Pore Pressure Response and Dissipation of Piezocone Test in Shallow Silty Soil of Yellow River Delta

Abstract

Soil dilatancy and partial drainage have great influence on the consolidation coefficient assessment of silty soils with clay content of less than 30% in the Yellow River Delta using the CPTu. This paper discussed the effect of soil dilatancy and partial drainage on the pore pressure response and dissipation of piezocone test in shallow silty soil of the Yellow River Delta through variable penetration rate tests in a pressure chamber and a series of supplementary soil element tests. The results show that the pore pressure dissipation curve is affected by soil type and degree of consolidation. The soil dilatancy is the key factor affecting consolidation coefficient inversion of shallow silt and silty clays. The initial pore pressure is negative and the pore pressure increases to u_max first, but the u_max value is very small in the Yellow River Delta silt. The inversion method used for shear contractile soil cannot be used to invert the mechanical properties of shallow silty soil directly, and a new consolidation curve normalization method is proposed. This paper provides a reference for the consolidation coefficient inversion of CPTu data in the Yellow River Delta area.

1. Introduction

As there are a lot of oil and gas transmission pipelines in the Yellow River Delta [1,2,3], the evaluation of soil consolidation parameters is of great significance to the evaluation of settlement caused by human activities. The cone penetration test (CPTu) is one of the most widely used geotechnical in situ testing methods. It is a fast, reliable, and economical means for obtaining soil properties [4,5]. Many inversion methods of the CPTu have been developed [6,7,8,9,10]. In fine-grained soils, dissipation tests are often carried out to estimate the consolidation coefficient [6,11].

As the consolidation coefficient cv of silts is larger than that of clay, partial drainage would usually affect CPTu test data at the standard penetration rate in silts, and the interaction between the structure and soil is also affected by partial drainage [12,13,14]. The effects of drainage on CPTu test data have been thoroughly investigated. DeJong and Randolph [15] discussed the influence of partial drainage on soil classification results; Randolph and Hope [16] discussed the influence of penetration rate on test results by centrifuge; Silva et al. [17], Yi et al. [18], and Mahmoodzadeh et al. [19] discussed the influence of partial drainage on test results by numerical method. The above research is mainly aimed at contractile soils (i.e., normally consolidated clay). The normalized velocity V = vD/c_v is used to represent the drainage condition. For sandy soil, Jaeger et al. [20], and Suzuki and Lehane [21] conducted centrifuge tests and small calibration tank tests on a normally consolidated clay–sand mixture. The results showed that the penetration rate had a significant influence on the penetration resistance of the mixture. The effect of penetration rate on the penetration resistance of sand–clay mixture is greater than that of clay.

For dilatant soils, negative excess pore pressures generated from changes in shear stress are greater than the positive excess pore pressures generated by increased mean stress. With the increase of penetration rate, penetration resistance and lateral friction resistance significantly increase, and negative pore water pressure significantly increases [22,23,24]. The penetration rate in dilatant soil affects the pore pressure response [25]. There are many silty soil layers in the Yellow River Delta [2]. The mechanical properties of silt in the Yellow River Delta changed obviously with the change of clay particles [26,27]. Wang et al. [28] and Zhang [29] studied the mechanical properties of silt in the Mississippi and Yellow River Delta, and test results show that the silty soil exhibits dilatancy. The CPTu inversion method used for shear contractile soil cannot be used to invert the mechanical properties of shallow silty soil directly. It is necessary to study the effects of penetration rate on the accuracy of the results of consolidation coefficient inversion in shallow silty soil.

This paper discusses the effect of dilatancy and partial drainage on the pore pressure response and dissipation of the piezocone test in the shallow silty soil of Yellow River Delta through variable penetration rate tests in a pressure chamber and a series of supplementary soil element tests. In this paper, the inversion methods of consolidation coefficient are summarized by experimental methods, which provides a reference for the inversion of CPTu data in the Yellow River Delta area.

2. Characteristics of Silts and Silty Clays

2.1. Particle Size Distribution of Silt and Silty Clays

The silt used in the experiment was collected from the tidal flat of the Yellow River Delta. As the clay content of in situ soil cannot be controlled accurately, two other silty clays were obtained by adding kaolin clay. The clay minerals in the Yellow River Delta are mainly illite and kaolin [2,26], so kaolin clay is selected to control the soil particle size distribution. Fine kaolin clay with particle size less than 0.005 mm was used in the test. Particle size distribution curves of the tested soils are shown in Figure 1. The plasticity index (PI) of three soils is shown in Figure 1, and it was used to distinguish silt and silty clay. When the PI is greater than 10, it is named silty clay according to the soil classification method in GB50021 [30].

2.2. Triaxial Test Results

Silt samples cannot be prepared by the direct sampling method due to how the sample preparation process will cause soil liquefaction, so silt samples were obtained with the dry method. Silty clay samples were prepared with the direct sampling method from the CPTu test chamber. The porosity ratio of silt was consistent with the CPTu test at 30 kPa. The test results are shown in Figure 2 and summarized in

Table 1. Summary of triaxial test results.

No	Soil Type	σc (kPa)	e	qmax (kPa)	Δu (kPa)	Af
1	silt (clay content 13%)	46.1	0.87	337	−86.3	−0.26
2	silt (clay content 13%)	99.2	0.82	177	26.4	0.15
3	silty clay (clay content 20%)	50	0.8	63	13.8	0.22
4	silty clay (clay content 30%)	50	0.81	25.4	38.3	1.51

A_f is ratio of excess pore water pressure to deviator stress at the critical state.

. By comparing the triaxial test results at 46.1 kPa and 99.2 kPa, it can be known that under the condition of low stress, the dilatancy of the soil was enhanced, and the properties of silt are similar to those of sandy soil. The slope of the q-p’ critical state line of silt is consistent. Comparing the triaxial test results of soil with different clay content, the dilatancy of soil increases with the decrease of clay content. The ratio of excess pore water pressure to deviator stress at the critical state A_f is related to the stress condition and clay content.

2.3. One-Dimensional Consolidation Test Results

The one-dimensional consolidation test results are shown in Figure 3. The c_v of silt is between 0.038 cm²/s and 0.097 cm²/s when σ’_v < 100 kPa. The partial drainage conditions were represented by V = vD/c_v [16]. With the standard penetration rate of 20 mm/s, the value of V is between 32 and 84. The undrained limit for V of around 30 was suggested by Randolph and Hope [16], Finnie and Randolph [31], Mahmoodzadeh et al. [19], and Yi et al. [18] through centrifuge test and finite element analysis; Ecemis and Karaman [32] suggested that the upper limit of partial drainage is 5–10 in sand with non-/low plastic fines, Chow et al. [33] suggested the upper limit in sand is 74, and Doan and Lehane [34] suggested that the upper limit in the kaolin–sand mixture is 7. The undrained limit is related to soil types. Partial drainage may affect the CPTu results in shallow silty soil of the Yellow River Delta according to the above recommended upper limits of partial drainage. It is necessary to use the variable penetration rate test to obtain the effect of partial drainage in dilatant silty soil.

2.4. Analysis of Mechanical Properties of Silty Soils

Under the condition of low stress, the dilatancy of soil is enhanced, and the properties of silt are similar to those of sandy soil. The soil strain around the probe exceeds 20%, and so negative pore pressure would be produced in the cone shoulder position. The dilatancy of soil affects not only the accumulation of pore pressure but also the dissipation curve of pore pressure [35], thus affecting the results of the consolidation coefficient inversion.

The method of obtaining the consolidation coefficient using the dissipation curve was proposed by Houlsby and Teh [36] using strain path method. A modified theoretical time factor T* is used to calculate the horizontal consolidation coefficient c_h. The T* equation is

$$T^{*}=\frac{c_{\mathrm{h}}t}{r^2{I}_r{}^{0.5}}$$

(1)

T* is related to the position of the pore pressure sensor. The standard probe pore pressure sensor is generally located at the cone shoulder. The T* of different dissipation degrees is shown in

Table 2. The values of modified theoretical time factor T* [36,37].

Consolidation degree	20%	30%	40%	50%	60%	70%	80%
T* in CPTu shoulder	0.038	0.078	0.142	0.245	0.439	0.804	1.600

.

The initial distribution of excess pore pressures has a major influence on pore pressure dissipation process [36]. This paper discussed the effect of the dilatancy and the partial drainage on the pore pressure response and dissipation of piezocone test in shallow silty soil of the Yellow River Delta through variable penetration rate tests in a pressure chamber.

3. CPTu Penetration Analysis in Remolded Silty Clay under Shallow Stress

3.1. CPTu Test System

The test equipment included a pressure consolidation chamber and a velocity control penetration system, as shown in Figure 4. The penetration rig is controlled by a servo motor. The segment distance and velocity were entered through the panel on the control box. The diameter of the chamber is 600 mm, and the distance between the CPTu and the chamber wall is more than 15R. R is the radius of the CPTu, which can eliminate the boundary effect of chamber wall on the cone. The diameter of the CPTu was 1.6 cm, and the cross-sectional area was 2 cm². The penetration depth is 250 mm below the soil surface. Pore pressure dissipation data is measured at u₂ position of CPTu. The pore pressure dissipation represents consolidation of soil. Saturation was carried out for 6 h before the penetration test to ensure the accuracy of the data. The filter is saturated by being repeatedly pumped (−100 kPa for half an hour) and pressurized (+100 kPa for half an hour) six times using CPTu saturation unit (Figure 5). The test soils were prepared by the slurry consolidation method with 1.2 times of liquid limit water content.

3.2. Test Plan

Variable penetration rate tests were carried out in three silty soils, all of which underwent 30 kPa of vertical stress to represent shallow soil of 3–5 m. The drainage conditions corresponding to each penetration rate are shown in

Table 3. Test plan.

Soil Type	Drainage Condition (V)			σ’v (kPa)	e	ρ (g/cm3)	cv (cm2/s)	Ir (50 kPa)	Estimated t80(s)
	v = 20 mm/s	v = 10 mm/s	v = 1 mm/s
silt (clay content 13%)	UD(53)	PD(26)	PD(2.6)	30	0.87	1.97	0.06	54	81
silty clay (clay content 20%)	UD(106)	UD(53)	PD(5.3)	30	0.84	1.91	0.03	43	136
silty clay (clay content 30%)	UD(457)	UD(228)	PD(23)	30	0.86	1.88	0.007	37	590

UD—undrained; PD—Partial, and V is between 0.3–30 [16]; FD—Fully drained.

. As the modified theoretical time factor T* requires an I_r value, the s_u and G of the triaxial test under 50 kPa vertical stress were recorded. The s_u and G of the soil changed with the stress, and the I_r changes little in a certain stress range. The I_r of the soils in the triaxial test under the condition of 50 kPa can be approximated.

After the completion of penetration, the pore pressure dissipation test was conducted, and the dissipation time was evaluated according to Houlsby and Teh’s method [36], in which c_h and c_v need to be transformed. Mahmoodzadeh et al. [19] suggested adopting an operative consolidation coefficient defined as

$$C_{\mathrm{h}}=\frac{3(1-v)}{(1+v)}{\left(\frac{\lambda }{\kappa }\right)}^{\alpha }{C}_{\mathrm{v}}$$

(2)

where α is assumed to be 0.5 [19]; For silt, λ/κ = 4.2–4.8 [29], so c_h ≈ 3.5c_v.

According to Houlsby and Teh’s method [36], the time to dissipate to 80% is estimated as shown in Table 3, which is used to estimate the time required for the dissipation test. Due to the large consolidation coefficient of the three silty soils, the duration is very short. To obtain a complete pore pressure dissipation curve, however, all dissipation times were increased to over 45 min.

4. Results and Discussion

4.1. Data Processing Method

In the laboratory test, the acquisition frequency of collecting instrument was 40 Hz, which allowed the initial pore pressure and its dissipation after penetration to be accurately measured. The pore pressure at the end of penetration in silt is negative, and the corresponding excess pore pressure at the end of penetration is Δu_initial. The excess pore pressure in dilatant soil first increases and then decreases, and the highest pore pressure is Δu_max. In the pore pressure dissipation stage, U and T* are used to normalize.

$$U=\frac{u_{\mathrm{t}}-u_0}{u_{initial}-u_0}=\frac{\mathsf{\Delta }{u}_{\mathrm{t}}}{\mathsf{\Delta }{u}_{initial}} \mathrm{or} U=\frac{u_{\mathrm{t}}-u_0}{u_{\max }-u_0}=\frac{\mathsf{\Delta }{u}_{\mathrm{t}}}{\mathsf{\Delta }{u}_{\max }}$$

(3)

where u_initial is the initial pore pressure value of cone shoulder, u_t is the pore pressure value at time t, u₀ is hydrostatic pressure, T* use Equation (1), c_h is obtained from Formula (2), and I_r is shown in Table 3.

The penetration resistance q_t needs to be corrected by pore pressure u₂, and the correction formula is as follows:

q_t = q_c + u₂(1 − A_a/A_c)

(4)

where the A_a/A_c of CPTu used in the test is 0.8.

4.2. Penetration Resistance and Pore Pressure Results

The test results of penetration resistance and excess pore pressure in the penetration stage are shown in Figure 6. The increase of surface penetration resistance is caused by the failure mode of surface soil and the influence of cover plate, which does not affect the penetration resistance and pore pressure at the stable penetration depth. The penetration resistance is related to both clay content and penetration rate. With the increase of clay content, pore pressure accumulation increases. The test results in

Table 4. Results of penetration resistance and excess pore pressure response.

v (mm/s)	Silt (Clay Content 13%) (kPa)			Silty Clay (Clay Content 20%) (kPa)			Silty Clay (Clay Content 30%) (kPa)
	Δumax	Δuinitial	qt	Δumax	Δuinitial	qt	Δumax	Δuinitial	qt
20	6.6	−37.8	343.7	28.1	−11.3	420.2	35.3	22.6	169.8
10	5.5	−36.2	344.4	28.3	−2.0	117.8	30.6	20.6	171.9
1	3.4	3.4	87.4	29.8	29.1	237.4	40.06	40.06	139.2

are the values of penetration resistance and excess pore pressure at the final penetration depth.

The penetration resistance, initial excess pore pressure after penetration, and the maximum excess pore pressure during dissipation are shown in Table 4.

4.3. Effect of penetration rate on Q_t-B_q

A Q_t-B_q diagram can be used as a soil classification diagram. Δu_initial and q_t from Table 4 are plotted in the Q_t-B_q diagram in Figure 7. The normalization method is as follows:

$$Q_{\mathrm{t}}=(q_{\mathrm{t}}-\sigma \mathrm{v}0)/{\sigma }^{\prime }\mathrm{v}0$$

(5)

$$B\mathrm{q}=(u_{\mathrm{initial}}-u_0)/(q_{\mathrm{t}}-\sigma \mathrm{v}0)=\mathsf{\Delta }{u}_{\mathrm{initial}}/q_{\mathrm{net}}$$

(6)

Figure 7 shows the combination of the classification diagram proposed by Robertson in 1990 [9] and Schneider in 2008 [13]. The test results show that the soil is a type of transitional soils, and a type of silt and silty clay. There is misjudgment of soil classification in the silt with clay content of 13% and the silty clay with clay content of 20%. With the increase of B_q, Q_t tends to decrease.

4.4. Pore Pressure Dissipation after Penetration

Pore pressure dissipation after penetration is shown in Figure 8. The dissipation curves of different soils differ significantly. Both silt and silty clay exhibit high dilatancy at high rates of penetration.

4.5. Selection Method of Modified Theoretical Time Factor T* for Consolidation Coefficient Inversion

The key to the inversion of the consolidation coefficient c_h is to determine the modified theoretical time factor. As the negative initial pore pressure is not conducive to estimating the dissipation curve, Δu_max was adopted as the normalized parameter, and the normalized U-T* curve is shown in Figure 9. The dissipation data of silty clay with clay content of 30% at 10 mm/s were wrong and are not shown in Figure 9. Other curves showed good regularity. Figure 9 shows that the U-T* curve is related to the soil type and the drainage degree. For silt, pore pressure accumulation is small, and the extremely low penetration rate of 1 mm/s is impossible. The dissipation curves of 10 mm/s and 20 mm/s coincide, which can be taken as T₅₀ = 13.2.

Mahmoodzadeh and Randolph [38] observed that the root time method gives the most reliable results with respect to the similarity of the shape of the measured and theoretical dissipation curves, and gives the determination of Δu_extrap with the root method applied to the dissipation. However, this method is not suitable for the soil in the test described in this paper. In Figure 10, the dissipation curve of silty clay with clay content of 20% is taken as an example. There is no dissipation segment close to a straight line to obtain Δu_extrap, and so it is difficult to use this method in practice. Figure 9 shows that each dissipation curve is close to a straight line near T₅₀. Δu_extrap/Δu_max = U_max/U_extrap, therefore, Δu_extrap/Δu_max can be obtained directly from the normalized U-t curve, as shown in Figure 11.

The new method was adopted to obtain the normalized dissipation curves U-T* of silty clay with clay content of 20% and 30%, as shown in Figure 12. The curves showed good coincidence at T₄₀, so the U-T* curve was obtained by using this method, and the T* value could be calculated and substituted into Formula (3) to obtain the horizontal consolidation coefficient c_h. After treatment, the influence of partial drainage is eliminated, but the influence of soil type is not eliminated. T₄₀ = 0.38 in silty clay with clay content of 30% and T₄₀ = 1.3 in silty clay with clay content of 20% is recommended.

The steps of this method can be summarized as follows: (1) obtain Δu_max; (2) treat the dissipation curve as a U(which is Δu_t/Δu_max)-t curve, mainly for the convenience of obtaining the position of T₅₀; (3) in the U(which is Δu_t/Δu_max)-t curve, obtain the value of Δu_extrap/Δu_max by the tangent line; and (4) using Δu_extrap to obtain the U(which is Δu_t/Δu_extrap)-t curve, obtain t corresponding to 40% dissipation, and T₄₀ = 0.38 in silty clay with clay content of 30% and T₄₀ = 1.3 in silty clay with clay content of 20%, using Formula (3) to obtain the horizontal consolidation coefficient c_h. I_r is generally obtained by the resonance column test or the triaxial test, or a regional empirical value is adopted.

5. Conclusions

In this study, laboratory CPTu tests were carried out for consolidation coefficient inversion methods considering partial drainage effects and dilatancy effects of silty soils in the Yellow River Delta. The three main findings are summarized below:

(1) The soil is a type of transitional soils belonging to silt and silty clay. There is misjudgment of soil classification in the silt with clay content of 13% and the silty clay with clay content of 20%. With the increase of B_q, Q_t tends to decrease. The dissipation curves of different soils differ significantly. Both silt and silty clay exhibit high dilatancy at high penetration rates;

(2) For silt in the Yellow River Delta, the initial pore pressure is negative and the pore pressure increases to u_max first, but the u_max value is very small. When the pore pressure dissipates to 50% u_max, the corresponding T₅₀ is used as the value of the modified theoretical time factor, and T₅₀ = 13.2;

(3) The pore pressure dissipation curve is affected by soil type and degree of consolidation. The dilatancy effect is the key factor affecting consolidation coefficient inversion of shallow silt and silty clays. A new consolidation curve normalization method is proposed and is described in detail in the last paragraph of Section 4.5. T₄₀ = 0.38 in silty clay with clay content of 30% and T₄₀ = 1.3 in silty clay with clay content of 20% is recommended to calculate the horizontal consolidation coefficient c_h.

This paper provides a reference for the consolidation coefficient inversion of CPTu data in the Yellow River Delta area. This will provide a reference for the influence of partial drainage on the interaction between structure and soil [39,40] in this area.