1 Introduction

The maintenance of railways built on permafrost soils detects numerous deformations of the subgrade, con-nected with the degradation of the permafrost. The main deformation in these terms is considered to be the long-term displacement of embankments. There are cases on the Trans-Siberian Railway where deformations have been recorded since its construction, up to the present—in other words, for over 100 years.

The main reason for these deformations is the warming impact of the subgrade structure on the permafrost soil of the embankment, which weakens while thawing and is unable to bear the load of traffic.

A situation like this makes it necessary to constantly fill and line the tracks, leading to numerous restrictions of train speed and, finally, increasing considerably the operating costs. The situation is especially complicated on the Trans-Siberian Railway where the train traffic is quite intensive (density of freight traffic is more than 100 million t/km of gross load per km), including the traffic of freight trains. One of these facilities is an embankment 4.0 m high and 6,278 km long on the Turinskaya-Karymskaya line of the Trans-Siberian Railway. At present, longstanding displacement of the embankment, with the depression of a track and heaves, is taking place on this facility. Because of the subgrade deformations, long-term restrictions of train speed are applied to this section, reducing carrying capacity and leading to significant losses in operation.

Therefore, it is important to work out proposals for strengthening the embankment and its roadbed to prevent deformations.

2 Description of a subgrade facility

The facility affected is a section of the subgrade on the Trans-Siberian Railway with a length of 6,278 km on the Turinskaya-Karymskaya line. On this section, the displacement and degradation of the embankment with the depression of the track and heaves have been recorded for a long time. The road category is I, a double-track line, electrified. The carrying traffic on this section is 62 train-pairs per day; the train speed is 90/80 km/h. The height of the embankment is up to 4.0 m; the angle of the slopes is from 1:1.5 to 1:2.0. The embankment consists of different grain-size sand and gravel-pebble soils. According to track maintenance records, the depression of the track is at 27 cm per year, with a daily maximum of 18 mm.

In the upper part of the roadbed under the embankment, there is silty, water-bearing sand in the thawing state with the strength characteristics c = 1 kPa and φ = 24°. Relying on the thixotropic properties of the roadbed soil, we used the calculated value of the angle of inner friction as φ_p = 15°. The permafrost under the embankment is located at the depth of 6.5 m to 8.0 m. Permafrost soils are in a plastic frozen state with the temperature above 1.0 °C; and according to the ice state, they belong to the icy soil with a relative depression under thawing δ = 0.3. Soils of the active layer of the roadbed are characterized as heavy, heaving soils.

3 Statement of the problem and method of solving it

To stabilize the embankment on this section with the length of 6,278 km, it is necessary to determine the causes of deformations and to identify ways to eliminate them. To achieve this, a simulation of the thermal regime in the embankment roadbed was performed, and calculations of the stress-strain state were done.

The forecast for the dynamics of the freezing and thawing border in the roadbed and on the railway was carried out by mathematical modelling in the computer program "WARM" (Khrustalev and Emelyanova, 1994), developed at the Department of Geocryology of Moscow State University. Data from the meteorological station in Chita were taken as the boundary conditions. The embankment was simulated with the height of 2.0 m, the width of the main field was 10.6 m, the angle of the slope was 1:2, and frozen sandy loam with the thickness of 3.2 m was placed on the roadbed at the depth of 4.0 m. The temperature of the frozen soil was set at −0.8 °C.

Simulating the stress-strain state (SSS) of the subgrade was carried out with the method of finite elements in the program PLAXIS (Brinkgreve, 2002), using the model Mohr-Coulomb for the soil. The finite-element mesh was plotted with the use of 15-nodal triangular elements, after a geometric model and input parameters of the material were created.

The value of the embankment displacement under the train and the safety factor of the subgrade were determined in the course of the calculation with the formula:

${\rm{Ksf = }}\frac{{c + {\textit{σ} _n}\tan \textit{φ} }}{{{c_r} + {\textit{σ} _n}\tan {\textit{φ} _r}}}$

(1)

where c and φ are input parameters of strength, and σ_n is actual normal voltage. Parameters c_r and φ_r are parameters of the given strength that is sufficient to maintain the equilibrium. The above mentioned principle is the base of the Phi-c-reduction method, which is used in the program PLAXIS for calculating the total safety factor. With such an approach, the adhesion and the tangent of the friction angle reduce in the same proportion.

$\frac{c}{{{c_r}}} = \frac{{\tan \textit{φ} }}{{\tan {\textit{φ} _r}}} = \text{Σ} Msf$

(2)

On calculating with the help of the Phi-c-reduction method, some additional displacement occurs. The complete displacements do not have any physical meaning, but their growth at the final step (under the destruction) indicates the probable mechanism of the destruction. The increment value of displacements is not important. To determine the vertical deformation under the train, we did the calculations relying on the filtrational consolidation with statically applied loads of a train on the first track p₁ = 60 kPa and on the second track p₂ = 80 kPa.

4 Analysis of the simulation results

The results of the thermal regime simulation showed that the initial layer of frozen soil, with the thickness of 3.0 m and the top of which is at the depth of 4.0 m, will degrade. The complete degradation of permafrost takes place toward year 20, with the average rate of thawing at 0.15 m per year and 0.25 m during the early years. Taking into consideration that the depression of thawing soils is δ = 0.3, the thermal displacement is about 8 cm per year during the early years, decreasing to 4~5 cm per year in subsequent years. Thus, the value of the thermal displacement is only about one-third of the total value of displacement; and it will continue to decrease.

SSS simulation showed that the total stability factor equaled Ksf = 1.26 when the trains passed on the two tracks; the maximum vertical deformations equaled Δ = 8.13 mm, and the deformation occurred closer to the sloping part of the embankment and at the top of the roadbed (Figure 1).

The vertical elastic displacement obtained under the train load exceeds the norm by more than four times; it should not be more than 2 mm according to the regulation (SP 238.1326000.2015). The results of the simulation show that at the top of the roadbed there exists some overstressing, which is transformed into the plastic deformations causing the displacements of the embankment. That is why it is necessary to strengthen the upper part of the roadbed in order to stabilize the embankment.

5 Proposals for the embankment stabilization

Strengthening the roadbed with cementation by jet technology is proposed as a method of embankment stabilization. The strengthened layer of soil in the roadbed presents a continuous plate strengthened with cement. To select the characteristics of the soil layer strengthened with cement, SSS simulation of the subgrade with the use of the finite-element method in the program PLAXIS was carried out. A series of calculations was done with the increased train load 90 kPa on both tracks. The thickness of the strengthened layer of the roadbed varied: 0, 1, 3, or 5 m. The characteristics of the soil of the strengthened roadbed taken in the calculation are the following: E = 100 MPa, c = 50 kPa, φ = 30°, and υ = 0.25. The results of the calculations turned out to be optimal for strengthening with the thickness of 3 m, in which the following was obtained: a stability factor Ksf = 1.92, and the vertical deformation reduced to Δ = 0.28 mm. The deformed mesh of the simulation for this case is shown in Figure 2.

As the calculation results show, with the thickness of 3 m of the strengthened roadbed soil by cementation, the stability of the embankment is achieved; and the elastic displacement turns out to be lower than the regulatory value of 2 mm.

With a strengthened layer 5 m thick, the displacement increases due to the raise in the plate weig-ht—the plate vertically dives in the weak soil under its own weight; and the thickness of 1 m is not sufficient to strengthen the soil.

6 Practical application of the results

In 2013~2014, the project was worked out on the basis the scientific recommendations of MSURE (Moscow State University of Railway Engineering) (Ashpiz, 2012) and the strengthening of the embankment roadbed was made on a 6,278-kilometer section of the Turinskay-Karymskaya line of the Trans-Siberian Railway with the use of jet technology. According to the project worked out by JSC Triada-Holding, soi-cement elements (SCE) create the strengthening layer and are arranged in transverse tilting rows of four elements on each side of the embankment at a pitch of 1,600 mm in the lengthwise direction and the shift of axle drilling from the opposite sides at 800 mm (Figure 3).

Observation of the results of the section after the strengthening was carried out by the engineering-geological base of the Trans-Siberian Railway. The observations in 2015 and 2016 showed that the implemented solution was effective for embankment stabilization, and the deformation of the embankment was actually coming to an end.

7 Conclusions

(1) The causes for the deformation of embankments maintained long-term on permafrost soils are to a lesser degree the thermal displacement caused by the degradation of permafrost; but in most cases, the plastic deformations in the layer of seasonal freezing and thawing are under the embankment.

(2) The simulation of the thermal regime of the embankment roadbed was applied to the chosen deformed facility of the subgrade on a 6,278-kilometer section of the Turinskaya-Karymskaya line of the Trans-Siberian Railway; and calculations of the stress-strain state were done, which showed that along with the degradation of permafrost and the thermal displacement, plastic deformations of the upper part of the roadbed under the embankment take place, which are the main cause of the displacement.

(3) A design solution was proposed to strengthen the top soil layer of the roadbed, using jet technology of cementation to stabilize the embankment. Characteristics of the strengthening layer were selected based on SSS simulation, with the use of the finite-element method; and the layer thickness was 3 m when the module of deformation was E = 100 MPa.

(4) Implementation of the strengthening was carried out in 2013–2014; and the results of observations made by the engineering-geological base of the Trans-Siberian Railway in 2015 and 2016 showed the efficiency of the proposed solution to stabilize the embankment.