Hazards and Treatment of Collapsible Loess Foundation on Ultrahigh Voltage Transmission Lines

. With the development of ultrahigh voltage transmission line construction in northwest China, an increasing number of overhead transmission lines are crossing the loess regions. Ensuring the stability of electricity transmission towers and mitigating the risk of collapse are crucial prerequisites for the construction of transmission lines. Taking the 750kV demonstration electricity transmission line in Guanting – Lanzhou East as an example, representative loess samples were selected for compression and collapsing sensitivity tests. Four foundation treatment schemes were designed, and the wetting deformation characteristics were investigated through numerical simulation of the rainfall in ﬁ ltration process. Corresponding optimisation schemes were proposed. The collapsing process was divided into four stages through laboratory collapsing tests. The relationship function between saturation and the Duncan – Chang model parameters of loess was established, which was introduced into the ﬁ nite element model to consider the rainfall in ﬁ ltration process. The analysis of the displacement ﬁ eld, and loess saturation ﬁ eld with time after rainfall in ﬁ ltration for the four schemes showed that adding a lime-stabilised soil cushion layer and waterproof layer to the inclined column foundation had the best effect. Given that the design scheme needs to consider safety and economy, the thickness of the cushion layer was optimised, thereby reducing the use of lime-stabilised soil by 20 % . Research ﬁ ndings provide meaningful guidance for the design of transmission tower foundations in loess areas.


Introduction
With the comprehensive advancement of the construction project of the 750 kV transmission backbone network in northwest China, many problems have emerged in the design and construction stages, making it urgent to conduct indepth research on the effects of collapsible geological conditions on the foundation to ensure the successful construction and stable operation of the electricity transmission line. As the first 750 kV transmission line in northwest China, the Guanting-Lanzhou East electricity transmission line has a total length of 146 km and is a crucial supporting project for the Gongboxia hydropower station. Figure 1 shows that the loess along the transmission line is mainly silty loess, with a large natural porosity and a tendency to collapse when encountering water [1][2][3]. As shown in (Figure 1(a)), its latitude range is 35°42′ N-36°00′ N and its longitude range is 102°36′ E-24°12′ E.
To economically and safely address the collapse sensitivity of loess when encountering water, various methods can be employed for foundation treatment. The goal is to eliminate collapse, increase bearing capacity, and ensure the stability of structures [4,5]. Traditionally, lime-stabilised soil cushion layers have been used to enhance the bearing capacity of loess foundations, but they may result in significant settlement if there is a weak soil layer underneath [6][7][8]. Alternatively, a gravel cushion layer consisting of well-graded gravel, pebbles, and sand can be used in areas with high groundwater levels [9,10]. Dynamic compaction is an economical method that disrupts the soil structure and forms a compacted layer, although its effectiveness decreases with depth [11][12][13]. Other methods include compacted piles of limestabilised soil [14][15][16], vibro-replacement stone piles [17][18][19], reinforced concrete precast piles [20][21][22], cast-in-place piles [23,24], and cement mixing piles [25][26][27]. These methods offer varying benefits such as increased bearing capacity, improved stability, and cost efficiency. However, each method has its own considerations, such as noise during construction or potential pollution on-site. Overall, selecting the appropriate foundation treatment method depends on factors such as the type of collapsibility, soil conditions, project scale, and economic and safety requirements.
In the case of transmission tower foundation, the main reason for foundation settlement is water immersion, which causes rapid destruction of the loess structure. The key to dealing with collapsible sensitivity in loess is to ensure that the foundation is not exposed to water [28]. In view of the tower type, terrain, geology, collapsibility level, and groundwater level, appropriate foundation treatment may be necessary when waterproofing cannot sufficiently meet the requirements for severe cases of waterlogging. Accounting for the special characteristics of electricity transmission line engineering and project experience, the commonly used method for foundation treatment is the lime-stabilised soil cushion layer. This method uses manual labour, requires no special equipment, is suitable for various terrain conditions, and has good effects on all levels of collapsible sensitivity in loess [29,30]. Thus, how can the size of the lime-stabilised soil cushion layer be determined for large transmission tower foundations on loess? This problem requires understanding of the collapsible deformation mechanism of loess and establishing corresponding predictive deformation models. The essence of collapsible deformation is a special type of plastic deformation, characterised by suddenness, discontinuity, and irreversibility [31]. To more accurately reflect the deformation characteristics of unsaturated soil, many scholars have established constitutive models for unsaturated soil within the framework of nonlinear elastic [31] or elastoplastic theory [32,33]. These models can reflect the deformation of unsaturated loess caused by changes in stress state but cannot account for the effect of the infiltration process. Centrifugal model tests [34,35] and on-site water immersion tests [36,37] can provide accurate results for the water infiltration process and development of collapsing deformation of loess foundations; however, these methods require a long time and relatively high costs. The Duncan-Chang model considers the nonlinear and time-dependent nature of soil response by incorporating hyperbolic equations. It can accurately capture the stress-strain relationships, including the initial elastic behaviour, yielding, and subsequent plastic deformations. This model has proven to be effective in simulating soil behaviour in different engineering applications, such as slope stability analysis, foundation design, and 2 Advances in Civil Engineering soil-structure interaction [38]. However, the Duncan-Chang model cannot reflect the influence of changes in soil moisture content. This article analysed the characteristics of collapsible loess, the situation of collapsible loess sites along the northwest 750 kV transmission project route, conventional treatment techniques for collapsible loess, and treatment techniques and effects used in transmission line projects. Using the demonstration electricity transmission line project in Guanting-Lanzhou East as an example, indoor experiments were conducted on the loess at the project site. On-site soil samples and treatments were experimentally studied and analysed using a self-developed program for finite element analysis. In addition, data from operating transmission lines were investigated to provide a basis for the design and construction of high-voltage tower foundations.

Test Soil and Main Physical Parameters
The tested loess were taken from the foundation pits of a transmission tower in Nantang Village, Liujiaxia, Gansu Province, as shown in Figure 2. The soil was collected at depths of 2 and 4 m below the current ground level, with a brownish-yellow colour, relatively large pores, well-developed wormholes, and low water content. At the soil collection site, the soil samples were made into cubes with side lengths of 20-30 cm, marked with the top and bottom orientations, wrapped in plastic wrap, and carefully transported to the laboratory for testing. Disturbance during soil collection and transportation was minimised as much as possible.
On the basis of the results of specific gravity tests, particle size analyses, permeability tests, and liquid limit tests, the main physical parameters of the loess at depths of 2 and 4 m are shown in Table 1. The samples had similar water contents, but the loess at 2 m had a higher silt particle content and smaller void ratio and permeability coefficient, whereas the loess at 4 m had a larger void ratio. According to the classification suggestion for loess types [39], both tested samples belong to silty loess, mechanical properties of which are greatly affected by changes in water content.

Compression Test
The compression test can reflect the compression characteristics and obtain the compression modulus of soil under different pressure ranges. To study the deformation and strength characteristics of undisturbed loess, 12 sets of samples with different water contents were selected for compression tests in this section.  3.1. Test Scheme. About 12 sets of samples were prepared by controlling the water content of samples through dehydration (natural drying method) and humidification (water film transfer method). The water content of undisturbed loess at 2 m is 7%, 11.2% (natural water content), 15%, 19%, 23%, and 36.8% (saturation water content); and the water content of undisturbed loess at 4 m is 7%, 10.8% (natural water content), 15%, 19%, 23%, and 39% (saturation water content). The prepared samples were placed in a moisturising device for more than 48 hr to ensure a uniform diffusion of moisture in the samples.
The lever-controlled consolidation instrument was used in the test. After the moisture of the samples was uniform, vertical loads were applied to the samples with different water contents in the order of 50, 100, 200, and 400 kPa. At each pressure level, when the deformation of the sample was stable (the deformation was less than 0.01 mm/hr), the stress and deformation of the soil sample were recorded. The method of multiple parallel samples in each group was used to reduce the adverse effect of soil randomness. Figures 3 and 4 show that the previous e-lg p curve is relatively flat at the same water content, with an obvious inflection point. Before this point, the stress in the soil did not reach the structural strength, and only partial connection points were broken or moved, resulting in only a small amount of deformation and a slight decrease in porosity. After the stress in the soil exceeded the structural strength, the framework of the interparticle void structure was damaged. As the particles rapidly slid into the cavities of the interparticle voids, the deformation of the soil rapidly increased and the porosity decreased rapidly.

Test Result.
The comparison of the e-lg p curves at different water contents indicated that the structural strength of the undisturbed loess decreases rapidly with the increase of water content, and the decrease in strength at low water content is considerably greater than at a high water content. As the initial water content increases, the difference between the e-lg p curves gradually becomes smaller, indicating that the collapsibility decreases with the increase of initial water content, and the compressibility increases with humidification.
The compression modulus is the ratio of the sample's vertical additional stress and vertical strain. The smaller the compression modulus E s is, the easier the soil will be compressed. The analysis of the relationship curves between the compression modulus and the saturation at different pressure intervals in Figures 5 and 6 implied that the compression modulus obtained from the samples at the saturation water content state is slightly smaller than that at the natural water content state, but the deviation is small and the data are reasonable. At the same saturation, the compression modulus increases with pressure. Within the same pressure interval, the compression modulus decreases with the increase  Void ratio e p (kPa) Advances in Civil Engineering in saturation, which can be fitted using an exponential function. The comparison of the compression modulus changes at different depths shows that the compression modulus of loess varies greatly at a low water content but is almost identical at the saturation state. Overall, the relationship between saturation and compression modulus can be described using an exponential function.

Loess Collapse Test
When loess is subjected to water immersion under a certain pressure, the structure will rapidly deteriorate, and significant additional settlement will occur. As a foundation for tower bases, its settlement is closely related to engineering safety and directly affects the design of foundation treatment.     After the first level of pressure was applied, the deformation readings were measured every hour until the sample deformation became stable, and the second level of pressure was then applied, and so on. After the sample deformation became stable under the specified pressure, pure water was injected into the container until the water level was above the top of the sample, and the deformation readings were measured every hour until the sample deformation became stable (with a deformation rate of less than 0.01 mm/hr). The  Advances in Civil Engineering collapsibility coefficient δ wp and the self-weight collapsibility coefficient δ zs were calculated using Equations (1) and (2). When determining the self-weight collapsibility coefficient, the overlying soil saturation was set to 85%, and the saturated self-weight pressures of the overlying soil at 2 and 4 m were determined to be 34.74 and 68.69 kPa, respectively. The selfweight collapsing deformation was measured by loading the sample to the saturated self-weight soil pressure of the overlying soil.
where h p is the height of the sample after stable deformation at a certain pressure level, h 0 p is the height of the sample after Advances in Civil Engineering 7 stable deformation due to immersion in water at a certain pressure level, and h is the initial height of the sample.
where h z is the height of the sample after stable deformation under saturated self-weight pressure and h 0 z is the height of the sample after stable deformation due to immersion and collapse under saturated self-weight pressure. Figures 7 and 8 show the relationship curves between the collapsibility coefficient and pressure for soil samples at different depths. The collapsibility coefficient is the highest at a vertical pressure of 200 kPa and then gradually decreases until the curves tend to convergence. Under the conditions of natural water content and vertical pressure as the overlying self-weight load, the collapsibility coefficient of loess at 2 m is 0.027, which belongs to mildly collapsible loess, and that at 4 m is 0.039, which belongs to moderately collapsible loess.

Test Result.
Under the same vertical pressure, the collapsibility coefficient is more sensitive to changes in water content when the initial water content is lower, whereas its sensitivity to changes in water content decreases when the initial water content is higher. Given the relatively large pores and low dry density, the collapsibility coefficient of the loess at 4 m is considerably higher than that at 2 m under low water content conditions, whereas they are more similar under high water content conditions. Under the same water content conditions, the δ s -p curve can be divided into four stages. In the additional compression deformation stage, the compression curve demonstrates an approximately linear behaviour, which can be attributed to the compression of pores and microstructural adjustments within the soil. During the collapsing initiation stage, as the pressure increases, the compression curve transitions into nonlinear characteristics. This phenomenon occurs due to further microstructural adjustments and rearrangement of the soil, resulting in an increased number of particle contacts and reorientation. In the collapsing development stage, within higher pressure ranges, the compression curve exhibits a steeper decline. This behaviour arises from the continuous increase in particle contacts and the attainment of a relatively dense microstructure. Finally, in the collapsing attenuation stage,   Given the particularity of the electricity transmission line, construction methods, such as dynamic compaction and cast-in-place pile, have complex construction procedures, making it difficult to maintain quality control. The comprehensive cost required during the construction period is also considerable. Moreover, in actual engineering projects, hands-on experience implementing these techniques is limited. Therefore, the handling of foundation pits in some electricity transmission line projects mainly relies on the use of a lime-stabilised soil cushion layer. How to determine the size of the lime-stabilised soil cushion layer to ensure the safety of transmission towers has become an urgent problem to be solved in construction.

Constitutive Model.
The E-v model is an incremental elastic model based on the hyperbolic stress-strain relationship of the soil, which is currently widely used. It is also known as the Duncan-Chang model, and Equation (3) shows that it has eight parameters. The model can reflect the nonlinearity of soil deformation and the influence of stress levels but cannot consider the effects of changes in soil moisture content.
where p a is the standard atmospheric pressure; p a ¼ 101: Þ; and K, n, φ, c, R f , G, F, and D are material constants. Table 2

Calculation Scheme.
According to the actual form of the transmission tower in engineering, transmission towers can be classified into corner and straight transmission towers. It can be divided into four schemes based on the treatment of the foundation and the measures taken to prevent seepage. The infiltration intensity is shown in Figure 11. In the calculation process, the displacement was interpolated using the quadrilateral eightnode isoparametric element, whereas the seepage was calculated using the quadrilateral four-node isoparametric element. The calculation model and grid division are shown in Figure 12, with a total of 4,200 elements, a vertical height of 20 cm, and a horizontal length of 20 cm. Four types of finite element calculation model are established for different foundation treatment schemes. Load and water infiltration conditions are applied according to the actual situation to make the numerical simulation as practical as possible. To obtain an initial stress field before infiltration that matches the actual situation, each scheme was divided into the following three calculation stages: (1) During the construction of the transmission tower, the stress and deformation of the foundation and the surrounding soil were calculated by applying 10 steps of load on the concrete tower foundation. The concrete foundation was modelled using a linear elastic model, whereas the surrounding soil was modelled using an E-v model.
(2) During a 30 hr rainfall, all the rainfall in the infiltration zone of the transmission tower could be absorbed into the ground. (3) During a 48 hr rainfall, the infiltration zone of the power transmission tower gradually filled up and water started to flow out. In this scenario, assuming a water head of 3 cm in the infiltration zone, the right side of the equation should be set to a water head of 3 cm. (In practical engineering, the water head in the infiltration area varies with rainfall duration, rainfall amount, and drainage conditions. In this study, the selection of a 3 cm water head was based on the investigation of the most unfavourable conditions.) For the hydraulic boundary during the rainfall stage, at the initial stage of rainfall, there exist many pores in the soil with strong water absorption capacity, and the infiltration volume is close to the rainfall volume; this boundary condition is called the flow rate boundary. As the rainfall duration increases, the soil moisture near the surface gradually rises and approaches saturation. Subsequent rainfall cannot fully infiltrate into the soil, and surface runoff occurs. Therefore, assuming that suction on the ground approaches zero after 30 hr of rainfall and the ground is covered by rainwater, the boundary condition is changed from a flow rate boundary to a water head boundary.  Figures 13-16 show displacement and saturation distribution fields at different stages for four calculation schemes; and Table 3 summarises the horizontal, vertical, and saturation data for the different schemes. The analysis shows that whether it is a straight or sloping foundation, without the use of antiseepage layer or lime-stabilised soil cushion layer treatment, the foundation will experience significant settlement under rainfall infiltration, which may lead to instability of the transmission tower.

Numerical Simulation.
The maximum settlement at the top of the tower foundation after 30 hr of rainfall for the four schemes is 6, 5, 3.4, and 11 cm. The maximum settlement at the bottom of the tower foundation for the four schemes is 0.5, 0.8, 0.3, and 8 cm. After 48 hr of rainfall, the maximum settlement at the top of the tower foundation for the four schemes is 6, 12, 5, and 24 cm; whereas the maximum settlement at the bottom of the tower foundation is 0.8, 2, 0.6, and 18 cm. Schemes 1-3 can meet the design requirements. From an economic perspective, Scheme 1 has a significantly larger foundation size compared with Scheme 2 or 3, and the construction difficulty for Scheme 3 is greater than for Scheme 2. In view of tower foundation deformation, inclination, construction, and economic factors, using Scheme 2 is recommended. Figure 16 shows that for straight foundations treated with a waterproof layer, the tower foundation will still experience significant settlement due to horizontal load, causing cracks between the foundation and waterproof layer.

Scheme Optimisation
In the previous section, Scheme 2 has the highest vertical stress; to achieve maximum economic benefit while meeting design requirements, it needed to be optimised. During optimisation, the foundation form, load, and infiltration method were kept constant, and only the thickness of the limestabilised soil cushion layer was changed. In Scheme 2, the thickness of the lime-stabilised soil cushion layer was 2,000 mm, whereas Optimised Schemes 1-3 used thicknesses of 1,000, 1,600, and 2,400 mm, respectively. Figures 17-19 show that as the thickness of the limestabilised soil cushion layer increases, the settlement at the midpoint of the foundation bottom decreases, which is generally consistent with the trend. In Optimised Scheme 1, the cushion layer thickness was 1,000 mm, and the midpoint settlement of the foundation was 2.5 cm, which was 0.5 cm higher than the Original Scheme 2. For Scheme 2, the cushion layer thickness was 1,600 mm, and the midpoint settlement of the foundation was 2.3 cm, an increase of 0.3 cm compared with the Original Scheme 2. In Optimised Scheme 2, the cushion layer thickness was 2,400 mm, and the midpoint settlement of the foundation was 1.4 cm, a decrease of 0.6 cm compared with the Original Scheme 2. Thus, Optimised scheme 2 yields the best results.
The curve relationship between the midpoint settlement at the bottom of the foundation and the cushion layer  thickness was established by comparing the optimised and original schemes (see Figure 20). When the cushion layer thickness is determined, the midpoint wet settlement at the bottom of the foundation can be directly obtained from the graph. This section optimised the treatment scheme for the inclined footing foundation actually used in the project. By adding a cushion layer with a thickness of 1,600 mm in the demonstration electricity transmission line project in Guanting-Lanzhou East, the design requirements can be meet. If the construction is conducted according to the Original Scheme 2, it will require 77 m 3 of lime-stabilised soil to be processed for one tower foundation. Using the optimised scheme would require only 62 m 3 of lime-stabilised soil, reducing the amount of lime-stabilised soil required by about 20% compared with the original treatment scheme.

Conclusions
Taking the 750 kV demonstration electricity transmission line project in Guanting-Lanzhou East as an example, this article selected typical samples and conducted compression and collapse tests. According to the extensive use of excavated foundation with expanded bottom and inclined footing foundation in the engineering field, multiple treatments for collapsible loess were designed and analysed using finite element analysis to simulate the rainfall infiltration process in the site. The following conclusions were drawn: (1) Undisturbed loess has a certain structural strength.
When the stress exceeds structural strength, loess deformation increases rapidly. The structural strength of loess decreases with the increase in water content. The relationship between saturation and compression modulus can be described using an exponential function. (2) The loess settlement process can be summarised into four stages: additional compression deformation stage at the beginning of the experiment, collapsing initiation stage as the soil sample gets soaked, collapsing development stage during the saturation period, and collapsing attenuation stage with smooth settlement. These stages correspond to the destruction and recombination process of the structure and have a close relationship with its microstructure evolution. (3) The analysis of the foundation displacement field and loess saturation field over time after rainfall infiltration shows that the scheme of adding a limestabilised soil cushion layer and waterproof layer to the inclined footing foundation used in the project is the most effective. For the scheme of adding a waterproof layer to the excavated foundation with expanded bottom, the foundation will shift under horizontal forces, causing cracks between the foundation and waterproof layer, leading to rainfall infiltration and settlement.      (4) Numerical analysis of the original treatment scheme of adding a waterproof layer to the inclined footing foundation shows that some room still exists for optimisation while satisfying the regulatory requirements. Given that the design scheme needs to balance safety and economy, the thickness of the cushion layer was optimised in this article. The final optimised result shows that a 1,600 mm lime-stabilised soil cushion layer can meet the design requirements while maintaining the same treatment range as before. (5) The experiment and research were conducted on the actual soil samples and foundation treatment schemes used in the project, combined with a survey of the operation of the transmission lines, proving that the lime-stabilised soil treatment technology used in the northwest region for many years is safe and reliable.

Data Availability
The data supporting the current study are available from thecorresponding author upon request.

Conflicts of Interest
The authors declare that they have no conflicts of interest.

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Advances in Civil Engineering