soil. Geotech. Geol. Eng. 2023, 41, 1485–1501. [Google Scholar] [CrossRef]
  8. Emirler, B.; Tolun, M.; Yildiz, A. 3D Numerical Response of a Single Pile Under Uplift Loading Embedded in Sand. Geotech. Geol. Eng. 2019, 37, 4351–4363. [Google Scholar] [CrossRef]
  9. Hjiaj, M.; Lyamin, A.V.; Sloan, S.W. Bearing capacity of a cohesive-frictional soil under non-eccentric inclined loading. Comput. Geotech. 2004, 31, 491–516. [Google Scholar] [CrossRef]
  10. Paolucci, R.; Pecker, A. Soil inertia effects on the bearing capacity of rectangular foundations on cohesive soils. Eng. Struct. 1997, 19, 637–643. [Google Scholar] [CrossRef]
  11. Burgan, B.A.; Sansom, M.R. Sustainable steel construction. J. Constr. Steel Res. 2006, 62, 1178–1183. [Google Scholar] [CrossRef]
  12. Kamali, M.; Hewage, K. Development of performance criteria for sustainability evaluation of modular versus conventional construction methods. J. Clean. Prod. 2017, 142, 3592–3606. [Google Scholar] [CrossRef]
  13. Pujadas-Gispert, E.; Sanjuan-Delmás, D.; Josa, A. Environmental analysis of building shallow foundations: The influence of prefabrication, typology, and structural design codes. J. Clean. Prod. 2018, 186, 407–417. [Google Scholar] [CrossRef]
  14. Yahia-Cherif, H.; Mabrouki, A.; Benmeddour, D.; Mellas, M. Bearing Capacity of Embedded Strip Footings on Cohesionless Soil Under Vertical and Horizontal Loads. Geotech. Geol. Eng. 2017, 35, 547–558. [Google Scholar] [CrossRef]
  15. Sieira, A.C.C.F.; Gerscovich, D.M.S.; Sayão, A.S.F.J. Displacement and load transfer mechanisms of geogrids under pullout condition. Geotext. Geomembr. 2009, 27, 241–253. [Google Scholar] [CrossRef]
  16. Xue, J.; Nag, D.K. Reliability analysis of shallow foundations subjected to varied inclined loads. Geotech. Saf. Risk 2011, 1, 377–384. [Google Scholar]
  17. Halder, K.; Chakraborty, D. Effect of inclined and eccentric loading on the bearing capacity of strip footing placed on the reinforced slope. Soils Found. 2020, 60, 791–799. [Google Scholar] [CrossRef]
  18. Achmus, M.; Thieken, K. On the behavior of piles in non-cohesive soil under combined horizontal and vertical loading. Acta Geotech. 2010, 5, 199–210. [Google Scholar] [CrossRef]
  19. Bang, S.; Jones, K.D.; Kim, K.O.; Kim, Y.S.; Cho, Y. Inclined loading capacity of suction piles in sand. Ocean Eng. 2011, 38, 915–924. [Google Scholar] [CrossRef]
  20. Meyerhof, G.G. The Uplift Capacity of Foundations Under Oblique Loads. Can. Geotech. J. 1973, 10, 64–70. [Google Scholar] [CrossRef]
  21. Choudhary, A.K.; Pandit, B.; Babu, G.L.S. Three-Dimensional Analysis of Uplift Behaviour of Square Horizontal Anchor Plate in Frictional Soil. Int. J. Geosynth. Ground Eng. 2018, 4, 14. [Google Scholar] [CrossRef]
  22. Ilamparuthi, K.; Dickin, E.A.; Muthukrisnaiah, K. Experimental investigation of the uplift behaviour of circular plate anchors embedded in sand. Can. Geotech. J. 2002, 39, 648–664. [Google Scholar] [CrossRef]
  23. Knappett, J.A.; Brown, M.J.; Bransby, M.F.; Hudacsek, P.; Morgan, N.; Cathie, D.N.; Maconochie, A.; Yun, G.; Ripley, A.G.; Brown, N.; et al. Capacity of grillage foundations under horizontal loading. Géotechnique 2012, 62, 811–823. [Google Scholar] [CrossRef]
  24. Kouzer, K.M.; Kumar, J. Vertical uplift capacity of two interfering horizontal anchors in sand using an upper bound limit analysis. Comput. Geotech. 2009, 36, 1084–1089. [Google Scholar] [CrossRef]
  25. Meyerhof, G. Some Recent Research on the Bearing Capacity of Foundations. Can. Geotech. J. 2011, 1, 16–26. [Google Scholar] [CrossRef]
  26. JGJ106-2014; Technical Code for Testing of Building Foundation Piles. China Architecture Press: Beijing, China, 2014.
  27. DL/T 5219-2014; Technical Code for Design of Foundation of Overhead Transmission Line. Standardization Administration of China: Beijing, China, 2014.
  28. Sadique, M.R.; Zaid, M.; Alam, M.M. Rock Tunnel Performance Under Blast Loading Through Finite Element Analysis. Geotech. Geol. Eng. 2022, 40, 35–56. [Google Scholar] [CrossRef]
  29. Kalos, A. Numerical Investigation of the Bearing Capacity of Strip and Rectangular Shallow Footings on Cohesive Frictional Soils Under Eccentric Loads. Geotech. Geol. Eng. 2022, 40, 1951–1972. [Google Scholar] [CrossRef]
  30. Kang, J.H.; Kim, G.H.; Choi, W.S. Impact-Contact Analysis of Prismatic Graphite Blocks Using Abaqus; Korea Atomic Energy Research Institute: Daejeon, Republic of Korea, 2010. [Google Scholar]
Buildings 14 03633 g001
Figure 1. Site plan of root foundation.
Figure 1. Site plan of root foundation.
Buildings 14 03633 g001
Buildings 14 03633 g002
Figure 2. Site construction.
Figure 2. Site construction.
Buildings 14 03633 g002
Buildings 14 03633 g003
Figure 3. Field installation diagram: (a) field drawing; (b) schematic drawing.
Figure 3. Field installation diagram: (a) field drawing; (b) schematic drawing.
Buildings 14 03633 g003
Buildings 14 03633 g004
Figure 4. Load–displacement curve of test foundation.
Figure 4. Load–displacement curve of test foundation.
Buildings 14 03633 g004
Buildings 14 03633 g005
Figure 5. m variation with displacement.
Figure 5. m variation with displacement.
Buildings 14 03633 g005
Buildings 14 03633 g006
Figure 6. TF1: (a) bracket numbering and position; (b) load–stress curve of bracket.
Figure 6. TF1: (a) bracket numbering and position; (b) load–stress curve of bracket.
Buildings 14 03633 g006
Buildings 14 03633 g007
Figure 7. RF2: (a) bracket numbering and position, (b) load–stress curve of bracket.
Figure 7. RF2: (a) bracket numbering and position, (b) load–stress curve of bracket.
Buildings 14 03633 g007
Buildings 14 03633 g008
Figure 8. TF1: (a) position diagram of base plate strain gauge; (b) load–stress curve of plate.
Figure 8. TF1: (a) position diagram of base plate strain gauge; (b) load–stress curve of plate.
Buildings 14 03633 g008
Buildings 14 03633 g009
Figure 9. RF2: (a) position diagram of base plate strain gauge; (b) load–stress curve of plate.
Figure 9. RF2: (a) position diagram of base plate strain gauge; (b) load–stress curve of plate.
Buildings 14 03633 g009
Buildings 14 03633 g010
Figure 10. TF1 and RF2 fracture distribution map of test foundation: (a) TF1; (b) RF2.
Figure 10. TF1 and RF2 fracture distribution map of test foundation: (a) TF1; (b) RF2.
Buildings 14 03633 g010
Buildings 14 03633 g011
Figure 11. Finite element model.
Figure 11. Finite element model.
Buildings 14 03633 g011
Buildings 14 03633 g012
Figure 12. Comparison of measured and simulated results.
Figure 12. Comparison of measured and simulated results.
Buildings 14 03633 g012
Buildings 14 03633 g013
Figure 13. Different base plate sizes: (a) load–displacement curves; (b) fitting curve.
Figure 13. Different base plate sizes: (a) load–displacement curves; (b) fitting curve.
Buildings 14 03633 g013
Buildings 14 03633 g014
Figure 14. Load–displacement curves of foundations with different lengths of root.
Figure 14. Load–displacement curves of foundations with different lengths of root.
Buildings 14 03633 g014
Buildings 14 03633 g015
Figure 15. Load–displacement curves of foundations with different numbers of roots.
Figure 15. Load–displacement curves of foundations with different numbers of roots.
Buildings 14 03633 g015
Buildings 14 03633 g016
Figure 16. Load–displacement curves of foundations with different spacing of root.
Figure 16. Load–displacement curves of foundations with different spacing of root.
Buildings 14 03633 g016
Table 1. Test foundation type.
Table 1. Test foundation type.
Foundation TypeNo.Base Plate Size/mDepth/mRoot NumbersRoot Length/m
Traditional foundationTF12.4 × 2.43——
0.8 m root foundationRF12.4 × 2.43120.8
0.6 m root foundationRF22.0 × 2.0380.6
Table 2. Physical parameters of soils.
Table 2. Physical parameters of soils.
Soil TypeLiquid Limit ωL/%Plastic Limit ωP/%Density ρ/g.cm−3Moisture Content ω/%Cohesive Forces c/kPaAngle of Internal Friction φ/°
Undisturbed soil27.8517.081.516.01933
Backfill——1.614.6810
Table 3. Comparison table of horizontal bearing capacity of test foundation.
Table 3. Comparison table of horizontal bearing capacity of test foundation.
No.Horizontal Bearing Capacity/kNIncrease Compared to TF1/%
TF160—
RF1140133.3
RF2120100
Table 4. Comparative table of economic benefits.
Table 4. Comparative table of economic benefits.
No.Horizontal Bearing Capacity/
kN		Steel Usage
/t		Earth Excavation Volume
/m3		Construction Time
/h
TF1602.420.2810
RF11402.820.2811
RF21202.014.5210
Table 5. Material parameters used in models.
Table 5. Material parameters used in models.
Density (ρ)/(g·cm−3)Elastic Modulus (E)/MPaPoisson Ratio (µ)Cohesive Force (c)/kPaFriction Angle (φ)/(°)
Soil1.5015.80.281725
Test foundation7.85209,000.00.25——
Table 6. Specific simulation conditions.
Table 6. Specific simulation conditions.
No.Foundation TypeBase Plate Size/mRoot NumbersRoot Length/mRoot Spacing/mBearing Capacity at 10 mm/kNIncrease Compared to 1#/%Bearing Capacity at 30 mm/kNIncrease Compared to 2#/%
1#Traditional foundation2.4 × 2.4———61—126−53.8
2#Root foundation2.0 × 2.080.60.811588.5273—
3#1.6 × 1.680.60.810267.2233−14.7
4#1.8 × 1.880.60.810877.0252−7.7
5#2.2 × 2.280.60.812198.42947.7
6#2.4 × 2.480.60.8127108.231615.8
7#2.0 × 2.040.60.810165.6224−17.9
8#2.0 × 2.0120.60.8128109.831716.1
9#2.0 × 2.0160.60.8128109.831816.5
10#2.0 × 2.0200.60.8129111.532217.9
11#2.0 × 2.080.40.810470.5238−12.8
12#2.0 × 2.080.50.811080.3256−6.2
13#2.0 × 2.080.70.811995.12885.5
14#2.0 × 2.080.80.8122100.030210.6
15#2.0 × 2.080.90.8127108.231816.5
16#2.0 × 2.081.00.8128109.832519.0
17#2.0 × 2.080.60.411080.3255−6.6
18#2.0 × 2.080.60.611588.52730
19#2.0 × 2.080.61.011588.52750.7
20#2.0 × 2.080.61.211791.82812.9
21#2.0 × 2.080.61.412198.42895.9
Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.

Share and Cite

MDPI and ACS Style

Ma, Z.; Wang, J.; Huang, X.; Sun, K.; Yang, S.; Yuan, J. Mechanical Characteristics of Grillage Root Foundation for High-Voltage Tower Under Horizontal Conditions. Buildings 2024, 14, 3633. https://doi.org/10.3390/buildings14113633

AMA Style

Ma Z, Wang J, Huang X, Sun K, Yang S, Yuan J. Mechanical Characteristics of Grillage Root Foundation for High-Voltage Tower Under Horizontal Conditions. Buildings. 2024; 14(11):3633. https://doi.org/10.3390/buildings14113633

Chicago/Turabian Style

Ma, Zehui, Junjie Wang, Xuefeng Huang, Kun Sun, Senlin Yang, and Jun Yuan. 2024. "Mechanical Characteristics of Grillage Root Foundation for High-Voltage Tower Under Horizontal Conditions" Buildings 14, no. 11: 3633. https://doi.org/10.3390/buildings14113633

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

Article Metrics

Back to TopTop