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Article

Study on the Reducing Measures to Reduce the Influence of Culvert Extension on Existing Lines in Loess Regions

School of Civil Engineering, Lanzhou Jiaotong University, Lanzhou 730070, China
*
Author to whom correspondence should be addressed.
Submission received: 30 December 2022 / Revised: 8 March 2023 / Accepted: 19 March 2023 / Published: 24 March 2023
(This article belongs to the Special Issue Railway Infrastructures Engineering: Latest Advances and Prospects)

Abstract

:
Due to the many constraint conditions, construction difficulties, and high control standards, and the impact of new line construction on existing lines, the construction of culvert extensions in widened sections of loess areas has become a form of control in railway construction projects. This work analyzes the technical difficulties of culvert extension construction schemes based on a practical engineering case. A scheme to provide culvert protection against slight disturbances is determined, and the construction schemes of the culvert extension structure and transition section filling are optimized. The rationality of culvert extension control measures and the influence of construction on the existing line are then studied based on the monitoring data for each stage. The results show that the implementation of the slight disturbance culvert protection has little influence on the existing line, and has the greatest influence during steel sheet pile construction (<0.5 mm). We symmetrically construct the culvert extension structures (transverse) and transition section filling (longitudinal and transverse) to effectively reduce the influence of differences in the deformation value between the two sides of the existing line at the same level as the existing line. The deformation of the upper side of the culvert fluctuates with the construction of the composite foundation and shows an overall upward trend, while the deformation increases first and then decreases in the transition section, and the deformation of the upper side of the culvert is larger than that of the transition section. The level gauge deformation of each side decreases abruptly at the filling stage of the bottom plate, side plate, top plate, and splayed wall. The settlement value of the level gauge of each station increases nonlinearly with the increase in the filling height of the transition section, and the settlement variation value of the transition section at each filling stage is higher than that of the upper side of the culvert.

1. Introduction

The development of high-speed railways in China has political significance, contributes to the economy, provides social benefits, and reflects cultural values. Due to the joint efforts of railway workers across the country, China has constructed the longest high-speed railway, with the largest construction scale and fastest commercial operation, in the world [1]. New railway improvements must connect with the existing railway before entering a station, thus forming a roadbed width structure or a culvert extension structure. Structures underneath the rail line also face higher requirements as train operating speeds increase. Thus, determining how to control the deformation of the structure under the rail has emerged as a technical problem in adjacent projects [2,3].
When a culvert extension structure is constructed in the widening section of a railway, the existing line culvert structure and the transition section will experience a certain level of post-construction settlement during the filling and service stages [4,5,6]. Scholars have considered novel materials and structures in their research to reduce the impact on existing lines during the construction of newly built structures. According to an actual roadbed width project, Sun [7,8] analyzed the weak point of the culvert extension, using reinforcing steel on the culvert tops and walls and geofoam and foam concrete to reduce loads on the culvert. Li [9] used a combination of manual excavation piles and H-shaped sheet piles to protect the existing subgrade before the construction of a high-fill culvert extension, which ensured that the settlement of the existing subgrade was within a reasonable range. Zuo [10] proposed the lengthening culvert types of the frame culvert and board culvert, and employed a prefabricated jacking construction scheme, for added second-line railway projects by Han-Chang and Han-Ji railways in order to ensure the construction safety of culverts on existing lines. Lian [11] combined a steel sheet pile and cross-bracing protection construction program for a speed-increasing reconstruction project in the eastern section of the Hainan Island Ring Railway. Chen [12] proposed a lateral jacking frame culvert scheme that was based on the actual difficulties of skew slab culvert lengthening construction of an existing railway line combined with actual engineering. Loess as a special soil, the soil structure is prone to produce significant deformation under the effect of additional stress or increased moisture [13]. It is one of the technical difficulties to carry out culvert extension project in the loess area but also the control projects in railway construction engineering. The impact of new railway engineering on existing lines in loess regions and the required control reduction measures are unclear due to a lack of research in this area. To address this, we first analyze the technical difficulties of the culvert extension scheme based on a culvert extension project in a loess region. The optimized control reduction measures are then determined based on the protection and structure construction schemes. The deformation data of the transition section of the existing line and culvert during the construction phase of the culvert extension and its transition section filling are monitored. The suitability of the reduction and control measures of the culvert extension and the impact of each phase of construction on the existing line is then analyzed.

2. Culvert Extension Project Profile

2.1. Engineering Geological Conditions

The studied sections are located in Shuping Town, Yongdeng County, and Lanzhou City. The lithology of the stratum in the sites are mainly sandy loess, coarse sand, and underlying mudstone intercalated with sandstone. Combined with geological prospecting documents, the physical and mechanical parameters of each stratum are provided in Table 1.

2.2. Culvert Extension Conditions and Monitoring Section

As shown in Figure 1, the foundation treatment of the existing line in Site 1 is a lime-soil compaction pile having a 40 cm pile diameter, 12 m pile length, 95 cm pile distance, and a plum-shaped arrangement. The foundation treatment of the existing line in Site 2 is in the form of a cement mixing pile of 50 cm pile diameter, 14 m pile length, 120 cm pile distance, and a plum-shaped arrangement. The foundation treatment of the culvert extension section is a high-pressure rotary jet pile of 50 cm pile diameter, 140 cm pile distance, and a square arrangement. The pile length at Site 1 is 12 m, and that at Site 2 is 13 m.
The culvert transition section and the surface layer on the foundation bed of the existing line and the new line were filled with respective layers of 3% cement-graded crushed stone and 5% cement-graded crushed stone (0.6 m) (shown in Figure 2). The length × width × height of the principal culvert part at Site 1 was 15.75 m × 6.0 m × 6.0 m. The extension on the uplink side was 7 m, and the extension on the downlink side was 9 m. The length × width × height of the principal culvert part at Site 2 was 15.0 m × 4.0 m × 4.0 m. The extension on the uplink and downlink sides was 13 m. In the operation stage of the existing line, a monitoring section was set at a distance of 1m from the culvert structures and the settlement observation markers were used for monitoring the settlement of line center and the road shoulder.(shown in Figure 2). A level gauge was also set longitudinally at the transition section of the existing line and at the toe of the ballast slope at the top of the culvert before the construction of the new subgrade.

3. Technical Difficulties and Construction Scheme of Culvert Extension

3.1. Technical Difficulties

3.1.1. Difficulties in Implementing a Protection Scheme

The original protection design scheme was similar to the one proposed in the literature [9] (shown in Figure 3), in which a manual excavation pile of 1.0 m diameter and 8.0 m length was used for support. Due to the existence of the composite foundation under the ground line of the existing subgrade, this process is difficult to implement when manual excavation piles are dug at the location. The position of the manual excavation piles at Site 1 (shown in Figure 4) was also close to the catenary column and its foundation, resulting in inevitable disturbance to it during construction and affecting the safety of the train operation. Furthermore, as the manual excavation piles were located in the principal part of the subgrade and the existing embankment filler was made of particle material, Under the action of the dynamic load of the train, the artificial digging piles were inclined to collapse during the digging process or before the strength of the retaining was formed. This threatened the safety of construction personnel and the existing line.

3.1.2. Selection of Old and New Combined Measures

As shown in Figure 5, Site 2 displays the phenomenon of mortar rubble damage caused by large post-construction deformation on both sides of the subgrade culvert transition section. Combined with the settlement-operation time relation curve of the settlement mark on one side of the transition section in Figure 6, the result shows that the settlement value in the settlement marker increases with the growth of operation time and that the settlement from the beginning of the operation to the end of 2017 is small and shows a basically stable trend. The settlement then enters an abnormal growth rate period caused by long-term rainfall, frost heaving, and the upper train load, resulting in large abnormal permanent deformation [14]. According to the results, by the end of 2020, the post-construction settlement at the central location of the transition section and the road shoulders on both sides would be 11.809, 4.608, and 5.031 mm, respectively. The difference in the consolidation degree of the composite foundation and filler between the newly-built line and the existing line means that the culvert extension structure and existing culvert structure are prone to differential settlement under the effect of the self-gravity load and the upper train. Due to the early large post-construction settlement value, this position displays an unstable phenomenon. A large additional stress can easily occur when the positions of the old and new structures are combined with a rigid connection, producing cracks. Flexible connections with joint seam are used to address this issue, but these create significant waterproofing problems [15].

3.1.3. High Lateral Pressure of Composite Foundation Construction

Considering the selection of a composite foundation for newly-built line widening sections, the high-pressure rotary jet pile can meet the requirement of low clearance for construction machinery, and has a simple technology and a short construction period. Therefore, a high-pressure rotary pile composite foundation was selected as the foundation treatment shape to achieve foundation reinforcement in this work [16,17]. Combined with the high-pressure jet grouting test results, the grouting pressure was determined as 25 MPa, and the lifting speed was about 0.2 m/min. The pressure around the pile was calculated as 220 kPa according to the empirical formula of blast pressure attenuation proposed in the literature [18,19]. The pressure will be transferred to the existing subgrade transition section and culvert through the lower composite foundation, resulting in deformation and affecting the operation quality of the train. Therefore, real-time monitoring is needed to reasonably control the existing structural deformation.

3.2. Construction Scheme

The construction scheme of a slight-disturbance culvert extension combined with the technical difficulties of culvert extension is determined in this section. The process was as follows: steel sheet pile protection construction → I-beam support installation → existing splayed wall demolition → waterproof implementation → culvert foundation construction → culvert main body construction.
Steel sheet pile protection construction: The outer side of the splayed wall was protected by SP-Ⅳ steel sheet piles, in which the single length of the steel sheet piles was 6.0 m. I-20a steel was set inside the top, and the steel sheet piles were connected with an I-beam using a u-shaped hoop.
I-beam support installation: I-32a type steel was used to support the existing splayed walls to strengthen the subgrade of the existing line, in which the upper plane of the support was 50 cm below the bottom of the existing top plane. Three I-beams were welded into a whole by continuous beams in the direction of the joint length, and the I-beams were welded to the eight-beam wall by drilling and grafting in the wall.
Existing splayed wall demolition: The new culvert part affected by the existing splayed wall was chiseled with a pneumatic pick, and the block was embedded without damaging the wall body.
Waterproof implementation: After the demolition of the existing splayed walls using epoxy resin mortar leveling, waterproof coating was applied, and the seam was filled with polyethylene foam board and PVC mastic. The top and bottom of the culvert were waterproofed with a back-fitted rubber water stop belt, including two outer layers of polyurethane waterproofing coating and a top layer made of 3 cm thick C40 fine stone concrete.
Culvert foundation construction: The high-pressure rotary piles were constructed form the near to the remote, relative to the boundary of the new and old composite foundation, by the pile jump method (shown in Figure 7). Thus, the first sequential construction was of pile rows P1 → P3 → P5 (odd). The subsequent pile strength was no less than 50% of the design requirements. The construction of pile rows P2 → P4 → P6 (even) was then carried out. The high-pressure rotary jet grouting piles was no longer constructed in the foundation area where the splayed wall was not removed. For Sites 1 and 2, nine and eight rows of piles were built, respectively.
Culvert main part construction: This mainly included the four stages of the bottom slab, side slab, top slab, and splayed wall pouring, during which the construction of reinforcement works and formwork installation was carried out (shown in Figure 8).

4. Monitoring Results and Analysis

4.1. Analysis of Deformation Observation Results in the Implementation Stage of Slight-Disturbance Protection Scheme

The relation curve of level gauge deformation with the implementation time of the protection scheme at each site is shown in Figure 9. The demolition of the existing downlink splayed wall at Site 1. follows the completion of the uplink culvert extension structure construction. The analysis shows that the level gauge deformation increases with the implementation time during the construction of steel sheet piles on the uplink and downlink. The deformation of the level gauge decreases when the I-beam support is installed, among which the deformation of the level gauge on the upper side of the culvert is 0.139–0.264 mm, while the deformation of the level gauge in the transition section is smaller (<0.1 mm). When the existing splayed wall is chiseled, the deformation of the level gauge on this side has a greater impact, the deformation of the level gauge on the upper side of the culvert tends to decrease, and the level gauge at the transition section tends to increase. For Sites 1 and 2, the deformation amplitude of the level gauges W1–W4 all appear in the steel sheet pile construction stage. These are 0.085, 0.145, 0.364, 0.371, 0.136, 0.197, 0.424, and 0.481 mm, respectively, illustrating that the implementation of the slight disturbance protection scheme has little influence on the existing line.
The variations in the above data are the result of composite action during the construction of steel sheet piles, in which lateral force is generated on the existing subgrade structure. While the phenomenon is more obvious in the high-density coarse granule subgrade filler, it plays a role in constraining the lateral deformation of the existing subgrade when the splayed wall is chiseled [20]. The self-weight of the I-beam support structure acts directly on the culvert structure, which has a greater impact on the vertical deformation of the culvert structure, whereby the anti-deformation capability of the culvert structure can be simultaneously improved in the later stage. The demolition of the existing splayed wall reduces the self-weight as well as the constraint effect on the existing line subgrade.

4.2. Analysis of Deformation Observation Results in the Construction Stage of the Culvert Extension Structure

The relation curve of level gauge deformation with the construction time of each stage at Site 1 is shown in Figure 10. The composite foundation treatment time of the uplink side was from June 15 to 18, 2021, and the composite foundation treatment time of the downlink side was from July 20 to 24, 2021. The analysis shows that when the composite foundation is under treatment on the uplink side, the deformation of level gauges W-2 and W-3 on the uplink side increases and then decreases with the construction and interval of everyday foundation treatment. The deformation of W-2 on the top of the culvert shows an overall increasing trend with the composite foundation treatment time, while the deformation of W-3 on the transition section is only obvious during the construction of P1 and P3 piles and then shows a decreasing trend. After the completion of composite foundation construction on the uplink side, the bulge deformation of W-2 and W-3 is 0.597 and 0.317 mm, respectively, while the deformation of level gauges W-1 and W-4 is smaller on the downlink side. When the culvert extension structure is under construction on the uplink side, the deformation of level gauges W-2 and W-3 on the uplink side decreases abruptly at the pouring stage of the bottom plate, side plate, top plate, and splayed wall. For W-2, the corresponding deformation values are −0.105, −0.924, −1.618, and −2.186 mm, respectively. For W-3, the corresponding deformation values are −0.069, −0.304, and −0.714 mm, respectively. The deformation values of level gauges W-1 and W-4 are smaller on the downlink side. When the composite foundation is under construction on the downlink side, the level gauges W-1 and W-3 on the downlink side show a similar pattern to that of W-2 and W-3 during composite foundation construction on the uplink side. Both display large bulge deformation in the level gauge on the uplink side and small uplift deformation in the level gauge of the transition section. When the culvert extension structure is under construction on the downlink side, the deformation of the level gauge on the uplink side decreases abruptly with the construction of each stage. Until the completion of the culvert extension structure under construction, the deformation values of W-1 to W-4 are −3.092, −2.451, −0.859, and −1.184 mm, respectively. Due to the differences in the composite foundation treatment area, culvert extension structure, and construction time on both sides, the deformation values of the level gauge on the upper side of the culvert (W-1, W-2) and transition section positions (W-3, W-4) on both sides are different. The maximum differences appear at the end of the composite foundation treatment on the downward side, and the maximum differences are 2.873 and 0.706 mm, respectively.
Transverse symmetric construction was adopted for the construction of the culvert extension structure at Site 2, and longitudinal and transverse symmetric construction was employed to fill the transition sections at Sites 1 and 2. These methods reduced the influence of the deformation value of the culvert’s upper side and both sides of the transition section on the existing track horizontal value (shown in Figure 11).
The relation curve of level gauge deformation with the construction time of each stage at Site 2 is shown in Figure 12. The analysis shows that the deformation of level gauges W-1 and W-2 on the upper side of the culvert fluctuates with the construction of the composite foundation and shows an overall upward trend until the completion of the composite foundation. The deformation values are 0.676 and 0.877 mm, respectively. The deformation of level gauges W-3 and W-4 increases first and then decreases in the transition section position with the construction of the composite foundation. At the late stage of composite foundation construction, due to the material accumulation in the transition section near the downlink side, the deformation values of the level gauge on the downlink side are lower than those on the uplink side for the upper side of the culvert and the transition section. When the culvert extension structure is constructed, the deformation values of W-1 to W-4 decrease abruptly under the pouring stage of the bottom slab, side slab, top slab, and splayed wall. Until the culvert extension structure is completed, the deformation values of W-1 to W-4 are −2.636, −3.009, −1.109, and −1.310 mm, respectively, and the deformation values of W-1 and W-2 are significantly higher than those of W-3 and W-4. The maximum difference values of the upper side of the culvert and the transition section position are 0.373 and 0.201 mm, respectively. Combined with Figure 10, the analysis shows that lateral symmetrical construction can significantly reduce the influence of the difference in deformation values between the upper side of the culvert and the transition section position on the horizontal values of the existing line track for culvert extension section construction.
The relation curve of level gauge deformation with the construction time of each stage at Site 2 is shown in Figure 11. The analysis shows that the deformation of level gauges W-1 and W-2 on the upper side of the culvert fluctuates with the construction of the composite foundation and shows an overall upward trend until the completion of the composite foundation. The deformation values are 0.676 and 0.877 mm, respectively. The deformation of level gauges W-3 and W-4 increases first and then decreases in the transition section position with the construction of the composite foundation. At the late stage of composite foundation construction, due to the material accumulation in the transition section near the downlink side, the deformation values of the level gauge on the downlink side are lower than those on the uplink side for the upper side of the culvert and the transition section. When the culvert extension structure is constructed, the deformation values of W-1 to W-4 decrease abruptly under the pouring stage of the bottom slab, side slab, top slab, and splayed wall. Until the culvert extension structure is completed, the deformation values of W-1 to W-4 are −2.636, −3.009, −1.109, and −1.310 mm, respectively, and the deformation values of W-1 and W-2 are significantly higher than those of W-3 and W-4. The maximum difference values of the upper side of the culvert and the transition section position are 0.373 and 0.201 mm, respectively. Combined with Figure 9, the analysis shows that lateral symmetrical construction can significantly reduce the influence of the difference in deformation values between the upper side of the culvert and the transition section position on the horizontal values of the existing track for culvert extension section construction.

4.3. Analysis of Deformation Observation Results in the Filling Stage of the Transition Section

Figure 13 shows the relation curve of the level gauge settlement–filling time for Sites 1 and 2, illustrating that the level gauge settlement at each site has a nonlinear increasing phenomenon with increasing filling height. The settlement variation at each filling stage in the transition section is higher than that at the upper side of the culvert, and the settlement difference between the upper side of the culvert and the transition section decreases first and then increases gradually. The maximum settlement differences of Sites 1 and 2 are 6.436 and 6.954 mm, respectively. Since the center position of the uplink and downlink lines is about 2.7 m from the foot of the ballast slope, the actual longitudinal level values of the uplink and downlink railways of Sites 1 and 2 are 0.8 mm/(10 m), 1.1 mm/(10 m), 1.1 mm/(10 m), and 1.2 mm/(10 m) respectively, which are lower than the control value (3 mm/(10 m)). For Site 1, the settlement values from W-1 to W-4 are 7.584, 6.349, 12.635, and 14.020 mm, respectively, until the completion of the transition section filling. For Site 2, the settlement values from W-1 to W-4 are 12.583, 14.125, 20.528, and 19.547 mm, respectively, all of these values meet the requirements of the post-construction settlement value (≤5 cm).
The reasons for the above phenomenon are analyzed in this section. Assuming that each layer is a uniformly distributed load (shown in Figure 14), the influence scope of the transition section of the new line on the existing subgrade increases non-linearly with the filling height as it fills up layer by layer and the longitudinal length of the transition section increases gradually with the height. The influence of the transition section filling layer on the culvert structure can be divided into the lateral area and the upper area. For the lateral area, it affects the culvert structure through the lateral wall of the culvert and the lower composite foundation. For the upper area, its vertical stress on the culvert structure is related to the ratio of the filling height and the culvert width [21]. The influence range also gradually increases as the transverse width of the newly-built subgrade increases. This then creates the phenomenon in which the influence of the filling of the transition section of the downlink side of Site 1 is greater than that of the uplink side.

5. Conclusions

This work addressed the technical difficulties in the actual engineering of a railway culvert extension in the widened section of a loess region by optimizing a construction scheme. Based on the monitoring data at each stage, the appropriateness of the culvert extension scheme and the impact of each stage’s construction on the existing line were studied. The main conclusions are as follows:
(1)
Combined with the difficulties of culvert extension in loess regions, a scheme of slight-disturbance culvert extension was determined. The results showed that the slight-disturbance protection method had little influence on the existing line (<0.5 mm).
(2)
Adopting transverse symmetrical construction of the culvert extension structure obviously reduced the influence of the difference in deformation values on both sides of the existing line on the level value of the existing track. The maximum difference values of the upper side of the culvert and the transition section position were reduced from 2.873 and 0.706 mm to 0.372 (Site 1) and 0.201 mm (Site 2), respectively.
(3)
During the filling stage of the transition section of the road culvert, the settlement value of the level gauge at each site increased non-linearly with rising filling height. Until the completion of the filling of the transition section, the maximum longitudinal level values of the two sites were 1.1 mm/(10 m) and 1.2 mm/(10 m), and the maximum settlement values were 14.020 and 20.528 mm, respectively, all of which satisfied the control requirements of the longitudinal level value (3 mm/(10 m)) and post-construction value (≤5 cm).

Author Contributions

Conceptualization, W.Z. and F.H.; theoretical investigation, W.Z.; data acquisition, F.H. and K.Z.; data analysis, F.H. and D.W.; writing original draft, D.W.; project administration, W.Z. and F.H. All authors have read and agreed to the published version of the manuscript.

Funding

This work was supported by the Gansu Youth Science and Technology Fund project (21JR1RA249), the Special Funds for Guiding Local Scientific and Technological Development by The Central Government (22ZY1QA005) and the Lanzhou Jiaotong University youth science foundation project (2019026). There is no conflict of interest regarding the publication of this paper.

Institutional Review Board Statement

This study did not involve humans or animals.

Informed Consent Statement

This study did not involve humans.

Data Availability Statement

This study did not report any data.

Conflicts of Interest

The authors declare no conflict of interest.

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Figure 1. Schematic diagram of the culvert extension project: (a) Site 1; (b) Site 2.
Figure 1. Schematic diagram of the culvert extension project: (a) Site 1; (b) Site 2.
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Figure 2. Schematic diagram of component layout in the existing railway. (a) profile diagram; (b) flat view.
Figure 2. Schematic diagram of component layout in the existing railway. (a) profile diagram; (b) flat view.
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Figure 3. The original scheme of culvert extension protection.
Figure 3. The original scheme of culvert extension protection.
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Figure 4. The position diagram of the catenary column and culvert (Site 1).
Figure 4. The position diagram of the catenary column and culvert (Site 1).
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Figure 5. A picture of the damaged mortar rubble in the subgrade–culvert transition section.
Figure 5. A picture of the damaged mortar rubble in the subgrade–culvert transition section.
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Figure 6. Settlement scale settlement–operation time relationship curve.
Figure 6. Settlement scale settlement–operation time relationship curve.
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Figure 7. Diagram of the construction sequence of high-pressure rotary piles in the culvert extension section.
Figure 7. Diagram of the construction sequence of high-pressure rotary piles in the culvert extension section.
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Figure 8. Concrete pouring construction drawing.
Figure 8. Concrete pouring construction drawing.
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Figure 9. Relation curve of level gauge deformation with the implementation time of the scheme: (a) Site 1; (b) Site 2.
Figure 9. Relation curve of level gauge deformation with the implementation time of the scheme: (a) Site 1; (b) Site 2.
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Figure 10. Relation curve of level gauge deformation with the construction time of each stage (Site 1): (a) composite foundation treatment of uplink side; (b) culvert extension structure construction of uplink side; (c) composite foundation treatment of downlink side; (d) culvert extension structure construction of downlink side.
Figure 10. Relation curve of level gauge deformation with the construction time of each stage (Site 1): (a) composite foundation treatment of uplink side; (b) culvert extension structure construction of uplink side; (c) composite foundation treatment of downlink side; (d) culvert extension structure construction of downlink side.
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Figure 11. Symmetrical construction drawing.
Figure 11. Symmetrical construction drawing.
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Figure 12. Relation curve of level gauge deformation with the construction time of each stage (Site 2): (a) composite foundation treatment; (b) culvert extension structure construction.
Figure 12. Relation curve of level gauge deformation with the construction time of each stage (Site 2): (a) composite foundation treatment; (b) culvert extension structure construction.
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Figure 13. Relation curve of the level gauge settlement-filling-time: (a) Site1; (b) Site 2.
Figure 13. Relation curve of the level gauge settlement-filling-time: (a) Site1; (b) Site 2.
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Figure 14. Schematic diagram of additional stress contour lines of uniformly distributed load at each layer in the filling stage: (a) schematic diagram of the cross section; (b) schematic diagram of the longitudinal section.
Figure 14. Schematic diagram of additional stress contour lines of uniformly distributed load at each layer in the filling stage: (a) schematic diagram of the cross section; (b) schematic diagram of the longitudinal section.
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Table 1. The physical and mechanical parameters of each stratum.
Table 1. The physical and mechanical parameters of each stratum.
Stratigraphic TypeThickness/mγ/(kN/m3)Poisson’s RatioCohesion/kPaAngle of Internal Friction/(°)
Site 1Site 2
② 422 Sandy loess2.03.218.50.3215.221.1
② 423 Sandy loess7.27.518.70.3218.421.4
② 833 Coarse sand2.52.118.80.318.222.4
⑨ 42 Mudstone with sandstone5.25.719.80.3313.123.1
⑨ 43 Mudstone with sandstone//20.10.3315.324.7
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Zhao, W.; Zhang, K.; Han, F.; Wang, D. Study on the Reducing Measures to Reduce the Influence of Culvert Extension on Existing Lines in Loess Regions. Appl. Sci. 2023, 13, 4138. https://0-doi-org.brum.beds.ac.uk/10.3390/app13074138

AMA Style

Zhao W, Zhang K, Han F, Wang D. Study on the Reducing Measures to Reduce the Influence of Culvert Extension on Existing Lines in Loess Regions. Applied Sciences. 2023; 13(7):4138. https://0-doi-org.brum.beds.ac.uk/10.3390/app13074138

Chicago/Turabian Style

Zhao, Wenhui, Ke Zhang, Feng Han, and Dingshun Wang. 2023. "Study on the Reducing Measures to Reduce the Influence of Culvert Extension on Existing Lines in Loess Regions" Applied Sciences 13, no. 7: 4138. https://0-doi-org.brum.beds.ac.uk/10.3390/app13074138

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