Estimating Deformation Modulus and Bearing Capacity of Deep Soils from Dynamic Penetration Test

The dynamic penetration test (DPT) and the Menard pressuremeter test (PMT) have been widely used in geotechnical survey of deep soils for megadam foundations in western China. The DPTmeasures are not well utilized due to the lack of correction factors and of empirical relationships for deep soils. This study investigates the relationships between the corrected DPT blow counts ( N 120 ′ ), pressuremeter modulus ( E PMT ), limit pressure ( p L ), deformation modulus ( E 0 ), and bearing capacity ( f ak ) derived from the PMTresults. Meanwhile, a nonlinear regression model is developed to predict the DPTcorrection factor ( a ) based on the raw DPT blow counts ( N 120 ) and the rod length ( L ) by integrating the available correction factors for shallow gravelly soils suggested by the code provisions and the deep soil data in this work. It is concluded that the proposed DPTcorrection factors match well with the code suggestions and the new compiled dataset, and the corrected DPT blow counts can be used to reasonably predict the engineering properties of deep sand and clay soils. Although the proposed correlations need to be tested among diﬀerent soil types and regions, the results shed the light on in situ geotechnical tests and data utilization for deep and thick overburden.


Introduction
Many megadams have been constructed on the valleys in western China to utilize the hydropower resources. e dam foundations are usually placed on the deep and thick overburden soils, which demand engineering properties of deep soils that are deeper than 20 meters. It is expensive to obtain undisturbed soil samples from the deep subsurface for laboratory tests. In situ tests have been widely used to estimate the engineering properties of these deep soils. e challenges in the interpretation of in situ soil tests mainly come from two aspects: (1) the complex soil behavior is influenced by intrinsic soil properties and many environmental factors such as temperature, pressure, and water availability [1]; (2) the lack of control and choice of the boundary conditions in field tests [2]. With increasing numbers of construction projects involving deep soils, it is desirable to explore the applications of in situ tests for these deep soils. e dynamic cone penetration test (DPT) is widely used in the geotechnical survey in river valleys consisting of deep and thick overburden soils because of its characteristics of easy operation, wide applicability to different soil types, and relative low cost. e test consists of repeatedly dropping a hammer weighing 1177 N (120 kg) from a height of 100 cm onto an anvil that is connected by 60 mm diameter drill rods to a solid cone tip with a diameter of 74 mm and a cone angle of 60° [3]. Each hammer drop has potential energy that is theoretically equivalent to 1177 J. e number of blows by the hammer needed for the cone to penetrate the 10 cm strata is the counted N-value (N 120 ). e DPT has been widely applied in Chinese geotechnical practices for foundation design since 1970s [3]. Recently, the DPT has been successfully applied to assess liquefaction of gravelly soils [3,4]. However, the empirical correlation between DPT measures and soil properties such as deformation modulus and bearing capacity is limited to shallow gravelly soils with depth less than 20 m especially from the Chengdu Plain [5] (see Appendix A).
ere are many factors that could influence the energy transmitted from the impact of the hammer on the anvil to the rod string and cone and thus affect the value of the blow count of hammer-impact penetration tests [6]. Calibration chamber tests [7,8] and in situ measurements [6] are usually conducted to evaluate the influential factors on penetration tests and standardization procedure. ere are few studies about the influential factors on DPT blow count and its correction. e energy transfer ratio (ETR), defined as the ratio of the energy that passes through the rods to the theoretical potential energy, is the most direct measure of the energy loss within the penetration test system. Cao et al. [3] reported that the Chinese DPT has an average ETR of 89% according to 1,200 hammer energy measurements within the shallow gravelly soils for liquefaction assessment. Zuo and Zhao [9] conducted a series of physical model tests that penetrate the soils within a model box with incremental rod lengths (up to 83 m) and compute the correction factors as the blow count of any rod length to the blow count of 2 m long rod under the same soil condition. eir results suggest that the correction factors of DPT gradually decrease with the increase of rod length (correction factor is around 0.5 when rod length is 83 m), which is independent of soil type and overburden pressure. Li et al. [10] measured the stress distribution at several rod depths using a series of in situ DPT tests.
eir results suggest that the maximum peak stress drops nonlinearly along the rod length (from the top and bottom) and the maximum peak stress drop ratio increases with the rod length. Based on numerical simulation results, they proposed empirical correlations to estimate the rod-length-dependent correction factors for DPT blow counts. Based on many engineering practices, the Chinese Code for Investigation of Geotechnical Engineering [11], hereinafter called Chinese Code, suggests that the correction factors for DPT blow counts are simultaneously affected by the raw DPT blow counts and the rod length. However, the DPT correction factors suggested by the Chinese Code are limited to rod length below 19 m and raw DPT blow count less than 40 (see Appendix B).
is study attempts to expand the DPTcorrection factors for deep soils and to use the corrected DPT blow counts to predict deformation modulus and bearing capacity of deep soils. For these purposes, a database consisting of 74 pairs of DPT and pressuremeter test (PMT) results is compiled from a geotechnical survey project for a dam designed on a deep overburden site in southwestern China. e geology and geotechnical conditions of the study site are described in Section 2, and the in situ tests and data processing are detailed in Section 3. e empirical relationships for estimating DPT correction factors and engineering properties of soil using DPT test results are shown in Section 4, and the last section draws the conclusions.

Geological and Geotechnical Conditions
e study area is a dam construction site located in southwestern China. A high-rise dam will be placed on the river valley that consisted of very deep and thick overburden. Many types of geological and geotechnical surveys (see Figure 1) have been conducted at the project site to investigate the structure and properties of the underlying soils. According to borehole data, the maximum thickness of overburden sediments reaches 567 m at the middle point of the river valley (ZKm304 in Figures 1 and 2). e overburden thickness decreases from the middle to the two sides, which is consistent with the old U-shape valley topography. e bedrock in the study area mainly consists of Precambrian gray gneiss (Pt 2-3 Nq a ) and is exposed on the valley slopes. e deep overburden can be divided to four major layers from the bottom to the top (i.e., from oldest to newest in geological age): Layer I (Pleistocene gravelly soil, see Figure 3(f )): it is located at the bottom of the old riverbed. Its burial depth ranges from 350 to 460 m according to borehole investigations at different site locations. e geological origin of this layer is glacial outwash deposits (Q 3 fgl+gl ). Layer II (Pleistocene cobbly soil, see Figure 3(e)): its burial depth ranges from 200 to 250 m. Its geological origin is alluvial and pluvial deposits (Q 3 al+pl ). Layer III (Pleistocene sand and clay soil): its burial depth ranges from 6 to 12 m and thickness ranges from 200 to 250 m. It majorly consists of sand, sandy silt, and silty clay. e geological origin of Layer III is alluvial and lacustrine deposits (Q 3 al+l ). Layer IV (Holocene gravelly soil, see Figure 3(a)): this layer is the modern alluvial deposit (Q 4 al ). e engineering properties of Layer III will be the focus of this work as this soil layer will be used as the foundation soil to support a high-rise dam. e Layer III is made up of the Pleistocene alluvium and lacustrine sediments. According to the soil characteristics explored by the boreholes, this layer is further divided into three sublayers, and the major soils within each sublayer are described as following (from the bottom to the top): Sublayer III-1: it is located at the bottom of Layer III. is sublayer majorly consists of dark gray to brownish-yellow sand (see Figure 3(d)). e particle size distribution is shown in Figure 4. Its average density is 1.78 g/cm 3 and average moisture content is about 4.8%. e void ratio is 0.515 and the specific gravity is 2.69. e liquid limit (LL) and plasticity index (PI) are 20.4 and 8.9, respectively. e soil gradation measures, uniformity coefficient (Cu), and coefficient of gradation (Cc) are 7.6 and 1.0, respectively. According to the Unified Soil Classification System (USCS) [12], the soil is classified as wellgraded sand with clay, with the group symbol as SW-SC (see Table 1). e burial depth of this sublayer ranges from 70 to 95 m. e layer thickness has large variation along the transverse (cross river) direction, with thickness of 20 to 40 m at two sides and 150 to 170 m at the middle.
Sublayer III-2: it is located at the middle of Layer III. It majorly consists of dark-gray clay and silt (see Figure 3(c)). e burial depth of this sublayer ranges from 50 to 80 m. e thickness ranges from 5.2 to 24.2 m, with an average value of 16 m. e major soil type of this sublayer is clay, with average density of 1.56 g/cm 3 and moisture content of 16.3%. e void ratio is 0.746, and the specific gravity is 2.72. e liquid limit and plasticity index are 37.3 and 16.6, respectively. According to USCS, this soil is classified as lean clay with the group symbol of CL (see Table 1).

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Sublayer III-3: it is located at the top of Layer III. It is made up of dark gray to brown sand (see Figure 3(b)). e burial depth ranges from 6 to 40 m. e thickness ranges from 36.85 to 53.8 m, with an average value of 46 m. e average density is 1.71 g/cm 3 , and the moisture content is 5.7%. e void ratio is 0.573, and the specific gravity is 2.68. e liquid limit and plasticity index are 19.3 and 8.5, respectively. e uniformity coefficient (Cu) and coefficient of gradation (Cc) are 6.6 and 1.1, respectively. According to USCS, the soil is classified as well-graded sand with clay, with the group symbol as SW-SC (see Table 1).

In Situ Tests and Data Processing
is study uses the dynamic cone penetration test (DPT) and pressuremeter test (PMT) results to develop regression models for estimating DPT correction factors and engineering properties of soils (pressuremeter modulus, limit pressure, deformation modulus, and bearing capacity) within Layer III (burial depth ranges from 6 to 40 m). In total, 74 sets of data are collected from the nine boreholes shown in Table 2. According to Table 2, there are 10, 15, and 49 pairs of data for soils within sublayers III-1, III-2, and III-3, respectively. e 11 pairs of data among the 49 ones within the III-3 layer have rod length less than 19 m where the correction factors in the Chinese Code (see Appendix B) can be applied. e remaining 63 DPT measures will require new correction factors that are not available in the Chinese Code. e testing procedure and data processing methods for the DPT and PMT are briefly described in the following sections.

Dynamic Penetration Test.
e dynamic penetration test (DPT) was developed in China during the early 1950s to measure the penetration resistance of gravelly soils.

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DPT could provide an important new procedure for characterization of gravels and fill a gap in present geotechnical practice between CPT/SPT and BPT testing [4].
e DPT has been widely applied in Chinese geotechnical practices since the code provisions providing guidance for the foundation design using DPT were published in the     [3]. e DPT apparatus consists of a 120 kg hammer with a free-fall height of 100 cm dropped onto an anvil attached to 60 mm diameter drill rods, which in turn are attached to a solid cone tip with a diameter of 74 mm and a cone angle of 60°( Figure 5) [11]. e blow counts for penetrating every 10 cm of soils are recorded and termed as N 120 . e DPT is applicable to gravelly soils and weathered extreme-soft and soft rocks [5].
e DPT is widely used in the geotechnical survey in valleys consisting of deep overburden in southwestern China because of its characteristics of easy operation, wide applicability to different types of soils, and cheap cost.
It is controversial about whether or not to correct the DPT blow count and how to correct it [5]. Currently, the Chinese Code suggests multiplying a correction factor (α) to the raw DPT blow counts following equation (1) to get the corrected DPT blow count (N 120 ′ ). Since DPT was widely used to support the foundation design on gravelly soils located in Chengdu Plain, the Design Code for Building Foundation of Chengdu Region [13], hereinafter called where N 120 ′ is the corrected DPT blow count, N 120 is the raw DPT blow count, and α is the correction factor that is available for rod length (L) less than 19 m and N 120 below 40 (see Appendix B). [14] to measure the deformation properties of soil and weak rock. e PMT consists of placing an inflatable cylindrical probe in a predrilled borehole and expanding this probe, while measuring the changes in volume and pressure in the probe [15]. e measured volume change of the probe is plotted against the applied pressure (see Figure 6). e pressuremeter modulus is determined as follows [15]:

Pressuremeter Test. e pressuremeter test (PMT) is an in situ test developed by Menard
where E PMT is the pressuremeter modulus (MPa), p 0 , p f , and p L are initial, yield, and limit pressure, respectively, V 0 is initial volume of the probe (cm 3 ), V m is the corrected volume reading in the center portion of ΔV (volume increase), ΔP is corrected pressure increase in the center part of the straight line portion of the pressure-volume curve, and μ is Poisson's ratio. It is noted that the PMT measures are associated with the horizontal stresses compared with the vertical resistance measured by the penetration tests (e.g., SPT, CPT, and DPT). Many empirical correlations have been proposed to convert PMT measures to various soil parameters [5,14] and other penetration test measures [16][17][18][19][20][21][22][23]. e PMT measures are commonly used [5] to calculate the bearing capacity and deformation modulus of foundation soils following equations (3) and (4). e bearing capacity and deformation modulus of soil samples in the compiled dataset are calculated and shown in Table 2: where f ak is bearing capacity (MPa), E 0 is the deformation modulus (MPa), and K is the ratio between the deformation modulus and pressuremeter modulus and is dependent on the soil type. e empirical model for cohesive soils (clay, silt, and sand) is used here: K � 1 + 61.1m − 1.5 + 0.0065(V 0 − 167.6), where m is the ratio between the pressuremeter modulus and the difference of limited pressure and initial pressure, i.e., m � (E PMT /p L − p 0 ) [5].

Results
With the DPT and PMT dataset compiled in Section 3, this section develops the empirical relationships for estimating correction factors (Section 4.1) and soil parameters (Section 4.2) from DPT test results using the regression analysis.

Empirical Relationship for DPT Correction Factor.
As mentioned in Section 3, the correction factors of N 120 in the Chinese Code are only available for rod length less than 19 m and raw DPT blow counts less than 40. is section aims to extend the correction factors for longer rod lengths (i.e., deeper soils). To achieve this purpose, 11 pairs of data with correction factors suggested by the Chinese Code (see Appendix B) are firstly filtered out to build a regression model between the deformation modulus E 0 and N 120 ′ . ese data are from the sublayer III-3, with rod length ranging from 10.5 to 17.5 m. e regression results are shown in equation (5) and Figure 7. e adjusted R 2 of this regression is 0.986, and the p value of the F-test and t-test is 0.000 (less than 0.05), indicating that the regression model is significant and reliable: where E 0 is the deformation modulus (MPa) and N 120 ′ is the corrected DPT blow count.
Using the reverse form of (5), N 120 ′ for the other 38 data from sublayer III-3 but with rod length exceeding 19 m is calculated in Table 2. en, its correction factors are calculated as the ratio of N 120 ′ over N 120 . Combining the inverted correction factors according to sublayer III-3 soil data and (5), with the correction factors suggested by Chinese Code (See Appendix B), nonlinear regression is undertaken using the Curve Fitting Toolbox of Matlab [24]. e empirical equation for predicting the DPT correction factor using raw DPT blow count and rod length is shown in the following equation: where α is the DPT correction factor, L is the rod length (m), and N 120 is the raw DPT blow counts. e 3D visualization of the regression model and the utilized dataset is shown in Figure 8. e relationship between correction factors and rod length for selected N 120 values (i.e., 10 to 50 with step of 10) is shown in Figure 9. According to Figure 9, we can see the correction factors decrease with rod length with gradually reducing change rates. e correction factors for higher N 120 values decrease faster than the ones for lower N 120 values. e DPT correction factors calculated using equation (6) are compared with ones suggested by Chinese Code (Figure 10). e results of the proposed model generally match well with the ones in code, except for very low and high N 120 values. e model underestimates the correction factors for N 120 of 1, while slightly overestimates the correction factors for N 120 of 40 for rod length exceeding 16 m.

Empirical Relationships Using Corrected DPT Blow Count.
Empirical relationships are widely used to predict unknown engineering properties of soils [25][26][27]. In this section, the relationships between the corrected DPT blow counts (N 120 ′ ) and soil parameters derived from pressuremeter measures (i.e., pressuremeter modulus and limit pressure) and engineering parameters used in the foundation design (i.e., soil deformation modulus and bearing capacity) were developed separately. e empirical relationships for engineering parameters are expected to be useful for geotechnical practices in China since soil deformation modulus and bearing capacity parameters are calibrated following the Chinese Codes (see equations (3) and (4)). Linear regression analyses are undertaken using all 74 data pairs belonging to soil Layer III and the reduced number of data pairs belonging to different sublayers of soil Layer III. e best-fit regression equations for soil Layer III (including both sand and clay soils) are shown in equations (7)-(10). e regression coefficients (intercept and slope values for linear regression) and corresponding statistical test results using data from each sublayer and all data from Layer III are summarized in Tables 3-6 and visualized in Figures 11 and 12. e coefficient of determination (adjusted R 2 value) is used to evaluate the goodness of fit of the regression model. e Ftest and t-test are used to assess the statistical significance of the regression models and the estimated regression coefficients, respectively. Models with larger F-statistic, tstatistic, and adjusted R 2 value are better: p L � 0.4655 + 0.0845N 120 ′ , adjusted R 2 � 0.957, (8) f ak � 0.2399 + 0.0305N 120 ′ , adjusted R 2 � 0.775, (10) where E PMT is the pressuremeter modulus (MPa) derived using equation (2), p L is limit pressure (MPa) measured in the pressuremeter test, E 0 is the deformation modulus (MPa) derived using equation (4), f ak is bearing capacity (MPa) derived using equation (3), and N 120 ′ is the DPT blow counts corrected using equations (1) and (6).  Advances in Civil Engineering Overall, the regression models using all data (equations (8)-(10)) have adjusted the R 2 value higher than 0.75 except for the regression model for estimating pressuremeter modulus (7). e regression models using all data generally have higher adjusted R 2 than the models using a subset data for different sublayers (see Tables 3-6). In total, 14 of the 16 regression models shown in Tables 3-6 have the p value for the F-test and t-test associated with the slope coefficient less than 0.1, which indicates that the linear regression models and regression coefficients are statistically significant for a 90% confidence level. e other two regression models (models for III-1 and III-2 data in Table 3) have not passed the F-test and t-test possibly due to the limited number of data used in the regression analyses. Nevertheless, these regression results show that the dynamic penetration tests can be used to provide a preliminary estimation of soil parameters calibrated by more expensive pressuremeter tests. Towards improving the predictive ability and reliability of these empirical relationships, future works can collect more explanatory variables and case data, integrate theoretical/numerical analyses [28,29], and use more advanced regression algorithms [30,31].      Figure 11: Correlations between corrected DPT blow counts N 120 ′ , pressuremeter modulus E PMT , and limit pressure p L for different soil sublayers.

Conclusions
e dynamic penetration test (DPT) has been increasingly used in the geotechnical survey of deep soils in western China. However, the correction factors and empirical relationships for estimating engineering parameters using dynamic penetration test blow counts are still limited to gravelly soils with depth less than 20 m. is work collects 74 DPT measures at a valley site in southwestern China that consists of more than 500-meter-thick overburden soils. A nonlinear empirical relationship dependent on the raw DPT blow counts and rod length is developed to predict the DPT correction factors for shallow and deep soils through analyzing the deep soil data collected in this work and the existing correction factors for the shallow soils suggested by Chinese Code. en, the corrected DPT blow counts are used to predict pressuremeter modulus, limit pressure, soil deformation modulus, and bearing capacity derived from more expensive and accurate pressuremeter tests. e results suggest that the proposed empirical relationships are significant and reliable for the investigated deep clay and sand soils. Further studies will be needed to explore the  Figure 12: Correlations between corrected DPT blow counts N 120 ′ , soil deformation modulus E 0 , and bearing capacity f ak for different soil sublayers.  Based on many engineering practices, the Chengdu Code provides several empirical relationships to use the corrected DPT blow counts to estimate the deformation modulus, compression modulus, and ultimate bearing capacity of gravelly soils in Chengdu Plain [5,13].
( Data Availability e data used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest
e authors declare that they have no conflicts of interest.