GONG Xiaolong, WANG Yuanzhan, and CHEN Tong

Strength Model of Soda Residue Soil Considering Consolidation Stress and Structural Influence

GONG Xiaolong1), 2), WANG Yuanzhan1), *, and CHEN Tong3)

1) State Key Laboratory of Hydraulic Engineering Simulation and Safety and Collaborative Innovation Center for Advanced Ship and Deep-Sea Exploration, Tianjin University, Tianjin 300354, China 2) Tianjin Port (Group) Co. Ltd., Tianjin 300461, China 3) Zhongnan Engineering Co. Ltd., Changsha 410014, China

Soda residue (SR) is a type of industrial waste produced in the soda process with the ammonia-soda method. Applying SR to backfilling solves the land occupation and environmental pollution problems in coastal areas and saves material costs for foundation engineering. The strength characteristics of soda residue soil (SRS) under different consolidation conditions are the key points to be solved in the engineering application of SRS. Triaxial compression tests were performed on the undisturbed SRS of Tianjin Port. The shear properties of SRS under different consolidation conditions were then discussed. Meanwhile, a structural strength model (SSM) based on Mohr-Coulomb theory was proposed. SSM reflects the influence of soil structure on undrained strength (C) and divides theCinto the following two parts: friction strength (C) and original structural strength (C0).C characterizes the magnitude of friction between soil particles, which is related to the consolidation stress. Meanwhile,C0represents the structural effect on soil strength, which is related to the soil deposition and consolidation processes. SSM was validated by the test data of undisturbed soils. Results reveal that the undisturbed soil generally had a certainC0. Therefore, the SRS strength model was established by combining the experimental law of SRS with SSM. Error analysis shows that the SRS strength model can effectively predict theCof undisturbed SRS in Tianjin Port under different consolidation conditions.

soda residue soil; triaxial test; strength model; soil structure; consolidation stress

1 Introduction

Soda residue (SR) is a type of industrial waste produced in the soda process with the ammonia-soda method. The annual production of SR in China has exceeded 5 million tons (He and Wang, 2018). The accumulation of a large amount of SR caused serious adverse effects on the urban ecological environment and obstructed the development of land resources (Hao, 2010). Therefore, the comprehensive utilization of SR has become an important research topic for maintaining the long-term development of the soda industry. SR is similar to natural soil because both are three-phase bulks, comprising solid particles, water, and air. Applying SR to backfilling solves the land occupation and environmental pollution problems in coastal areas and saves material costs for foundation engineering (Li, 2015). Therefore, a large-scale soda residue soil (SRS) foundation engineering has been built in the Tianjin Port area. However, SRS at different positions is usually consolidated under different stress conditions due to the load effect in the construction, preload, and operation processes. On the one hand, preloading and unloading in- duce a larger preconsolidation pressure than the current con- solidation pressure, which will lead to overconsolidation of SRS. This phenomenon affects their consolidation history (Cai, 2018). On the other hand, under a load of self-weight and building, the vertical consolidation stress of SRS is often larger than the transverse consolidation stress, and the ratio of principal consolidation stress is always different for SRS in various positions. Thus, this phenomenon affects the consolidation types of SRS (Ye, 2011). The shear characteristics of SRS changes with the consolidation process; that is, SRS at different positions has varying shear behaviors. Consequently, calculating the bearing capacity of the SRS foundation is difficult. This difficulty markedly limits the engineering application of the SRS groundwork. Therefore, establishing a reasonable and practical strength model to describe the change in the strength of undisturbed SRS under different consolidation conditions is encouraged.

At present, the theoretical and practical experiences of applying SR to projects are relatively scarce; researchers only conducted some experimental studies on the basic physical and mechanical properties of SRS (Yan, 2007; Liu, 2015; Yang, 2017; Ma, 2019; Wang, 2020). Literature on the effect of consolidation stress on the strength of SRS is currently unavailable. Achievements in other types of soil can be used for this paper due to the similarity of material composition between SRS and natural soils. For the effect of consolidation history on soil strength, Ladd and Foott (1974) and Ladd(1977) introduced stress history and normalized soil engineering properties (SHANSEP) theory and established the relationship between normalized undrained strength of overconsolidated soil and normalized undrained strength of normally consolidated soil:

Since then, Mayne (1980) obtained the same equation as Eq. (1) according to the critical state theory of the Cambridge model and verified it through a large number of test data. The result shows that Eq. (1) applies not only to isotropically consolidated soil but also to anisotropically consolidated clay and silt. Stró?yk and Tankiewicz (2014) conducted triaxial shear tests on heavily overconsolidated clay (= 3 – 28) and concluded that Eq. (1) applies to natural overconsolidated clay. Owing to the wide applicability of the SHANSEP theory, many scholars have exerted this theory to study the effect ofon soil strength (Pra- shant and Penumadu, 2005; Wang and Luna, 2012; Qian, 2019). These results show that the test parameters0are generally different for various types of soil. Ajmera(2018) found that0of soil is closely related to the content of clay mineral and plastic characteristics through the direct shear test. Moreover, for the effect of consolidation type on soil strength, Atkinson(1987) designed0consolidation and isotropic consolidation tests for kaolin and concluded that the consolidation type can considerably affect the stress-strain relationship of kaolin. Georgiannou and Konstadinou (2014) and Toyota(2013) also obtained similar conclusions through torsional shear tests. Cai(2018) found that the shear strength of Wenzhou overconsolidated clay increased with the consolidation ratio (the ratio of axial consolidation stress to transverse consolidation stress) and observed a linear relationship between them.

The aforementioned studies reveal the variation law of soil strength under different consolidation conditions to a certain extent and provide a reliable basis to study the influence of consolidation stress on the strength of SRS. However, most of the theories, methods, and models involved in these studies were based on the experimental law of remolded soil without considering the influence of soil structure. Undisturbed soil is the actual object involved in practical projects; this soil usually has structural properties under the influence of long-term geological action. Therefore, studying the structural influence on the strength of SRS and establishing a structural strength model (SSM) for SRS is crucial to evaluate the actual bearing capacity of the SRS foundations accurately.

Over the past few decades, many kinds of structural con- stitutive models have been proposed to describe the struc- tural effect on soil. Based on the Cambridge model, Liu and Carter (2002) and Carter and Liu (2005) adopted five structural parameters to establish the Structured Cam Clay (SCC) model. The results calculated by SCC show that SCC can describe the drained and undrained shear characteristics of natural structured soils. Kavvadas and Amorosi (2000) established a critical state incremental plastic model based on the theory of incremental plastic and critical state, which can describe the strength weakening caused by struc- tural damage. Dafalias and Manzari (2004) introduced a sand plasticity model controlled by a simple stress ratio, which can consider the fabric changefabric expansion tensor during loading. Papadimitriou(2005) investigated the effect of sampling methods on the shear properties of Toyoura sand based on the model of Dafalias. They found that the difference in sampling methods would lead to the difference in initial fabric, which will affect the expansion and hardening of sand in the shearing process. Callisto (2002) simulated the shear behavior of intact Pisa clay by using the motion- hardening boundary surface plastic model. This model can consider the progressive loss of the soil structure due to the increase in plastic strain. Shen (2000) presented a model of masonry, which used the damage function to explain the soil damage deformation. This model can describe the structural damage of natural clay under the deformation process. The aforementioned models described the structural influence on the mechanical properties of soil from different aspects, which provided a reference for the study on undisturbed SRS. How- ever, these models contain many parameters and equations; some parameters do not even have a clear physical meaning. Thus, using these models to consider the influence of consolidation stress and structural properties on soil strength simultaneously is difficult.

The special structure of foundation soil is formed in the long-term deposition and consolidation. Determining the influence of consolidation stress and structure on foundation soil is necessary to evaluate the capacity of engineering foundations accurately. Previous research did not yet consider the effects of consolidation stress and structure on SRS comprehensively. Therefore, this paper seeks to conduct the triaxial compression tests on undisturbed SRS in Tianjin Port and analyze the shear characteristics of undisturbed SRS under different consolidation conditions. Meanwhile, the authors establish an SSM based on Mohr- Coulomb theory to reflect the structural influence on un- drained strength. Therefore, by combining the test data of undisturbed SRS with the SSM, the SRS strength model is proposed to describe the variation law of undisturbed SRS under different consolidation conditions. This model can serve as a reference for the engineering construction of the SRS foundation.

2 Experimental Programs

2.1 Test Specimens

The specimens studied in the test include the undisturbed SRS from Tianjin Port, China. A relatively homogeneous soil layer of SRS from 2 m to 6 m below the surface was chosen for this paper. Thin-walled steel tubes were adopted to obtain the sample, and only the soils in the central part of the tube were used to make specimens to ensure their quality.

Specimens appear white and mainly comprise silt particles. The surface of the specimens is slightly slippery and sticky. The basic physical and mechanical parameters of the specimens are shown in Table 1. SRS is characterized by high water content, high void ratio, low density, high compressibility, and poor plasticity. The aforementioned characteristics and the well-developed pore structure of SRS contribute to its difference from other types of soil (Yang, 2017). According to the Casagrande plasticity chart, SRS is classified as inorganic silt with a high liquid limit.

Table 1 Basic physical and mechanical parameters of SRS in Tianjin Port

2.2 Test Plans

The instrument used in the test is DSC3000M automatic triaxial apparatus produced by the British company VJ- Tech. Before the start of the test, the specimen was cut into a cylinder with a diameter of 39.1 mm and a height of 80 mm. The specimen was then saturated by the vacuum pumping method. If the pore water pressure coefficient B was less than 0.98, then the specimen will undergo saturation by backpressure until its saturation reaches the requirement.

This test investigates the influence of confining pressure, consolidation history, and consolidation type on the shear properties of SRS; the test includes the following three parts. The first part is the conventional CU (consolidated undrained) test (including S01–S03), the second part is the CU test of overconsolidated SRS (including S04 – S12), and the third part is the CU test of anisotropic consolidated SRS (including S13 – S21). The specific scheme of the test is shown in Table 2.

Table 2 Triaxial test scheme for SRS

Notes:=σ/σ, whereσis the consolidation confining pressure;=σ0/σ, whereis the consolidation ratio, andσ0is the axial consolidation stress.

Different parts of the test have varying loading steps. The specimens for the test of S01–S03 were isotropically consolidated for 24 h. After the pore pressure dissipated, the drainage valve was closed, and monotonic undrained shear was conducted with a rate of 0.1 mm min?1by strain control. The specimens for the test of S04 – S12 were also isotropically consolidated first. The specimens swelled suf- ficiently when the confining pressure was released. The undrained shear process was finally conducted until the specimens broke. For the test of S13 – S21, the specimens were also isotropically consolidated first and then anisotro- pically consolidated for 24 h. Finally, the monotonic load was utilized in the specimens under undrained conditions.

2.3 Test Results

2.3.1 Stress-strain relationship

The normalized stress-strain curves of SRS at differentare shown in Fig.1. The figure reveals the softened stress-strain curves of SRS at different. The peak point of the stress-strain curve is chosen as the failure point (small black dot in Fig.1). The axial deviator stress () corresponding to the failure point is the peak strength (q) of the specimens. Fig.1 shows the differences in specimen form before and after failure. The specimens have a fracture surface that penetrates the entire body and dislocates up and down along the fracture surface after failure. When the axial strain (?) reaches 15%, the specimen maintains a certain residual strength (q), but theqdecreases by 5 – 20 kPa compared with theq. In addition, the initial tangential stiffness (0) andqof the specimens gradually decreased with the increase in. This finding indicates that the change inwill substantially affect the stress-strain characteristics of SRS.

The normalized stress-strain curves of SRS at different consolidation ratios () are shown in Fig.2. The stress- strain curves at differentalso softened. Whenis equal to 1.8,qwill decrease by approximately 40 kPa compared with theq. In addition, the0andqof the specimens increase with, while the?of the specimens gradually decreases. On the one hand, this trend shows that the increase in the axial consolidation stressσ0will enhance the shear strength of the specimens. On the other hand, it will reduce the shear plasticity of the specimens and lead to brittle failure of the specimens.

Fig.1 Normalized stress-strain curves of SRS at different OCR.

Fig.2 Normalized stress-strain curves of SRS at different K.

2.3.2 Undrained strength

The undrained strengthC (half ofq) of SRS under different consolidation conditions is shown in Figs.3 and 4. These figures reveal thatChas a linear relationship withσwhenandare both maintained. Ifσdoubles, thenCwill increase by 65% – 85%. This condition may be attributed to the decrease in the initial void ratio after consolidation. Whenσandare maintained, the largewill lead to the smallσ; that is, the load constraint of the specimens weakens, and theCof the specimens decreases accordingly. Ifincreases from 1 to 6, thenCwill decrease by 25% – 30%. Whenσandare both maintained, the largeindicates a largeσ0. In this case, additional pore water can be discharged from the soil during the consolidation process, and the friction between soil particles strengthens, which will enhance the shear capacity of SRS. Ifincreases from 1.0 to 1.8, thenCwill increase by 40% – 50%. Thus, consolidation stress will considerably affect the strength characteristics of the SRS.

Fig.3 Undrained strength of SRS at different σc and OCR.

Fig.4 Undrained strength of SRS at different σc and K.

2.3.3 Shear pore pressure

The development curves of the shear pore pressure (u) of SRS at differentare shown in Fig.5. The specimen was drained from its top during the consolidation process, and the measured pore pressure was at the bottom of the specimen. Therefore, the initial pore pressure before shearing (after consolidation) is not zero. When specimens are normally consolidated, theiru rapidly increases in the initial stage. However, after reaching a certain level, the growth rate ofubegins to decrease with the increase in?.ufinally stabilizes. When the specimen is lightly overconsolidated (= 2), itsu-?curve is similar to that of the normally consolidated specimen, but theuof the lightly overconsolidated specimen in the stable stage decreases by approximately 50 kPa compared with that of the normally consolidated specimen. When the specimen is heavy overconsolidated (= 4 or 6), itsu-?curves show a different trend from that of lightly overconsolidated and normally consolidated specimens. Theuof heavily overconsolidated specimens increases first and then decreases with the increase in?and finally stabilizes. Theuof heavily overconsolidated specimens are negative at the stable stage, which decreases by approximately 20 kPa compared with that of lightly overconsolidated specimens. However, the decreasing amplitude shows a decreasing trend. No difference was observed in theuat the stable stage for the heavily overconsolidated specimens whoseis equal to 4 or 6.

Normalizedu-?curves of SRS at differentare shown in Fig.6. The development law ofuat differentin Fig.6 is similar due to the normal consolidation of the specimens. The effect ofon the development ofuis not as remarkable as that of. Althoughuin the stable stage decreases gradually with the increase in, the decrease in amplitude is not evident in that of.

Fig.5 Normalized us-?a curves of SRS at different OCR.

Fig.6 Normalized us-?a curves of SRS at different K.

2.3.4 Effective stress path

The normalized effective stress paths of SRS at differentare shown in Fig.7. The development trend of effective stress path varies with. When the specimen is normally consolidated, the effective average principal stress () increases first and then decreases with the increase in. The stress point finally falls on the critical state line (CSL) and slides downward along the CSL, whose slopeis equal to 1.84. When the specimen is overconsolidated, a largeindicates the strong dilatancy of the specimen, which will result in the small pore water pressure coefficient. In this case, theuincrement produced by the same q increment decreases. Therefore, theof overconsolidated specimens increases all the time. Overconsolidated specimens have different tendencies of effective stress paths from those of normally consolidated specimens. A largeleads to a largeincrement due to the sameincrement. Thus, Fig.7 shows that the effective stress path inclines to the transverse axis gradually whenincreases. If the specimen is heavily overconsolidated (= 4 or 6), then its effective stress path will exceed the CSL and fall on the CSL eventually.

The normalized stress paths of SRS at differentare shown in Fig.8. The starting point and peak value of each curve are different. The largewill lead to the large initial,q, and. The variation trend of effective stress paths at differentis similar due to the normal consolidation of the specimens. The peak stress points of the speci- mens at differentfall on the CSL. The stress points slide downward along the CSL after the failure of the specimens. The effective stress paths at differentdiffer only in the aspect of curvature.

Fig.7 Normalized effective stress paths of SRS at different OCR.

Fig.8 Normalized effective stress paths of SRS at different K.

3 Structural Strength Model Based on Mohr-Coulomb Theory

3.1 Modeling

As a classical strength theory, Mohr-Coulomb strength theory has been widely applied in geotechnical engineering. The Mohr-Coulomb model describes the relationship between shear stress (τ) and normal stress (σ) on the failure surface of the soil. The model parameters are few, and their physical meaning is clear, reflecting the basic characteristics of friction strength of bulk material (Bai and Wierzbicki, 2010). According to the Mohr-Coulomb theory, there is a relationship betweenτandσon the failure surface of the soil.

wherefis shear stress on the failure surface (kPa),σis normal stress on the failure surface (kPa),is the internal friction angle (?), andis cohesion (kPa).

Ifτandσare total stresses, then the values ofandobtained by Eq. (2) are the total strength indexes of soil. Ifτandσare effective stresses, then the values ofandobtained by Eq. (2) are the effective strength indexes of soil. In practical engineering, the effective stress must be calculated in accordance with the pore water pressure, which is inconvenient to measure. Therefore, in engineering practice, the total strength indexes are often used for design, while the effective strength indexes are mostly used for verification. The model established in this paper is the total strength model to promote its application to practical projects.

The specimen is in the limit equilibrium state when it is about to break. In this case:

where1fis the large principal stress on the specimen at failure (kPa), and3fis the small principal stress on the specimen at failure (kPa), which is equal toσin the triaxial test.

Eqs. (3) and (4) are substituted into Eq. (2). The following equation is then obtained:

The undrained strength of specimens in triaxial tests has a relationship with1fand3faccording to its definition:

Eq. (6) can be converted to:

Substituting Eq. (7) into Eq. (5) and replacing3fbyσyields:

Let

Then, Eq. (8) can be written as:

where,are the strength parameters of the soil.

Eq. (11) shows that A is only related to. Whenandchange, the consolidated state of the specimens will be different, which will affect the stress-strain characteristics of the specimens in the shearing process leading to the change in specimen strength. Therefore, the total strength indexesandof specimens at differentandare generally different.is related toand:

However, Eq. (10) shows that strength parameteris related toand. When the consolidation conditions change, judging the possible variation ofis not intuitive. Therefore, four specimens (1, 2, 3, and 4) are assumed to have the same, and theirobey:

If theσof each specimen remains unchanged, then specimens with a largeOCRhave a smallσ, which will lead to the smallCin the shearing process. Supposing that Eq. (11) still applies whenσis zero, then the following inequation can be obtained:

where1,2,3, and4are the strength parametersof specimens 1, 2, 3, and 4, respectively. Eq. (15) can then be further obtained:

In another case, if theσof each specimen remains unchanged, then specimens with a largeOCRhave a largeσ, which leads to a largeCin the shearing process. Eq. (11) still applies whenσis zero, and then the following inequation can be obtained:

Eq. (17) can then be further obtained:

Combining Eq. (15) with Eq. (17) yields:

Eq. (18) shows that the strength parameterdoes not change with. Similarly, the same method mentioned above can be used to consider the effect ofon strength parameter. Replacingwith, a similar conclusion that parameterdoes not change withcan be obtained. Therefore,can be regarded as a strength parameter independent of the consolidation stress.is equal to the un- drained strength of specimens without confinement, according to Eq. (11). This condition reflects the magnitude of macroscopic resistance of structures under soil shearing.

Consequently, the SSM is proposed on the basis of the above conclusions. In this model, theCof the soil can be divided into two parts: the first part is the friction strength (C), which represents the magnitude of friction between soil particles and is related to the consolidation stress. The second part is the original structural strength (C0), which is generated from the long-term deposition and independent of the consolidation stress (excluding the time effect of load in the long-term consolidation process).

3.2 Model Verification

According to Eq. (11), the data points of SRS on theC-σcoordinate system at differentandare linearly fitted. Figs.9 and 10 show that ifandare both maintained, then the correlation coefficient (2) indicates that the data points at differentσlie on the fit curves. The strength parameterof SRS increases withand, while strength parameterof SRS is equal to 20 kPa and does not change withand. This finding is consistent with the law reflected in Eqs. (12) and (18) and proves the accuracy of the hypothesis made in Section 3.1.

Undisturbed soil is the product of long-term deposition and consolidation processes. Its unique structure was form- ed in this period. Therefore, undisturbed soil generally has a certainC0. However, remolded soil is a kind of experimental soil created in accordance with the moisture content and density of undisturbed soil. The remolding process often destroys the natural structure and leads to the loss ofC0. Thus, the shear resistance of remolded soils is weak- er than that of undisturbed soils. Applying the SSM to describe undisturbed soils can reflect the contribution of natural structure to soil strength.

Some test data from other investigations are cited to verify the applicability of SSM to different types of undisturbed soil. Fig.11(a) shows the data points of silty clay in Yantai Port onC-σcoordinate system with different(Wang, 2015); Fig.11(b) is the data points of sedimentary flood plain soft soil of Yangtze River on theC-σcoordinate system with different(Wang, 2018). Fig. 11 shows that both specimens have a certainC, which does not change with the consolidation type. The two kinds of specimens are taken from different areas; thus, their sedimentary environments are quite different, which leads to differentC. The influence of consolidation type onCis mainly manifested in the difference in the slope of each curve. Hence, specimens with differenthave varyingC, which will lead to the difference inCcorrespondingly.

Fig.12(a) shows the data points of silty clay in Yantai Port on theC-σcoordinate system with different consolidation degrees () (Yin, 2017). Fig.12(b) shows the data points of silty clay from somewhere on theC-σcoordinate system with different(Tang, 2009). Fig.12 reveals that theC0of the two types of undisturbed soil does not also change with. By comparing Figs.11(a) and 12(a), specimens from the same area have the sameC0, which will not change with the consolidation conditions. The effect ofonCis also reflected inC. The sample with a highwill have large friction between soil particles, which will lead to a largeC. Based on the experimental results of these undisturbed soils, the undisturbed soils usually have the certain original structural strengthC0. If the sample comes from the same area, then itsC0will be almost identical.

Fig.9 Relationship between Cu and σs of SRS at different OCR.

Fig.10 Relationship between Cu and σs of SRS at different K.

Fig.11 Relationship between Cu and σs of undisturbed soils with different consolidation types. (a), silty clay in Yantai Port; (b), sedimentary floodplain soft soil of Yangtze River.

Fig.12 Relationship between Cu and σs of undisturbed soils with different consolidation degrees. (a), silty clay in Yantai Port; (b), silty clay from somewhere.

4 SRS Strength Model

4.1 Effect of Consolidation History on the Strength of SRS

Scholars have conducted numerous studies on the influence of consolidation history on soil behaviors. Among them, Ladd and Foott (1974) and Ladd(1977) proposed Eq. (1) based on the SHANSEP method. According to Fig.9, theC0of SRS in Tianjin Port is equal to 20 kPa and does not change with. The influence of consolidation history onCof SRS is mainly reflected inC. Therefore,Cin Eq. (1) shall be replaced byCfor SRS. In this case, Eq. (1) is converted to

As shown in Fig.13, the data points of overconsolidated SRS are fitted in accordance with Eq. (22), and the0of SRS equal to 0.77 is obtained.

Fig.9 shows that for normally consolidated SRS,

0= 0.77 and Eq. (23) are substituted into Eq. (22). Then, the following equation can be obtained:

is equal to 1 for normally consolidated soil. Therefore, Eqs. (23) and (24) can be expressed by the same equation:

TheCof SRS at differentcan be calculated by Eq. (25). Combining Eq. (25) with Eqs. (20) and (12), the following equation can be obtained:

Eq. (26) shows that the strength parameterof SRS has a power function relationship withwhen SRS is isotropically consolidated (= 1).

Fig.13 Relationship between and OCR.

4.2 Effect of Consolidation Type on the Strength of SRS Undrained

Previous experiments show that the normalized strength (C/σ0) underconsolidation is a constant (Skempton, 1948; Larsson, 1980). Moreover, Fig.4 reveals that the sample with a largehas a smallCwhenσ0is maintained. Therefore,C/σ0has a relationship with, andC/σ0should decrease with the increase in. Fig.10 indicates that theC0of SRS in Tianjin Port does not change with. Overall, a relationship between normalized friction strength (C/σ0) andshould be observed. Consequently, the data points of SRS onC/σ0–coordinate system are fitted (Fig.14). Then, the function of the fit curve can be obtained as follows:

σ0Kσaccording to the definition of; substituting it into Eq. (27) yields:

In the case of= 1,σis equal toσ. Thus, Eq. (28) can be transformed into:

If theσis maintained, then the relationship betweenCof SRS andis a linear function according to Eq. (29). This finding is consistent with the experimental law obtained by Cai(2018). By combining Eq. (29) with Eqs. (20) and (12), the following equation can be obtained:

Eq. (30) shows that the strength parameterof SRS linearly increases withwhen SRS is normally consolidated (= 1).

Fig.14 Relationship between Cuf/σv0 and K.

4.3 SRS Strength Model

Integrating Eq. (26) with Eq. (30), Eq. (31) can be obtained on the basis of the assumption that no couple- influence exists betweenand:

TheC0of SRS is equal to 20 kPa according to Figs.9 and 10. By substituting Eq. (31) into Eq. (19), the following equation can be obtained:

By substitutingσ=σ/into Eq. (32), the following equation can be obtained:

Eq. (33) is the strength model of undisturbed SRS in Tianjin Port, which can be used to predict the undrained strength of SRS under different consolidation conditions.

4.4 Verification of SRS Strength Model

Fig.15 shows the comparison of the predicted values of the SRS strength model and the measured values in the test. Most of the data points are located near the isoline, and the relative error between the predicted and measured values is less than 5%. This finding shows that the predicted result of the SRS strength model is good. Consequently, the SRS strength model can be used to predict theCof undisturbed SRS in Tianjin Port under different consolidation conditions and offers a reference for calculating the bearing capacity of SR foundations in Tianjin Port.

Fig.16 shows the deviation between theCpredicted by the SRS strength model (, the predicted value ofCof SRS without considering original structural strengthC0) and the measuredCin the test. This figure reveals that the predictedCis smaller than the measured value under various conditions, and the maximum relative error is close to ?40%. Therefore, considering the influence of natural structure on the strength of remolded soil is necessary when the test takes the remolded soil as the research object. Otherwise, it will lead to the inaccurate evaluation of the bearing capacity of the foundation and affect the design of the foundation structures.

Fig.15 Comparisons between of SRS strength model and .

Fig.16 Comparisons between of SRS strength model and .

5 Conclusions

The triaxial compression tests were performed on undisturbed SRS in Tianjin Port, and the shear behaviors of SRS under different consolidation conditions were analyzed. Meanwhile, the author established SSM according to Mohr-Coulomb theory and validated SSM based on the test data of undisturbed soils. Therefore, the SRS strength model was proposed by combining the test data of SRS with the SSM. This model can calculate theCof undisturbed SRS under different consolidation conditions. The following conclusions can be drawn from the results of this work.

1) TheCof undisturbed soils can be divided into two parts:CandC0. TheCof undisturbed soils is related to the consolidation confining pressure, history, and type. Meanwhile, theC0of undisturbed soils is independent of consolidation stress.C0represents the influence of natural structure on soil strength and originates from the process of soil formation.

2) The triaxial test data of different undisturbed soils show that the SSM has good applicability to undisturbed soils. Undisturbed soils are affected by long-term geological processes and have certainC0. The C0of soils from the same area is identical.

3) The test results of SRS in Tianjin Port show that theC0of SRS is equal to 20 kPa. If SRS is isotropically consolidated (= 1), then the strength parameterhas a power function relationship with, andCincreases withwhenσremains unchanged. If SRS is normally consolidated (= 1), then the strength parameterhas a linear relationship with, andCincreases withwhenσis maintained. Eq. (33) can predict theCof undisturbed SRS under different consolidation conditions when the coupling effect ofandon the strength of SRS is excluded.

4) Differences are observed in theCof SRS under various consolidation conditions. Stress level and stress history in consolidation considerably affect the strength characteristics of the soil. When theσof SRS doubles, theCof SRS increases by 65% – 85%. When theof SRS increases from 1 to 6, theCof SRS decreases by 25% – 30%. When theof SRS increases from 1.0 to 1.8, theCof SRS increases by 40% – 50%. Therefore, the influence of overconsolidation on the strength of SRS should be fully considered in the engineering design, and reinforcement treatment must be conducted to improve the strength of SRS effectively before utilizing the foundation.

5) The predictedCof SRS is smaller than the measured value under various conditions, and the maximum relative error is close to ?40%. The result shows that the strength of undisturbed soil is considerably higher than that of remolded soil. Therefore, in the process of SRS foundation engineering design, the difference in soil structural strength between undisturbed and newly backfilled foundations should be fully considered.

Acknowledgements

We are grateful for the financial support from the National Natural Science Foundation of China (No. 51979191), the National Key Research and Development Program of China (Nos. 2016YFC0802204, 2016YFC0802201), the National Natural Science Fund for Innovative Research Groups Science Foundation (No. 51321065), the Construction Science and Technology Project of the Ministry of Transport of the People’s Republic of China (No. 201432 8224040), and the Science and Technology Plan Project of Tianjin Port (No. 2020-165).

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(December 22, 2021;

April 28, 2022;

May 10, 2022)

? Ocean University of China, Science Press and Springer-Verlag GmbH Germany 2023

. E-mail: yzwang@tju.edu.cn

(Edited by Xie Jun)