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Design parametersA new type of Debris-flow grille dam is proposed to be built with a height of 8 m. Column section 500 mm × 700 mm, spacing 5000 mm. The cross section of the beam is 400 mm × 300 mm, and the spacing is 4000 mm. The section steel adopts I-steel 45a, the spacing is 250 mm. The counterfort wall is 300 mm thick and 6500 mm high. Pile foundation adopts manual digging pile, pile by 1000 mm, 5000 mm deep. The concrete is C30; Stressed bar is HRB335; Stirrups is HRB300; Stay Cable is 3 (emptyset) s15.2. The design size of the anchor piers is shown in Fig. 12. In the Figure where (T = 2 times 10^{5} N); (L_{l} = 8500;{text{mm}}); (E_{l} = 1.95 times 10^{5} ;{text{N/mm}}^{2}); (A_{l} = 420;{text{mm}}); (D_{e} = 1000;{text{mm}}); (L_{m} = 1200;{text{mm}}); (E_{e} = 3.0 times 10^{4} ;{text{N/mm}}^{2}); (H = 1000;{text{mm}}); (mu = 0.2); (E = 20;{text{N/mm}}^{2}). The parameter of gully bed soil is shown in Table 1.Figure 12The parameters of anchor piers.Full size imageTable 1 The parameters of gully bed soil.Full size tableAnalysis of results(1) The effect of the elastic modulus and Poisson’s ratio of the surrounding soil on the displacement deformation of the anchor-pulling system.The elastic modulus (E) and Poisson’s ratio (mu) are important parameters for calculating the displacement deformation of soil. They have something to do with both the properties of materials and the stress level. To analyze the effect of the physical parameter variation of the surrounding soil on the displacement deformation of the anchor-pulling system, we can study changing the elastic modulus and Poisson’s ratio. The variation range of the elastic modulus is 15–45 N/mm2, and the variation range of Poisson’s ratio is 0.15–0.25.Figure 13 shows the variation curve in which the displacement deformation increases with the elastic modulus of the soil around the anchor pier. We can see that as the elastic modulus of the soil around the anchor pier increases, the displacement deformation decreases gradually. When the elastic modulus is in the range of 15–35 N/mm2, the curve is steep, and the decrease in deformation is apparent. After 35 N/mm2, the curve becomes smooth, and the decrease in deformation tends to be stable.Figure 13The effect of the elastic modulus E(15–45 N/mm2) of the surrounding soil on the displacement of the anchor-pulling system.Full size imageIn Fig. 14, the displacement deformation increases linearly with Poisson’s ratio of the soil around the anchor pier. However, the total impact is not large. From calculation, the variation of elastic modulus of the soil around the anchor pier has nothing to do with elastic deformation of the stayed cable ((S_{1} )), but mainly influences relative shear displacement between anchor piers and the surrounding soil ((S_{2} )) and the compression performance of the soil on the front of anchor piers ( (S_{3} )). where ((S_{2} )) accounted for 89% and (left( {S_{3} } right)) accounted for 11%. When the Poisson ratio increases, the displacement deformation also increases. Poisson’s ratio has the greatest influence on the relative shear displacement ((S_{2} )) of the anchor pier and soil, accounting for approximately 96.4%. The design parameters should be selected correctly during design. The influence of parameters on the deformation of anchor system is analyzed by using control variable method. The influence of a single variable on the results can be intuitively obtained. However, the elastic modulus E and Poisson ‘ s ratio (mu) of rock and soil are not independent. Therefore, Matlab is used to analyze the influence of the two aspects on the deformation of the tensile anchor system, and the results are shown in Fig. 15. It can be seen from Fig. 15 that the influence of elastic modulus E on the deformation of tensile anchor system is much greater than that of Poisson’s ratio (mu). And the variation of the curve is basically the same, so the interaction between the two is weak.Figure 14The effect of Poisson’s ratio (mu)(0.15–0.26) of the surrounding soil on the displacement of the anchor-pulling system.Full size imageFigure 15Influence of elastic modulus E (15–45 N/mm2) and Poisson’s ratio (mu left( {0.15 – 0.26} right)) on deformation of anchor system.Full size image(2) The effect of the design parameters of anchor piers on the displacement deformation of the anchor-pulling system.The design parameters of anchor piers include the equivalent width (D_{e}), length (L_{m}) and height (H). Different design parameters have varying effects on the displacement deformation of the anchor-pulling system. Keep other parameters unchanged and let ( D_{e} ) vary in 0.5–1.5 m, (L_{m}) vary in 0.6–2.0 m, and (H) vary in 0.5–1.5 m. Analyzing their effect on the displacement deformation of the anchor-pulling system, the results are shown in Figs. 16 and 17.Figure 16The effect of equivalent width (D_{e})(500–1500 mm) on the displacement of the anchor-pulling system.Full size imageFigure 17The effect of equivalent length (L_{m})(600–2000 mm) on the displacement of the anchor-pulling system.Full size imageAs illustrated in Figs. 16 and 17, the effects of the design parameters of the anchor piers on the displacement deformation of the anchor-pulling system are almost the same. As the size increases, the displacement deformation gradually decreases, and the front section decreases quickly, while the rear section becomes gradually smooth. Here, the equivalent width (D_{e}) and length (L_{m}) mainly affect the compression performance of the soil on the front of anchor piers (left( {S_{3} } right)). The anchor piers can be seen as rigid bodies where horizontal displacement takes place. Increasing the size means increasing the contact area between the anchor pier and soil body. With this increase, the compression performance of the soil on the front of the anchor piers decreases. However, the effect of the height (H) on the displacement deformation of the anchor-pulling system is the contribution to the relative shear displacement between the anchor piers and the surrounding soil ((S_{2} )). When (H) grows, ((S_{2} )) grows accordingly. However, theoretically, the larger the effect of the size, the better it is. Because of the constraint of topographic conditions, construction conditions and economic benefits in practical engineering, it is necessary to choose the best size. the anchor pier provides enough anchor force and saves all kinds of resources. The best design dimensions suggested are (D_{e}) = 1.2 m–1.8 m, (L_{m}) = 1.5 m–2.5 m, and (H) = 1.0 m–1.6 m.It can be seen from Fig. 18 that the width (D_{e}) and the height (L_{m}) of anchor pier influence each other greatly. When (D_{e}) is 600 mm, with the increase of (L_{m}), the deformation of tension anchor system will first decrease and then increase. When (D_{e}) is greater than 800 mm, with the increase of (L_{m}), the deformation of tension anchor system will continue to decrease. And with the increase of (L_{m}), the decreasing trend is more obvious. When (L_{m}) is 500 mm, with the increase of the height of the anchor pier (D_{e}), the deformation of the anchor system will increase first. When (L_{m}) is greater than 800 mm, with the increase of (D_{e}), the deformation of the anchor system will continue to decrease. But the decreasing trend is not much different.Figure 18Influence of Anchor Pier Width (D_{e} left( {500 – 1500;{text{mm}}} right)) and Anchor Pier Height (L_{m} left( {600 – 2000;{text{mm}}} right)) on Deformation of Anchorage System.Full size imageThe numerical validationThe establishment of the finite element modelWhen the finite element model of the anchor-pulling system and surrounding soil is created, the constitutive model of the surrounding soil uses the Mohr–Coulomb elastoplastic model. The anchor pier and surrounding soil use eight nodes as oparametric elements, such as solid45, of which the basic grid unit is cubic units. When the grid is divided, the grid between the anchor pier and the surrounding soil contact is dense. The LINK10 unit is used to simulate cables, which have a bilinear stiffness matrix. It can simulate not only tensile bar units but also compressed bar units. For example, when the pull-up option is used alone, if the unit is under pressure, its stiffness disappears, so it can be used to simulate the relaxation of cables or chains. This feature is very significant for the static problem of wire rope, which uses a unit to simulate the entire cable. It can also be used for dynamic analysis with inertial or damping effects when the needed relaxation unit should pay attention to its performance rather than its movement. The soil is homogeneous. The soil physical parameters and structure design parameters are consistent with the theoretical calculation parameters mentioned above. The tensile force of the cable is exerted on the nodes as a force. The top surface of the model is free, and the normal displacements of the remaining faces are constrained such that the displacements are zero. The contact of the anchor pier and surrounding soils is a rigid-flexible surface-to-surface contact element to reflect the interaction. The surface of the anchor pier is regarded as the “target” surface, and the surface of the soil body is regarded as the “contact” surface. The coefficient of friction and normal penalty stiffness are 0.35 and 0.15, respectively. The scope of interaction between the anchor pier and the surrounding soil in the model is taken as 15 m × 11 m × 12 m, referring to past experience in engineering and the research data of the effect scope that the related anchors have had on the soil. The values of the model geometric parameters and physical and mechanical parameters are the same as in “Design parameters” section. The finite element model is shown in Fig. 19.Figure 19Finite element model of the anchor-pulling system and surrounding soil.Full size imageResearch on finite element model gridIn order to verify the convergence of numerical simulation, the soil was divided into three different mesh sizes. Condition 1 is fine finite element meshing. The stress nephogram of condition 1 is shown in Fig. 20. Condition 2 is medium finite element mesh. The stress nephogram of condition 1 is shown in Fig. 21. Condition 3 is coarse finite element mesh. The stress nephogram of condition 1 is shown in Fig. 22. See Table 2 for specific grid division.Figure 20Condition 1 stress cloud diagram.Full size imageFigure 21Condition 1 stress cloud diagram.Full size imageFigure 22Condition 1 stress cloud diagram.Full size imageTable 2 Mesh size of three working conditions.Full size tableIt can be seen from the stress nephogram of the three working conditions that the thicker the grid is, the greater the displacement of the anchor system is. The maximum displacement difference between condition 2 and condition 3 is 2.6%; the maximum displacement of condition 1 is 17% different from that of condition 2. The finer the mesh, the more accurate the numerical simulation results. But with the increase in computing time. It can be seen from Table 2 that the maximum iteration of condition 1 is 10 times, and the result will converge. The maximum iterations of condition 2 and 3 only need 7 times, and the results can converge.The calculation resultsFigure 23 and Fig. 24 are the displacement nephograms of the soil around the anchor piers for 100 kN and 400 kN, respectively. The soil displacement increases with increasing load, the affected area will increase and become uniform, and the area under load will also increase. The soil within the range of 1–3 m around the anchor pier is greatly affected, accounting for 80% of the total force. The soil around the anchor pier should be reinforced, and the anchoring force should be enhanced in the design.Figure 23Displacement fringe of soil around the anchor piers for 100 kN.Full size imageFigure 24Displacement fringe of soil around the anchor piers for 400 kN.Full size imageIn order to further study the influence of anchorage pier size on the displacement and deformation of anchorage system, finite element models with different sizes are established by finite element method. The stress nephogram is shown in Figs. 25, 26 and 27.Figure 25Top 800 mm, bottom 800 mm anchor pier stress nephogram.Full size imageFigure 26Top 1000 mm, bottom 1000 mm anchor pier stress nephogram.Full size imageFigure 27Top 800 mm, bottom 1000 mm anchor pier stress nephogram.Full size imageFrom Figs. 25, 26 and 27, it can be seen that when the anchor pier is rectangular, the deformation of the tensile anchor system decreases with the increase of the size of the anchor pier, but the degree is small. When the anchor pier is trapezoidal, the material is small, but the deformation is more ideal than the rectangular. It can be seen that reasonable selection of anchor pier size is crucial, not blindly increase the size of anchor pier.Figure 28 shows that the displacement of the soil around the anchor pier increases with increasing load, and the added value is obvious at approximately 2–3 mm. Figure 29 shows that the increase in load has a great effect on the soil in front of the anchor pier. As the load increases, the compressive deformation of the soil gradually increases. As the distance from the anchor pier increases, the displacement of the soil decreases, and the scope of influence gradually decreases. The displacement of the soil tends to be stable beyond 4–5 m from the anchor pier.Figure 28The displacement of soil around anchor pier.Full size imageFigure 29The horizontal displacement of soil along cable axis.Full size imageComparison of theoretical calculation and numerical simulation results at the time of load variationTo verify the correctness of the theoretical calculation, we compare the theoretical calculation with numerical simulation results of displacement deformation of anchor-pulling system under different pulling force of stayed cable. The results are shown in Fig. 30, see Table 3 for data.Figure 30Comparison of theoretical calculation and numerical simulation results.Full size imageTable 3 Comparison between theoretical calculation and numerical simulation.Full size tableAs seen from Fig. 30, the theoretical and numerical simulation results are consistent, showing a linear growth trend. The slope difference of the two straight lines is approximately 5%, which meets the accuracy requirements of geotechnical engineering. As the restraint effect of the surrounding soil on the anchor pier is not fully considered, the theoretical calculation result is too large. The deformation of anchor (left( {S_{1} } right)) in displacement deformation is the same, and the relative shear displacement (left( {S_{2} } right)) of the anchor pier and the soil and the compressive deformation ((S_{3} )) of the soil at the front end of the anchor pier are 1.25 times and 1.08 times the numerical simulation results, respectively. The change in (left( {S_{2} } right)) in the calculation results is large and should be taken into account in the design. More

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