By using the dual stress state variable representation method, the expression of the vertical slope height self-stability height under the condition that the suction force is uniformly distributed along the depth and the linear decrease with the depth is considered. Studies have shown that the height of self-stabilization depends not only on the strength of the soil, but also on the suction of the matrix. On the one hand, the matrix suction increases the shear strength of the soil, which helps to improve the stability of the vertical slope; on the other hand, the depth of the surface dry crack increases with the increase of suction, so that the increase of suction will weaken the slope. Stability. Compared with the case of not considering dry cracks, the limit of self-stabilization of vertical cut slopes will be reduced when considering dry cracks. These results have theoretical guiding significance and engineering application value for unsupported excavation of foundation pits. 0 Introduction Foundation pit excavation and support is an important part of urban high-rise structural engineering construction. Since most foundation pit projects are temporary projects, under the premise of ensuring safety, the natural strength of soil should be fully utilized as much as possible. Minimize support workload and reduce engineering costs. At the same time, because most of the northwestern and southwestern regions of China are located in arid or semi-arid areas, a large number of roads, railways, airports and other infrastructure are often directly built on unsaturated soil foundations. It is urgent to strengthen the study of unsaturated soil engineering properties and engineering applications. The actual geotechnical project to be solved. Water and gas are present in the unsaturated soil voids. The pressure difference between the pore gas pressure and the pore water pressure is called matrix suction. This matrix suction makes the deformation and strength characteristics of unsaturated soil more complicated than the engineering characteristics of fully saturated soil. It is generally believed that the matrix suction will improve the soil. Intensity, so that in the excavation of the foundation pit, the self-stabilizing height of the vertical or near vertical slope will increase as the suction increases. When the suction depth is constant above the entire groundwater level, the self-stabilizing height increases linearly with the increase of suction; when the suction decreases linearly above the groundwater level, the self-stabilizing height will change parabolically with suction. Unilaterally from the above point of view, suction can certainly increase the strength of the soil; but from another point of view, when the suction reaches a certain level, the surface will inevitably appear dry cracks, and the appearance of cracks will inevitably weaken the stability of the slope. Therefore, it can be expected that the self-stabilizing height of the vertical slope does not always increase with the increase of suction, but depends not only on the strength of the soil, but also on the distribution pattern of the suction depth along the soil and the surface it induces. The combined effect of cracks. This article provides a comprehensive analysis of this issue. 1 Stress state and strength analysis of unsaturated soil It is generally believed that unsaturated soil consists of solid (mineral particles), gas and liquid (usually water) three-phase, but in fact the interface between water and gas in soil is shrink film The nature is different from water and gas, and some people think that it should be considered independently according to the fourth phase. It is the presence of the shrinkage film that causes the presence of surface tension, resulting in capillary phenomena and matrix suction. The two phases of the soil skeleton and the shrink film are deformed under the action of force; and the gas and water phases flow under the stress gradient. For fully saturated soil, according to the Terzaghi effective stress principle, the deformation and strength of the soil depends on the effective stress state variable e' as the pore water pressure. The deformation and strength characteristics of non-saturated soils are more complicated. At present, there are more than ten forms of stress state variables recommended for unsaturated soils. Bishop Aitchison and Jennings and other proposed forms have been consistently recognized and widely used. Fredlund et al. applied the principle of multiphase continuous mechanics to analyze <8, 9>, pointing out that the overall stress state of unsaturated soil can be represented by three stress state variables, namely (two independent stress state variables in e-). Where u is the pore gas pressure, (u) is called matrix suction, and (eu) is total stress. The dual stress state variables (eu) are expressed in matrix form as Fredlund's application of the "zero" test to verify its theory. Chen Zhenghan applied the continuum stress theory and the basic law of the axiomatic theory system of geotechnical mechanics, and demonstrated the objectivity and rationality of describing the mechanical properties of unsaturated soils by using the above two independent state variables. Using the Mohr-Coulomb failure criterion, the shear strength of saturated soil can be expressed as effective stress: f) shear stress and normal effective stress on shear failure surface at failure; e and u are shear at failure The normal total stress and pore water pressure on the failure surface; c' and O' are the effective stress intensity indicators, which are the adhesion force and the internal friction angle, respectively. Similarly, based on the extended Mohr circle shown in Figures 2 and 3, the shear strength of the unsaturated soil can be expressed as the limit Mohr circle: (e is the net normal stress on the shear failure surface at the time of failure, Pore ​​gas pressure and matrix suction; O' is the internal friction angle associated with the net normal stress component e; O is the internal friction angle associated with the matrix suction component u. In the state of unsaturated soil, the crack depth is in the K state. When there is matrix suction in the soil, the horizontal stress will decrease and be a function of depth. In the shallower part, the small suction force can make the net horizontal stress become zero or negative. When the tensile strength of the soil is not considered, the crack will be formed from the vicinity of the earth's surface. According to the theory of elasticity, the following relationship exists between lateral horizontal stress and strain in isotropic homogeneous unsaturated soil: where: X is horizontal normal strain; e and e are vertical total method Li Shunqun, etc.: considering dry crack The critical self-stabilizing height and the lateral horizontal total normal stress of the vertical slope of the unsaturated soil; ν is the Poisson's ratio; E is the deformation modulus associated with the deformation; H is the deformation modulus related to the suction component (u) . In the K state, the soil is in a state of lateral deformation, so = 0, so that it can be assumed that the soil has no tensile strength, then when the e=0 is satisfied, vertical dry cracks will appear in the depth range, at this time, the soil layer The vertical self-weight stress at the middle depth Z is (edgZ=VZ, where d and V are the mass density and gravity of the soil respectively. When the suction is evenly distributed along the depth, the suction at any depth is equal and equal to the surface suction (u0. then the crack Depth and when the matrix suction varies linearly along the depth, as shown in Figure 5, the suction at any depth is: fgD, which is the ratio of pore water pressure to hydrostatic pressure, d is the density of water, and D is the depth of the water table. Substituting equation (8) into equation (6), we can obtain the surface crack depth when the matrix suction varies linearly along the depth. 3 Critical self-stability height For unsaturated soil, no matter the form of the suction along the depth distribution, there are dry cracks on the surface. The depth is determined by equation (7) or (9). The depth of the crack will affect the self-stabilizing height of the vertical cut slope. In the past, the influence of surface cracks induced by suction was generally not considered in the design of foundation pit engineering, or the soil weight in the depth of dry crack was simply applied as the overburden pressure on the top surface of the vertical slope. In fact, in general, the depth of dry cracks depends on the groundwater level and suction, so the effect of surface dry cracks on the stability of vertical slopes will depend on the combined effects of groundwater level and suction. For the two cases of considering suction and not considering suction, the stress Mohr circle in the active failure and passive failure ultimate stress state in the soil layer is given. It can be seen that when considering the suction force, on the one hand, the shear strength of the soil is obviously enhanced, thereby improving the stability of the slope; on the other hand, the depth of the dry crack increases with the increase of the suction force, thereby reducing the stability of the vertical slope. . Therefore, the influence of suction on the slope stability depends on both the positive and negative factors of the simultaneous change of shear strength and surface crack depth caused by suction. For vertical slope cutting, due to the existence of matrix suction, the surface dry crack is deep in zc, and the depth from the surface is Z=c, where z is the depth from the bottom end of the surface dry crack. According to Fig. 3, the limit equilibrium condition considering suction can be obtained by simplification, and the following limit equilibrium conditions are obtained, where k is the Rankine active earth pressure coefficient, and generally the pore gas pressure is connected with the atmosphere, at this time u=0, some The total vertical stress of a depth is the self-heavy stress, ie (e), which is substituted into the formula (11), and the lateral stress is 0 (ie, the condition of the tensile zone depth 3.1 suction is uniformly distributed along the depth when the suction is When the depth is evenly distributed, the equation (7) and the condition are substituted into the equation (13), and the depth of the tension zone is obtained. See Figure 6. According to the limit equilibrium condition, the critical self-stability height of the vertical slope can be obtained by derivation or the journal of Dalian University of Technology. And should meet H ≤ D, in fact, from a geometric point of view, the self-stabilizing height is the sum of the depth of the surface dry crack and the depth of the tension zone. The dependence between the self-stabilizing height and the suction is specifically discussed below through analysis. First, according to formula (15), the following derivative relationship is obtained. It can be found that when the height of 4tanO is not dependent on suction, H is at this time; when >E/νH, the height of self-stabilization increases with suction. =D. That is, when the suction tends to infinity, the dry crack will extend all the depth above the groundwater level, and the self-stabilizing height will be equal to the depth of the water table. There will be no lateral sliding force on the slope, similar to several independent soil columns cut by ground cracks resting on the foundation. Therefore, in theory, as long as certain measures are taken to ensure that the soil column does not collapse laterally, the entire soil slope will be stable. →0, which is equivalent to the influence of the suction of unsaturated soil and the influence of surface dry cracks. It can be seen from equations (15) and (19) that the self-stabilization height is consistent with the traditional limit analysis upper limit solution. The effect of the surface dry crack caused by the surface on the self-stabilizing height of the vertical slope is analyzed for the same soil quality = 14°, and the conventional analysis method without considering the influence of suction is used to analyze the common effect of suction and surface crack simultaneously. The method estimates the maximum self-stabilizing height of the vertical slope and compares it. According to the definition of the stability number N in the conventional soil slope stability analysis, that is, the N-sense dimension and the stable number Li Shunqun, etc.: Considering the critical self-stabilizing height of the vertical slope of the unsaturated soil when considering the dry crack, as the comparison object in the comparative analysis, When the suction force is evenly distributed along the depth, for the different values ​​of the parameter A=E/νH, consider the critical auto-stability height when the dry crack is not considered, such as the dimension-stable number and the suction and adhesion obtained after the treatment. The relationship between the force ratios is shown in Figure 8. It can be seen that compared with the situation of surface dry crack caused by suction, the self-stabilization height of the slope is significantly reduced when considering suction, so the conventional method usually estimates the critical self-stabilization height of the soil slope too high. When the suction force is along the depth = E / νH = 0.4857), the critical self-stabilizing height of the vertical slope is shown in Fig. 9. Wherein A, B, C, and D respectively represent c'=5kPa and the groundwater level is 9m and 5m, the dry crack is not considered, and the self-stabilizing height of the dry crack is considered; E, F, G, and H respectively indicate c'=15kPa Corresponding critical auto-stability height, wherein there is a falling section of the relationship between the self-stabilizing height and the suction when c'=15 kPa and D=5 m. The relationship between critical auto-stability height and suction after dimensioning is shown in Fig. 10. It can be seen that when considering the linear decrease of the matrix suction along the depth and the surface dry crack caused by the surface, the critical self-stabilizing height of the vertical slope does not increase with the increase of the surface matrix suction, but the local surface matrix suction reaches a certain A value is stabilized at a certain limit value, or reaches a certain maximum value and then decreases slowly as the surface matrix suction increases. 5 Conclusions (1) The self-stabilizing height is a composite function of soil parameters such as matrix suction, groundwater level, deformation modulus of unsaturated soil, internal friction angle and cohesive force, and its dependence is far more complicated than that of saturated soil. (2) On the one hand, the matrix suction can increase the shear strength of the soil and enhance the stability of the vertical slope; on the other hand, the matrix suction will cause the surface dry crack, and the depth of the dry crack increases with the increase of suction. Therefore, the stability of the slope will be weakened, so the dependence of the self-stabilizing height on the suction and the trend of change are determined by a combination of multiple relevant soil parameters. (3) Compared with the calculation results without considering dry cracks, the critical self-stabilizing height of vertical cut slopes will be significantly reduced when considering dry cracks. It is beneficial to maintain the slope stability by taking appropriate measures to maintain the suction force within a certain range. Sex. 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