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A Brief Analysis of the Design of Retaining Walls for Mountain Roads 1 Introduction Road retaining walls are structures used to support the fill material of roadbeds or soil on slopes, thereby preventing deformation or instability of such fill materials or soil. In subgrade engineering, retaining walls can be used to stabilize embankment and cut slope slopes, reduce the volume of earthwork and the land area required, prevent water flow from eroding the subgrade, and are often employed to address subgrade defects such as landslides and collapses. There are various types of retaining walls. Based on their structural characteristics, they can be classified into stone masonry gravity type, stone masonry counterweight type, reinforced soil lightweight type, concrete semi-gravity type, reinforced concrete cantilever and buttress type, column-plate type, anchor rod type, anchor plate type, and parapet type, among others ； Based on their position in the cross-section of the roadbed, they can be further divided into: shoulder walls, embankment walls, and cut walls ； Based on the environmental conditions, they can be further classified into retaining walls for general areas, retaining walls for flooded areas, and retaining walls for earthquake-prone areas. When considering retaining wall design options, a technical and economic comparison with other engineering solutions should be carried out to assess their technical feasibility, reliability, and economic rationality. Only after that can a design option be determined, and the appropriate type of retaining wall can be selected based on the actual conditions. On mountain roads, where the terrain conditions are more complex and the slopes are steeper, retaining walls are used more frequently. Over the past few years, the author has been involved in the design of more than 20 sections of mountain roads (grades 2 and 3), covering a total distance of over 300 kilometers. The main responsibilities included working on roadbed protection projects, with a focus on the design of retaining walls. Through this experience, the author has gained certain knowledge and insights regarding the design of retaining walls for mountain roads, which are presented here for reference in similar engineering projects. 2 Basic information and design parameters for retaining wall design 2.1 Basic information For the design of a retaining wall, the following information is necessary: route plan views, longitudinal sections, cross-sectional views, geological data (including engineering geology survey reports and engineering geophysical exploration reports), seismic exploration reports, hydrological data, overall design documents, and a list of structures, etc. 2.2 Selection of Design Parameters 2.2.1 Physical and mechanical properties of the fill material For the design of retaining walls on secondary and tertiary roads in hilly areas, when experimental data are unavailable, the calculated internal friction angle and unit weight of the fill material can be selected referencing Tables 1 and 2: Table 1 Reference values for the internal friction angle ψ of fill materials Type of soil Boulders Large pebbles, crushed stone Small pebbles, gravel, coarse sand, stone dust Medium and fine sand, sandy soil Silt Clay Internal friction angle (°) 45 40 35 30 26 14–21 Table 2 Standard unit weight of fill materials Type of soil Gravel, crushed stone, gravelly soil Sand, sandy soil Silt, clay When ωlB/6 results in tensile stress at the foundation base, and considering that foundations generally cannot withstand tensile forces, this tensile component is ignored and the maximum tensile stress at the base is calculated based on stress redistribution: σ1 = 2(W + Ey) / 3Zn. If negative eccentricity occurs, Zn in the above formula should be replaced with (B – Zn). 5.4 For the verification of the wall section strength, usually one or two sections are selected for checking. The checking section can be selected at the base of the foundation, at 1/2 of the wall height, or at the junction of the upper and lower walls, etc. The verification of the wall section strength includes the verification of normal stress and shear stress. Shear stress includes horizontal shear stress and diagonal shear stress; gravity retaining walls are checked only for horizontal shear stress, while counterweight retaining walls also require verification of shear stress in the diagonal sections. 6 After taking measures to complete the design of the retaining wall’s cross-section as well as the checks for stability and strength, it is necessary to take appropriate actions to ensure the safety of the retaining wall. 6.1 Foundation Reinforcement Measures 6.1.1 To reduce the compressive stress on the foundation and enhance stability against overturning, a step is extended at the base of the wall to widen the foundation area. The width of the wall toe step should be no less than 20 cm, and the height-to-width ratio of the step can be 3:2 or 2:1. 6.1.2 When the foundation is composed of soft soil layers, high-quality materials such as sand and gravel, crushed stone, slag, or lime soil can be used for backfilling in order to distribute the base compressive stress and meet the design requirements. 6.2 Drainage measures: For rammed earth retaining walls, a drainage hole should be provided above the ground level in front of the wall. When the wall is tall, drainage holes can be added at the upper part of the wall. The drainage holes are square or circular holes with dimensions of 10×10 cm, spaced 2 to 3 meters apart; the upper and lower drainage holes are arranged offset from each other. A filter material should be installed at the water inlet of the drain hole. 6.3 Settlement joints and expansion joints are provided to prevent cracks in the wall structure caused by uneven settlement of the foundation. Settlement joints should be installed according to the wall height and variations in the properties of the foundation. Meanwhile, expansion joints are necessary to reduce cracks that occur in masonry structures due to shrinkage, hardening, and temperature changes. The settlement joints and expansion joints of the retaining wall are provided together, with one joint installed every 10–15 meters. The width of each joint is 2–3 cm, extending from the top of the wall to its base. Elastic materials such as asphalt-wrapped hemp, asphalt-treated bamboo fibers, or asphalt-coated wooden boards should be used to fill these joints, which should be filled along the inner, outer, and upper sides of the wall, with a filling depth of not less than 15 cm. 6.4 Connection between the wall top and the road surface: When the width of the wall top is greater than that of the earth shoulder, a space equivalent to the thickness of the road surface structure should be reserved in the part of the retaining wall that extends into the earth shoulder for paving the road surface. 6.5 Measures to ensure the safe operation of vehicles: For the shoulder wall, a layer of C20 concrete is poured 50 cm below the top surface of the wall, with rebar embedded in it; an impact barrier or impact wall is then installed on top of this layer. 7 Material Requirements 7.1 The stone must be selected carefully, with uniform texture, no cracks, and resistance to weathering. 7.2 The compressive strength of the stone shall be not less than 30 MPa. 7.3 Try to use larger stones for construction; the blocks should be roughly square in shape, with a thickness of not less than 15 cm, while their width and length should be 1.5–2.0 times and 1.5–3.0 times respectively the thickness. 7.4 Masonry shall be constructed using mortar grade 7.5, with joints filled using mortar grade 10. 8 Design Insights 8.1 Selection of Design Parameters Since the Coulomb theory used to calculate active earth pressure is more suitable for sandy soils, it can lead to certain errors in the calculation of pressure for cohesive soils. Therefore, when calculating retaining walls filled with cohesive soils, the values of design parameters such as the internal friction angle of the filler should be chosen in a more conservative manner. Since Coulomb’s theory is a simplified method for calculating earth pressure, for retaining walls filled with sandy soil, the design parameters should also be set at relatively conservative values based on actual conditions. 8.2 Selection of the safety factor: For retaining walls with a height of ≥6m, it is recommended to increase the safety factor by 20% in actual design to ensure their safety. 8.3 The slope of the wall surface is chosen for aesthetic reasons and to facilitate construction; a single wall slope is typically used for an entire section of retaining wall. For retaining walls on mountain roads, using a steeper wall slope can effectively reduce the wall height and save materials. Under normal circumstances, a wall slope of 1:0.05 is sufficient for gravity retaining walls (tilted type), and a slope of 1:0.25 is suitable for counterweight retaining walls; both values meet the design requirements. 8.4 Selection of the back slope of the wall: The back slope of an inclined retaining wall generally does not exceed 1:0.3, with the specific value determined based on the temporary slope created during excavation. The back slope of an inclined retaining wall is generally set at 1:0.2, and as the wall height increases, the width at the top of the wall increases accordingly. For counterweight shoulder retaining walls, when the wall height is ≤ 8 m, the slope on the upper side of the wall is set at 1:0.25; when the wall height is > 8 m and ≤ 10 m, the slope on the upper side of the wall is set at 1:0.3 ； The slope on the back side of the lower wall shall be 1:0.25. If it is a embankment wall, the slope on the back side of the wall should be increased accordingly. 8.5 Key design controls: For inclined retaining walls, due to the large earth pressure they are subjected to, attention must be paid during design to the verification of their stability and resistance to overturning. For counterweight retaining walls, it is generally easier to meet the stability requirements; therefore, the strength of the wall section becomes the main criterion in the design of such retaining walls, which necessitates the use of high-strength materials for construction. 9 Conclusion Highway retaining walls are an important part of subgrade protection projects. Retaining walls are more widely used on mountain roads. When designing a retaining wall, detailed investigations and surveys should be carried out to determine the form and dimensions of the structure. Appropriate theories should be used to calculate the earth pressure, and checks should be performed regarding stability and cross-sectional strength. Reasonable and feasible measures must be taken to ensure the safety of the retaining wall.