Research on the Relationship between Soil Shear Stress Level and Safety Factor

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Introduction
Both engineering practice and laboratory test studies have confrmed that the failure of soil is mainly caused by shearing [1].Tere are three main types of engineering problems related to the shear strength of soil: the stability of soil slopes, the lateral pressure of soil on engineering buildings, and the bearing capacity of building foundations [2].Tese three types of questions have always been the focus of scholars' research.In particular, the research on the use and calculation methods of these common geostructure safety factors is becoming more in-depth.From the traditional slip line method and limit analysis method to the recent strength reserve method [3], the calculation of the safety factor has a tendency to be more and more accurate [4,5].
But the fact is that in engineering, the safety factor used in the design of geotechnical structures has never deviate from the specifed value in the specifcation, that is, the engineering experience value.Te specifcation stipulates that for permanent geotechnical structures, the safety factor of active earth retaining structure is 1.2∼1.4 and the safety factor of passive earth retaining structure are 3.0.For permanent slope engineering, its safety factor is taken as 1.3∼1.5; the safety factor of foundation bearing capacity is taken as about 3.0.Te above safety factor widely used in engineering has effectively guaranteed the safety of the structure in the engineering, but there are always the following two problems that have not been rationally explained in theory: First, what is the theoretical basis for the values of these safety factors in engineering?Second, whether the geotechnical structure, especially the permanent geotechnical structure, designed according to the safety factor selected in the specifcation can resist the long-term deformation efect of the soil mass?In order to provide theoretical answers to the above questions, the author conducts an in-depth study on the relationship between soil shear stress level and soil stability.

Preliminary Discussion on the Relationship between Soil Shear Stress Level and Safety Factor
Zheng and Zhao [3] pointed out a problem in the selection of the safety factor in the engineering design of the slope (landslide).Diferent defnitions of safety factor will cause confusion in slope design, so it is necessary to unify the selection of safety factor.Te study of [4] pointed out that there are two defnitions of the safety factor of geotechnical structures.Te two methods of calculating the safety factor are the ratio of the ultimate load to allowable load and the ratio of the existing strength parameter to the strength parameter required to maintain stability.Te latter calculation method has wider applicability than the former calculation method.Te literature also pointed out that the calculation method of the safety factor of diferent geotechnical structures should be unifed.Te above studies show that experts and scholars have reached a consensus on the unifed use of safety factors in the design of geotechnical structures.Tis study believes that the unifcation of the safety factor should not be a simple unifcation of the algorithm but the unifcation of the theoretical basis used in the calculation of the safety factor.Since the failure form of soil is mainly shear failure, the calculation method of the safety factor of the geotechnical structure should be unifed according to the shear stress level of the soil.According to the general defnition of safety factor proposed in the literature [4], the safety factor of soil is the ratio of the shear strength parameter of the soil to the minimum shear strength parameter required to maintain stability.Tat is to say, when the geotechnical structure is designed according to the minimum shear strength required for stability, the stability of the soil mass can be guaranteed.However, the magnitude of the minimum shear strength value required to keep the structure stable and the magnitude of the force referenced in the calculation of the safety factor of the geotechnical structure are not clearly given in the literature.Murayama and Shibata [6] gave an approximate stress level value of 0.71 times the failure strength of soil when the soil slope has a long-term stability efect in the long-term strength study of soil slopes, but this value is only an approximate value and is not accurate enough, so it has not been obtained.Promotion and Application.Murayama and Shibata [6] proposed that when the soil slope has a longterm stability efect, the stress level of the soil is approximately 0.71 times the failure strength of the soil.Since this value is only approximate and not exact enough, it has not been promoted and applied.
In the theoretical study of the earth pressure of retaining structures [7], the author obtained the ratio table of the Rankine theory earth pressure coefcient and the static earth pressure coefcient, as shown in Table 1.
It can be seen from Table 1 that when the internal friction angle is 20 °, the ratio of the static earth pressure coefcient to the active earth pressure coefcient is K 0 /K a � 1.3.According to the design specifcation of the retaining wall, for the retaining structure moving away from the flling direction, the earth pressure that can be borne in the design is 1.2∼1.4times of the active earth pressure.Tis ratio is consistent with the load subitem factor used in the design of the retaining structure specifed in the retaining wall design code.Te earth pressure that the designed retaining structure can bear is close to the static earth pressure.On the contrary, when the partial load coefcient used in the design of the retaining wall is higher than this value, the earth pressure borne by the designed structure is less than the static earth pressure.In practice, it is found that the designed retaining wall structure is unsafe.
In the design, when the selected load subitem coefcient is lower than 1.3, it is equivalent to the internal friction angle selected in the design is less than 20 °.At this time, the earth pressure that the designed retaining structure can bear will be greater than the static earth pressure, which is relatively safe.On the contrary, when the load subitem coefcient used in the design of the retaining wall is higher than 1.3, the earth pressure borne by the designed structure is less than the static earth pressure.In practice, it has been found that this kind of retaining wall structure is not safe.
For the case where the external force forces the retaining structure to move towards the flling direction, the external force that the retaining structure specifed in the code can bear shall not exceed 1/3 of the passive earth pressure value of the soil behind the wall.Terefore, the load partial factor specifed in the code is approximately 0.3.When the internal friction angle is 20 °, K p /K 0 � 3.1, the allowable external force of the retaining structure designed according to the code is also close to the static earth pressure.
According to the above analysis, it can be concluded that over time, the earth pressure on the structure will develop towards the static earth pressure, whether the retaining structure leaves or squeezes the fll.Te minimum shear

Study on the Relationship between Soil Shear Stress Level and Stability
Te rheological properties of the soil have a great infuence on the long-term stability of the soil.Te rheological trend and rheological rate of the soil are related to the magnitude of the shear stress that the soil bears.Existing research divides the rheological process of soil under diferent shear stress levels into three stages.In the frst stage, under the lower stress level, the soil body undergoes deceleration rheology, and the soil body deformation is small and quickly stabilized.In the second stage, when the stress level was slightly higher, the rheological rate of the soil decreased with time.After a period of time, the soil's rheological rate decays to a value of zero in a region, and the soil maintains a constant rheological process.In the third stage, when the stress is greater, the soil undergoes accelerated rheology, the strain rate increases with time, and fnally, the soil is destroyed [8,9].Summarizing the above research, it is found that with the increase of soil shear stress, the rheological properties of soil also change, and there is a transition from decay-steady state to decay-constant rheology.In this process, the critical shear stress corresponding to the time when the soil is stable and begins to undergo constant velocity rheology is the minimum shear strength for the stability of the geotechnical structure.Tis shear stress is the stress on which the safety factor is calculated in the design of geotechnical structures.It is called "upper yield value" or "third yield value" [6].Te soil masses with diferent geological conditions in fve regions are selected for research to ensure the universal applicability of the research results.Trough the statistical analysis of the law between the shear stress and rheology of the soil in fve regions, the relationship between the shear stress value when the soil remains stable and the shear stress value corresponding to the static earth pressure of the soil is discussed.Te basic properties of the fve soils and the parameters of the triaxial rheological test are listed in Table 2.
Figures 1 and 2 demonstrate when a small deviator stress of 12.6 kPa is applied to the consolidated Wenzhou soft soil under K 0 state, the shear strain of the soil mass develops slightly, and the strain rate decays continuously.Within a period of time after the test, the strain rate of the soil mass decays to a nearly stable value.Figures 3-14, respectively, show the triaxial rheological curves of the soft soil of the Shantou-Jieyang expressway, the fller of Huaihua Xinjiang expressway, the structural hydraulic fll soft soil of Tianjin Binhai New Area and the typical muddy silty clay in Wangjiang area under diferent confning pressures.Te soils in these diferent areas show three similar rheological laws.First, when the stress of soil sample is small, the soil has only instantaneous elastic deformation.Second, when the stress level is in a slightly higher range, the rheological curve of soil shows a rapid rheological in the early stage, and gradually slows down and shows a stable growth trend in the later stage.Te rheological curve eventually tends to be   smooth and keeps increasing at approximately constant speed.Tird, under high deviator stress, the rheological curve appears accelerated rheological, the rheological deformation does not converge, and the soil tends to be damaged [18].Te rheological law shown by the measured data of soils in diferent regions is consistent with the previous theoretical assumptions.Now, the stress levels corresponding to the fnal stability of these fve soils and the occurrence of nondestructive isokinetic rheology are counted and listed in Table 3.
It can be seen from Table 3 that the vertical earth pressure corresponding to the deceleration rheology of the soil mass to the fnal stable state of the soil mass is less than the static earth pressure of the soil mass.On the contrary, the vertical earth pressure of the soil is higher than the static earth pressure of the soil when the constant or constant rheological stage occurs.In other words, when the stress level of the soil is lower than the K 0 stress level, the rheology of the soil is the frst stage of deformation, and the deformation can converge quickly at this time.When the stress level of soil exceeds a small range of the K 0 stress state, the soil will produce nonconvergent rheological deformation.Te rheological law of soil mass in the test shows that the stable shear stress level of the soil mass is K 0 stress level.Under the long-term time efect, the earth pressure borne by the structure will tend to static earth pressure.Tis verifes the correctness of the conclusions in the Section 2, and shows that the long-term stability of the geotechnical structure can be ensured only when the earth pressure is calculated according to the static earth pressure in the design of the permanent geotechnical structure.
Based on the study of soil rheological law, it is found that it is reasonable to use the safety factor specifed in the code

Conclusion
(1) Te relationship between the earth pressure coefcient and the static earth pressure coefcient in Rankine's earth pressure theory and design code of retaining structure is studied.It is found that the ultimate safety of retaining structure is related to whether the design bearing capacity exceeds the static earth pressure.When the design bearing capacity σ design ⟶ σ 0 , the structures will keep safe.(2) According to the rheological characteristics of the soil in fve diferent regions, it can be obtained that the vertical earth pressure of the soil is less than the static earth pressure of the soil at the stage of deceleration rheological to the fnal stable state of the soil.Te vertical earth pressure of the soil is higher than the static earth pressure of the soil at the stage of constant rheological or constant rheological.Te rheological law of the soil in the test shows that the fnal stable shear stress level of the soil is the shear stress level at K 0 .(3) Te safety factor in the existing geotechnical structure design code comes from engineering experience, but the safety factor summarized from engineering experience is always lack of theoretical support.Te research results of this paper clarifes the use of safety factor in the code and change the geotechnical structure design from empirical design to theoretical design.Te research results provide a reliable method for the design of geotechnical structures, especially the design of permanent geotechnical structures.By calculating the allowable bearing capacity of geotechnical structures according to the static earth pressure σ 0 , the structures' safety under the long-term time efect can be ensured.Te research results can also be used to check the long-term stability of existing geotechnical structures to determine whether they have long-term stability.

Figure 1 :Figure 2 :
Figure 1: Te variation curve of shear strain of Wenzhou soft clay with time.

Table 1 :
Ratio of Rankine theory earth pressure coefcient and the static earth pressure coefcient.

Table 2 :
Basic soil parameters and rheological test parameters.
Te basis is that the safety factor in the specifcation is taken around the safety factor of the soil under the K 0 shear stress level, and the stable shear stress level of the soil is the K 0 shear stress level.Te study gives the specifc value of the shear stress level based on which the safety factor is calculated, transforms the previous empirical design into the theoretical design, and can theoretically check the design bearing capacity of the geotechnical structure, ensuring the long-term stability of the geotechnical structure.Figure 13: Rheological curve of typical silty clay in Wangjiang area under confning pressure of 200 kPa.

Table 3 :
Vertical earth pressure corresponding to fnal stability of soil mass/constant velocity rheology.